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Giaimo S, Shah S, Raatz M, Traulsen A. Negligible Long-Term Impact of Nonlinear Growth Dynamics on Heterogeneity in Models of Cancer Cell Populations. Bull Math Biol 2025; 87:18. [PMID: 39751987 PMCID: PMC11698897 DOI: 10.1007/s11538-024-01395-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2024] [Accepted: 12/03/2024] [Indexed: 01/04/2025]
Abstract
Linear compartmental models are often employed to capture the change in cell type composition of cancer cell populations. Yet, these populations usually grow in a nonlinear fashion. This begs the question of how linear compartmental models can successfully describe the dynamics of cell types. Here, we propose a general modeling framework with a nonlinear part capturing growth dynamics and a linear part capturing cell type transitions. We prove that dynamics in this general model are asymptotically equivalent to those governed only by its linear part under a wide range of assumptions for nonlinear growth.
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Affiliation(s)
- Stefano Giaimo
- Department of Theoretical Biology, Max Planck Institute for Evolutionary Biology, August-Thienemann-Str. 2, Plön, 24306, Germany.
| | - Saumil Shah
- Department of Theoretical Biology, Max Planck Institute for Evolutionary Biology, August-Thienemann-Str. 2, Plön, 24306, Germany
| | - Michael Raatz
- Department of Theoretical Biology, Max Planck Institute for Evolutionary Biology, August-Thienemann-Str. 2, Plön, 24306, Germany
| | - Arne Traulsen
- Department of Theoretical Biology, Max Planck Institute for Evolutionary Biology, August-Thienemann-Str. 2, Plön, 24306, Germany
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2
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Stålhammar G, Hagström A, Ermedahl Conradi M, Williams PA. Choroidal nevi and melanoma doubling times and implications for delays in treatment: A systematic review and meta-analysis. Surv Ophthalmol 2025; 70:38-46. [PMID: 39343315 DOI: 10.1016/j.survophthal.2024.09.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2024] [Revised: 09/17/2024] [Accepted: 09/23/2024] [Indexed: 10/01/2024]
Abstract
The prognostic implications of delaying treatment for primary uveal melanoma remain debated. We evaluate the impact of choroidal nevi and melanoma doubling times on metastatic death incidence and compare this impact across different tumor sizes. A literature search in PubMed and Web of Science targeted studies published after 1980 that quantified growth rates for choroidal or ciliochoroidal melanomas or nevi based on serial imaging found 199 melanomas and 87 growing nevi from 5 studies. In a random effects model, the estimated average volume doubling time was 360 days across all patients, with doubling times of 717, 421, and 307 days for small, medium, and large melanomas, respectively, and 6392 days for growing nevi. A mixed-effects model estimated that the 10-year incidence of metastatic death increases by 0.3, 1.8, and 4.0 percentage points every month a small, medium, and large melanoma remains untreated. Similar results were produced using two independent sources for survival data. These findings suggest that choroidal melanoma growth follows a super-exponential curve, with larger tumors exhibiting shorter doubling times. Based on these growth rates, delaying definitive treatment increases the risk of metastatic death by nearly zero to several percentage points per month, depending on tumor size.
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Affiliation(s)
- Gustav Stålhammar
- Ocular Oncology Service, St. Erik Eye Hospital, Stockholm, Sweden; Department of Clinical Neuroscience, Division of Eye and Vision, Karolinska Institutet, Stockholm, Sweden; St. Erik Ophthalmic Pathology Laboratory, Stockholm, Sweden.
| | - Anna Hagström
- Department of Clinical Neuroscience, Division of Eye and Vision, Karolinska Institutet, Stockholm, Sweden
| | | | - Pete A Williams
- Department of Clinical Neuroscience, Division of Eye and Vision, Karolinska Institutet, Stockholm, Sweden
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3
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Wang H, Arulraj T, Ippolito A, Popel AS. Quantitative Systems Pharmacology Modeling in Immuno-Oncology: Hypothesis Testing, Dose Optimization, and Efficacy Prediction. Handb Exp Pharmacol 2024. [PMID: 39707022 DOI: 10.1007/164_2024_735] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2024]
Abstract
Despite an increasing number of clinical trials, cancer is one of the leading causes of death worldwide in the past decade. Among all complex diseases, clinical trials in oncology have among the lowest success rates, in part due to the high intra- and inter-tumoral heterogeneity. There are more than a thousand cancer drugs and treatment combinations being investigated in ongoing clinical trials for various cancer subtypes, germline mutations, metastasis, etc. Particularly, treatments relying on the (re)activation of the immune system have become increasingly present in the clinical trial pipeline. However, the complexities of the immune response and cancer-immune interactions pose a challenge to the development of these therapies. Quantitative systems pharmacology (QSP), as a computational approach to predict tumor response to treatments of interest, can be used to conduct in silico clinical trials with virtual patients (and emergent use of digital twins) in place of real patients, thus lowering the time and cost of clinical trials. In line with improved mechanistic understanding of the human immune system and promising results from recent cancer immunotherapy, QSP models can play critical roles in model-informed drug development in immuno-oncology. In this chapter, we discuss how QSP models were designed to serve different study objectives, including hypothesis testing, dose optimization, and efficacy prediction, via case studies in immuno-oncology.
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Affiliation(s)
- Hanwen Wang
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD, USA
| | - Theinmozhi Arulraj
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD, USA
| | - Alberto Ippolito
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD, USA
| | - Aleksander S Popel
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD, USA.
- Department of Oncology, and the Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins University School of Medicine, Baltimore, MD, USA.
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4
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Yang S, Ge Y, Wang J, Liu R, Fu L. Predicting alfalfa leaf area index by non-linear models and deep learning models. FRONTIERS IN PLANT SCIENCE 2024; 15:1458337. [PMID: 39588090 PMCID: PMC11586217 DOI: 10.3389/fpls.2024.1458337] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/02/2024] [Accepted: 10/17/2024] [Indexed: 11/27/2024]
Abstract
Leaf area index (LAI) of alfalfa is a crucial indicator of its growth status and a predictor of yield. The LAI of alfalfa is influenced by environmental factors, and the limitations of non-linear models in integrating these factors affect the accuracy of LAI predictions. This study explores the potential of classical non-linear models and deep learning for predicting alfalfa LAI. Initially, Logistic, Gompertz, and Richards models were developed based on growth days to assess the applicability of nonlinear models for LAI prediction of alfalfa. In contrast, this study combines environmental factors such as temperature and soil moisture, and proposes a time series prediction model based on mutation point detection method and encoder-attention-decoder BiLSTM network (TMEAD-BiLSTM). The model's performance was analyzed and evaluated against LAI data from different years and cuts. The results indicate that the TMEAD-BiLSTM model achieved the highest prediction accuracy (R² > 0.99), while the non-linear models exhibited lower accuracy (R² > 0.78). The TMEAD-BiLSTM model overcomes the limitations of nonlinear models in integrating environmental factors, enabling rapid and accurate predictions of alfalfa LAI, which can provide valuable references for alfalfa growth monitoring and the establishment of field management practices.
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Affiliation(s)
- Songtao Yang
- College of Information Engineering, Ningxia University, Yinchuan, China
| | - Yongqi Ge
- College of Information Engineering, Ningxia University, Yinchuan, China
- Ningxia Key Laboratory of Artificial Intelligence and Information Security for Channeling Computing Resources from the East to the West, Yinchuan, China
| | - Jing Wang
- College of Information Engineering, Ningxia University, Yinchuan, China
| | - Rui Liu
- College of Information Engineering, Ningxia University, Yinchuan, China
- Ningxia Key Laboratory of Artificial Intelligence and Information Security for Channeling Computing Resources from the East to the West, Yinchuan, China
| | - Li Fu
- College of Resources Environment and Life Sciences, Ningxia Normal University, Guyuan, China
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5
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Fonti N, Parisi F, Lachi A, Dhein ES, Guscetti F, Poli A, Millanta F. Age at Tumor Diagnosis in 14,636 Canine Cases from the Pathology-Based UNIPI Animal Cancer Registry, Italy: One Size Doesn't Fit All. Vet Sci 2024; 11:485. [PMID: 39453077 PMCID: PMC11512385 DOI: 10.3390/vetsci11100485] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2024] [Revised: 10/01/2024] [Accepted: 10/02/2024] [Indexed: 10/26/2024] Open
Abstract
Cancer is the most common cause of death in adult dogs. All dogs would benefit from early diagnosis, but there are no specific guidelines regarding the schedule of cancer screening in companion animals. The aim of this study was to retrospectively evaluate the age at diagnosis in Italian oncological canine patients. A total of 14,636 canine histologically confirmed neoplastic cases were coded according to the Vet-ICD-O-canine-1 and stratified by malignancy, sex, neutering status, breed, cephalic index, body size, and tumor type. Differences in age distribution were analyzed and the influence of these variables on the time of first malignancy diagnosis was assessed using an event history analysis model. The median age at diagnosis for benign and malignant tumors was 9 and 10 years, respectively. Intact and purebred dogs were diagnosed earlier, but the median age differed significantly by breed. The earliest age at diagnosis was recorded for lymphomas and mast cell tumors. The model showed an accelerating effect of large size, brachy- and dolichocephaly, and sexual integrity in female dogs on the time of malignancy diagnosis. Our results confirm that a "one-size-fits-all" approach to cancer screening is not accurate in dogs and provide relevant data that may lead to the establishment of breed-based screening schedules.
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Affiliation(s)
- Niccolò Fonti
- Department of Veterinary Sciences, University of Pisa, Viale delle Piagge n. 2, 56124 Pisa, Italy; (F.P.); (A.P.); (F.M.)
| | - Francesca Parisi
- Department of Veterinary Sciences, University of Pisa, Viale delle Piagge n. 2, 56124 Pisa, Italy; (F.P.); (A.P.); (F.M.)
| | - Alessio Lachi
- Saint Camillus International University of Health and Medical Sciences (UniCamillus), Via Sant’Alessandro n. 8, 00131 Rome, Italy;
- Department of Statistics, Computer Science, Applications “Giuseppe Parenti” (DiSIA), University of Florence, Viale Giovanni Battista Morgagni 59, 50134 Florence, Italy
| | - Elena Sophie Dhein
- Institute of Veterinary Pathology, Vetsuisse Faculty, University of Zurich, Winterthurerstrasse 268, 8057 Zurich, Switzerland; (E.S.D.); (F.G.)
| | - Franco Guscetti
- Institute of Veterinary Pathology, Vetsuisse Faculty, University of Zurich, Winterthurerstrasse 268, 8057 Zurich, Switzerland; (E.S.D.); (F.G.)
| | - Alessandro Poli
- Department of Veterinary Sciences, University of Pisa, Viale delle Piagge n. 2, 56124 Pisa, Italy; (F.P.); (A.P.); (F.M.)
| | - Francesca Millanta
- Department of Veterinary Sciences, University of Pisa, Viale delle Piagge n. 2, 56124 Pisa, Italy; (F.P.); (A.P.); (F.M.)
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Nieto C, Igler C, Singh A. Bacterial cell size modulation along the growth curve across nutrient conditions. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.09.24.614723. [PMID: 39386733 PMCID: PMC11463677 DOI: 10.1101/2024.09.24.614723] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 10/12/2024]
Abstract
Under stable growth conditions, bacteria maintain cell size homeostasis through coordinated elongation and division. However, fluctuations in nutrient availability result in dynamic regulation of the target cell size. Using microscopy imaging and mathematical modelling, we examine how bacterial cell volume changes over the growth curve in response to nutrient conditions. We find that two rod-shaped bacteria, Escherichia coli and Salmonella enterica, exhibit similar cell volume distributions in stationary phase cultures irrespective of growth media. Cell resuspension in rich media results in a transient peak with a five-fold increase in cell volume ≈ 2h after resuspension. This maximum cell volume, which depends on nutrient composition, subsequently decreases to the stationary phase cell size. Continuous nutrient supply sustains the maximum volume. In poor nutrient conditions, cell volume shows minimal changes over the growth curve, but a markedly decreased cell width compared to other conditions. The observed cell volume dynamics translate into non-monotonic dynamics in the ratio between biomass (optical density) and cell number (colony-forming units), highlighting their non-linear relationship. Our findings support a heuristic model comparing modulation of cell division relative to growth across nutrient conditions and providing novel insight into the mechanisms of cell size control under dynamic environmental conditions.
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Affiliation(s)
- César Nieto
- Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA
| | - Claudia Igler
- Institute of Integrative Biology, ETH Zurich, Zurich, Switzerland
- Division of Evolution, Infection and Genomics, School of Biological Sciences, University of Manchester, Manchester M13 9PT, UK
| | - Abhyudai Singh
- Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA
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Watson SI, Gkini E, Bishop J, Scandrett K, Napit I, Lilford RJ. Modelling wound area in studies of wound healing interventions. BMC Med Res Methodol 2024; 24:206. [PMID: 39285279 PMCID: PMC11403831 DOI: 10.1186/s12874-024-02326-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2024] [Accepted: 08/29/2024] [Indexed: 09/22/2024] Open
Abstract
BACKGROUND Experimental studies of wound healing often use survival analysis and time to event outcomes or differences in wound area at a specific time point. However, these methods do not use a potentially large number of observations made over the course of a trial and may be inefficient. A model-based approach can leverage all trial data, but there is little guidance on appropriate models and functional forms to describe wound healing. METHODS We derive a general statistical model and review a wide range of plausible mathematical models to describe wound healing. We identify a range of possible derived estimands and their derivation from the models. Using data from a trial of an intervention to promote ulcer healing in patients affected by leprosy that included three measurement methods repeated across the course of the study, we compare the goodness-of-fit of the models using a range of methods and estimate treatment effects and healing rate functions with the best-fitting models. RESULTS Overall, we included 5,581 ulcer measurements of 1,578 unique images from 130 patients. We examined the performance of a range of models. The square root, log square root, and log quadratic models were the best fitting models across all outcome measurement methods. The estimated treatment effects magnitude and sign varied by time post-randomisation, model type, and outcome type, but across all models there was little evidence of effectiveness. The estimated effects were significantly more precise than non-parametric alternatives. For example, estimated differences from the three outcome measurements at 42-days post-randomisation were - 0.01 cm2 (-0.77, 0.74), -0.44 cm2 (-1.64, 0.76), and 0.11 cm2 (-0.87, 1.08) using a non-parametric method versus - 0.03 cm2 (-0.14, 0.06), 0.06 cm2 (-0.05, 0.17), and 0.03 cm2 (-0.07, 0.17) using a square-root model. CONCLUSIONS Model-based analyses can dramatically improve the precision of estimates but care must be taken to carefully compare and select the best fitting models. The (log) square-root model is strongly recommended reflecting advice from a century ago.
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Affiliation(s)
- Samuel I Watson
- Institute of Applied Health Research, University of Birmingham, Birmingham, B15 2TT, UK.
| | - Eleni Gkini
- Institute of Applied Health Research, University of Birmingham, Birmingham, B15 2TT, UK
| | - Jon Bishop
- Institute of Applied Health Research, University of Birmingham, Birmingham, B15 2TT, UK
| | - Katie Scandrett
- Institute of Applied Health Research, University of Birmingham, Birmingham, B15 2TT, UK
| | | | - Richard J Lilford
- Institute of Applied Health Research, University of Birmingham, Birmingham, B15 2TT, UK
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8
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Geady C, Abbas-Aghababazadeh F, Kohan A, Schuetze S, Shultz D, Haibe-Kains B. Radiomic-based prediction of lesion-specific systemic treatment response in metastatic disease. Comput Med Imaging Graph 2024; 116:102413. [PMID: 38945043 DOI: 10.1016/j.compmedimag.2024.102413] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Revised: 04/08/2024] [Accepted: 06/15/2024] [Indexed: 07/02/2024]
Abstract
Despite sharing the same histologic classification, individual tumors in multi metastatic patients may present with different characteristics and varying sensitivities to anticancer therapies. In this study, we investigate the utility of radiomic biomarkers for prediction of lesion-specific treatment resistance in multi metastatic leiomyosarcoma patients. Using a dataset of n=202 lung metastases (LM) from n=80 patients with 1648 pre-treatment computed tomography (CT) radiomics features and LM progression determined from follow-up CT, we developed a radiomic model to predict the progression of each lesion. Repeat experiments assessed the relative predictive performance across LM volume groups. Lesion-specific radiomic models indicate up to a 4.5-fold increase in predictive capacity compared with a no-skill classifier, with an area under the precision-recall curve of 0.70 for the most precise model (FDR = 0.05). Precision varied by administered drug and LM volume. The effect of LM volume was controlled by removing radiomic features at a volume-correlation coefficient threshold of 0.20. Predicting lesion-specific responses using radiomic features represents a novel strategy by which to assess treatment response that acknowledges biological diversity within metastatic subclones, which could facilitate management strategies involving selective ablation of resistant clones in the setting of systemic therapy.
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Affiliation(s)
- Caryn Geady
- Princess Margaret Cancer Centre, University Health Network, Toronto, Canada; Medical Biophysics, University of Toronto, Toronto, Canada
| | | | - Andres Kohan
- Princess Margaret Cancer Centre, University Health Network, Toronto, Canada
| | - Scott Schuetze
- Department of Medicine, University of Michigan, Ann Arbor, MI, USA
| | - David Shultz
- Princess Margaret Cancer Centre, University Health Network, Toronto, Canada; Medical Biophysics, University of Toronto, Toronto, Canada; Department of Medicine, University of Michigan, Ann Arbor, MI, USA; Vector Institute for Artificial Intelligence, Toronto, Canada; Ontario Institute for Cancer Research, Toronto, Canada; Department of Computer Science, University of Toronto, Toronto, Canada; Department of Biostatistics, Dalla Lana School of Public Health, Toronto, Canada
| | - Benjamin Haibe-Kains
- Princess Margaret Cancer Centre, University Health Network, Toronto, Canada; Medical Biophysics, University of Toronto, Toronto, Canada; Vector Institute for Artificial Intelligence, Toronto, Canada; Ontario Institute for Cancer Research, Toronto, Canada; Department of Computer Science, University of Toronto, Toronto, Canada; Department of Biostatistics, Dalla Lana School of Public Health, Toronto, Canada.
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9
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Porthiyas J, Nussey D, Beauchemin CAA, Warren DC, Quirouette C, Wilkie KP. Practical parameter identifiability and handling of censored data with Bayesian inference in mathematical tumour models. NPJ Syst Biol Appl 2024; 10:89. [PMID: 39143084 PMCID: PMC11324876 DOI: 10.1038/s41540-024-00409-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Accepted: 07/21/2024] [Indexed: 08/16/2024] Open
Abstract
Mechanistic mathematical models (MMs) are a powerful tool to help us understand and predict the dynamics of tumour growth under various conditions. In this work, we use 5 MMs with an increasing number of parameters to explore how certain (often overlooked) decisions in estimating parameters from data of experimental tumour growth affect the outcome of the analysis. In particular, we propose a framework for including tumour volume measurements that fall outside the upper and lower limits of detection, which are normally discarded. We demonstrate how excluding censored data results in an overestimation of the initial tumour volume and the MM-predicted tumour volumes prior to the first measurements, and an underestimation of the carrying capacity and the MM-predicted tumour volumes beyond the latest measurable time points. We show in which way the choice of prior for the MM parameters can impact the posterior distributions, and illustrate that reporting the most likely parameters and their 95% credible interval can lead to confusing or misleading interpretations. We hope this work will encourage others to carefully consider choices made in parameter estimation and to adopt the approaches we put forward herein.
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Affiliation(s)
- Jamie Porthiyas
- Department of Mathematics, Toronto Metropolitan University, Toronto, ON, M5B 2K3, Canada
| | - Daniel Nussey
- Department of Mathematics, Toronto Metropolitan University, Toronto, ON, M5B 2K3, Canada
| | - Catherine A A Beauchemin
- Department of Physics, Toronto Metropolitan University, Toronto, ON, M5B 2K3, Canada
- Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) Program, RIKEN, Wako-shi, Saitama, 351-0198, Japan
| | - Donald C Warren
- Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) Program, RIKEN, Wako-shi, Saitama, 351-0198, Japan
- Florida Institute of Technology, Melbourne, FL, 32901, USA
| | - Christian Quirouette
- Department of Physics, Toronto Metropolitan University, Toronto, ON, M5B 2K3, Canada
| | - Kathleen P Wilkie
- Department of Mathematics, Toronto Metropolitan University, Toronto, ON, M5B 2K3, Canada.
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10
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Geady C, Abbas-Aghababazadeh F, Kohan A, Schuetze S, Shultz D, Haibe-Kains B. Radiomic-Based Prediction of Lesion-Specific Systemic Treatment Response in Metastatic Disease. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2024:2023.09.22.23294942. [PMID: 37873411 PMCID: PMC10593058 DOI: 10.1101/2023.09.22.23294942] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2023]
Abstract
Despite sharing the same histologic classification, individual tumors in multi metastatic patients may present with different characteristics and varying sensitivities to anticancer therapies. In this study, we investigate the utility of radiomic biomarkers for prediction of lesion-specific treatment resistance in multi metastatic leiomyosarcoma patients. Using a dataset of n=202 lung metastases (LM) from n=80 patients with 1648 pre-treatment computed tomography (CT) radiomics features and LM progression determined from follow-up CT, we developed a radiomic model to predict the progression of each lesion. Repeat experiments assessed the relative predictive performance across LM volume groups. Lesion-specific radiomic models indicate up to a 4.5-fold increase in predictive capacity compared with a no-skill classifier, with an area under the precision-recall curve of 0.70 for the most precise model (FDR = 0.05). Precision varied by administered drug and LM volume. The effect of LM volume was controlled by removing radiomic features at a volume-correlation coefficient threshold of 0.20. Predicting lesion-specific responses using radiomic features represents a novel strategy by which to assess treatment response that acknowledges biological diversity within metastatic subclones, which could facilitate management strategies involving selective ablation of resistant clones in the setting of systemic therapy.
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Affiliation(s)
- Caryn Geady
- Princess Margaret Cancer Centre, University Health Network, Toronto, Canada
- Medical Biophysics, University of Toronto, Toronto, Canada
| | | | - Andres Kohan
- Princess Margaret Cancer Centre, University Health Network, Toronto, Canada
| | - Scott Schuetze
- Department of Medicine, University of Michigan, Ann Arbor, MI, USA
| | - David Shultz
- Princess Margaret Cancer Centre, University Health Network, Toronto, Canada
- Medical Biophysics, University of Toronto, Toronto, Canada
- Department of Medicine, University of Michigan, Ann Arbor, MI, USA
- Vector Institute for Artificial Intelligence, Toronto, Canada
- Ontario Institute for Cancer Research, Toronto, Canada
- Department of Computer Science, University of Toronto, Toronto, Canada
- Department of Biostatistics, Dalla Lana School of Public Health, Toronto, Canada
| | - Benjamin Haibe-Kains
- Princess Margaret Cancer Centre, University Health Network, Toronto, Canada
- Medical Biophysics, University of Toronto, Toronto, Canada
- Vector Institute for Artificial Intelligence, Toronto, Canada
- Ontario Institute for Cancer Research, Toronto, Canada
- Department of Computer Science, University of Toronto, Toronto, Canada
- Department of Biostatistics, Dalla Lana School of Public Health, Toronto, Canada
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11
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Gao Y, Feder AF. Detecting branching rate heterogeneity in multifurcating trees with applications in lineage tracing data. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.06.27.601073. [PMID: 39005367 PMCID: PMC11244928 DOI: 10.1101/2024.06.27.601073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/16/2024]
Abstract
Understanding cellular birth rate differences is crucial for predicting cancer progression and interpreting tumor-derived genetic data. Lineage tracing experiments enable detailed reconstruction of cellular genealogies, offering new opportunities to measure branching rate heterogeneity. However, the lineage tracing process can introduce complex tree features that complicate this effort. Here, we examine tree characteristics in lineage tracing-derived genealogies and find that editing window placement leads to multifurcations at a tree's root or tips. We propose several ways in which existing tree topology-based metrics can be extended to test for rate heterogeneity on trees even in the presence of lineage-tracing associated distortions. Although these methods vary in power and robustness, a test based on theJ 1 statistic effectively detects branching rate heterogeneity in simulated lineage tracing data. Tests based on other common statistics ( s ^ and the Sackin index) show interior performance toJ 1 . We apply our validated methods to xenograft experimental data and find widespread rate heterogeneity across multiple study systems. Our results demonstrate the potential of tree topology statistics in analyzing lineage tracing data, and highlight the challenges associated with adapting phylogenetic methods to these systems.
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Affiliation(s)
- Yingnan Gao
- Department of Genome Sciences, University of Washington, Seattle, WA
| | - Alison F Feder
- Department of Genome Sciences, University of Washington, Seattle, WA
- Herbold Computational Biology Program, Fred Hutchinson Cancer Center, Seattle, WA
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12
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Gunnarsson EB, Kim S, Choi B, Schmid JK, Kaura K, Lenz HJ, Mumenthaler SM, Foo J. Understanding patient-derived tumor organoid growth through an integrated imaging and mathematical modeling framework. PLoS Comput Biol 2024; 20:e1012256. [PMID: 39093897 PMCID: PMC11324155 DOI: 10.1371/journal.pcbi.1012256] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2024] [Revised: 08/14/2024] [Accepted: 06/11/2024] [Indexed: 08/04/2024] Open
Abstract
Patient-derived tumor organoids (PDTOs) are novel cellular models that maintain the genetic, phenotypic and structural features of patient tumor tissue and are useful for studying tumorigenesis and drug response. When integrated with advanced 3D imaging and analysis techniques, PDTOs can be used to establish physiologically relevant high-throughput and high-content drug screening platforms that support the development of patient-specific treatment strategies. However, in order to effectively leverage high-throughput PDTO observations for clinical predictions, it is critical to establish a quantitative understanding of the basic properties and variability of organoid growth dynamics. In this work, we introduced an innovative workflow for analyzing and understanding PDTO growth dynamics, by integrating a high-throughput imaging deep learning platform with mathematical modeling, incorporating flexible growth laws and variable dormancy times. We applied the workflow to colon cancer organoids and demonstrated that organoid growth is well-described by the Gompertz model of growth. Our analysis showed significant intrapatient heterogeneity in PDTO growth dynamics, with the initial exponential growth rate of an organoid following a lognormal distribution within each dataset. The level of intrapatient heterogeneity varied between patients, as did organoid growth rates and dormancy times of single seeded cells. Our work contributes to an emerging understanding of the basic growth characteristics of PDTOs, and it highlights the heterogeneity in organoid growth both within and between patients. These results pave the way for further modeling efforts aimed at predicting treatment response dynamics and drug resistance timing.
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Affiliation(s)
- Einar Bjarki Gunnarsson
- Applied Mathematics Division, Science Institute, University of Iceland, Reykjavík, Iceland
- School of Mathematics, University of Minnesota, Twin Cities, Minnesota, United States of America
| | - Seungil Kim
- Ellison Institute of Technology, Los Angeles, California, United States of America
| | - Brandon Choi
- Ellison Institute of Technology, Los Angeles, California, United States of America
- Keck School of Medicine, University of Southern California, Los Angeles, California, United States of America
| | - J. Karl Schmid
- School of Mathematics, University of Minnesota, Twin Cities, Minnesota, United States of America
| | - Karn Kaura
- The Blake School, Minneapolis, Minnesota, United States of America
| | - Heinz-Josef Lenz
- Keck School of Medicine, University of Southern California, Los Angeles, California, United States of America
| | - Shannon M. Mumenthaler
- Ellison Institute of Technology, Los Angeles, California, United States of America
- Keck School of Medicine, University of Southern California, Los Angeles, California, United States of America
- Department of Biomedical Engineering, Viterbi School of Engineering, University of Southern California, Los Angeles, California, United States of America
| | - Jasmine Foo
- School of Mathematics, University of Minnesota, Twin Cities, Minnesota, United States of America
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13
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Schirru M, Charef H, Ismaili KE, Fenneteau F, Zugaj D, Tremblay PO, Nekka F. Predicting efficacy assessment of combined treatment of radiotherapy and nivolumab for NSCLC patients through virtual clinical trials using QSP modeling. J Pharmacokinet Pharmacodyn 2024; 51:319-333. [PMID: 38493439 DOI: 10.1007/s10928-024-09903-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2023] [Accepted: 02/05/2024] [Indexed: 03/19/2024]
Abstract
Non-Small Cell Lung Cancer (NSCLC) remains one of the main causes of cancer death worldwide. In the urge of finding an effective approach to treat cancer, enormous therapeutic targets and treatment combinations are explored in clinical studies, which are not only costly, suffer from a shortage of participants, but also unable to explore all prospective therapeutic solutions. Within the evolving therapeutic landscape, the combined use of radiotherapy (RT) and checkpoint inhibitors (ICIs) emerged as a promising avenue. Exploiting the power of quantitative system pharmacology (QSP), we undertook a study to anticipate the therapeutic outcomes of these interventions, aiming to address the limitations of clinical trials. After enhancing a pre-existing QSP platform and accurately replicating clinical data outcomes, we conducted an in-depth study, examining different treatment protocols with nivolumab and RT, both as monotherapy and in combination, by assessing their efficacy through clinical endpoints, namely time to progression (TTP) and duration of response (DOR). As result, the synergy of combined protocols showcased enhanced TTP and extended DOR, suggesting dual advantages of extended response and slowed disease progression with certain combined regimens. Through the lens of QSP modeling, our findings highlight the potential to fine-tune combination therapies for NSCLC, thereby providing pivotal insights for tailoring patient-centric therapeutic interventions.
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Affiliation(s)
- Miriam Schirru
- Laboratoire de recherche en pharmacométrie, Faculté de pharmacie, Université de Montréal, Montreal, Canada.
| | - Hamza Charef
- Laboratoire de recherche en pharmacométrie, Faculté de pharmacie, Université de Montréal, Montreal, Canada
| | - Khalil-Elmehdi Ismaili
- Laboratoire de recherche en pharmacométrie, Faculté de pharmacie, Université de Montréal, Montreal, Canada
| | - Frédérique Fenneteau
- Laboratoire de recherche en pharmacométrie, Faculté de pharmacie, Université de Montréal, Montreal, Canada
| | - Didier Zugaj
- Clinical Pharmacology, Syneos Health, Quebec, Quebec G1P 0A2, Canada
| | | | - Fahima Nekka
- Laboratoire de recherche en pharmacométrie, Faculté de pharmacie, Université de Montréal, Montreal, Canada
- Centre de recherches mathématiques (CRM), Université de Montréal, Montreal, Canada
- Centre for Applied Mathematics in Bioscience and Medicine (CAMBAM), McGill University, Montreal, Canada
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14
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Zhou H, Mao B, Guo S. Mathematical Modeling of Tumor Growth in Preclinical Mouse Models with Applications in Biomarker Discovery and Drug Mechanism Studies. CANCER RESEARCH COMMUNICATIONS 2024; 4:2267-2281. [PMID: 39099194 PMCID: PMC11360417 DOI: 10.1158/2767-9764.crc-24-0059] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2024] [Revised: 06/11/2024] [Accepted: 08/01/2024] [Indexed: 08/06/2024]
Abstract
Oncology drug efficacy is evaluated in mouse models by continuously monitoring tumor volumes, which can be mathematically described by growth kinetic models. Although past studies have investigated various growth models, their reliance on small datasets raises concerns about whether their findings are truly representative of tumor growth in diverse mouse models under different vehicle or drug treatments. In this study, we systematically evaluated six parametric models (exponential, exponential quadratic, monomolecular, logistic, Gompertz, and von Bertalanffy) and the semiparametric generalized additive model (GAM) on fitting tumor volume data from more than 30,000 mice in 930 experiments conducted in patient-derived xenografts, cell line-derived xenografts, and syngeneic models. We found that the exponential quadratic model is the best parametric model and can adequately model 87% studies, higher than other models including von Bertalanffy (82%) and Gompertz (80%) models; the latter is often considered the standard growth model. At the mouse group level, 7.5% of growth data could not be fit by any parametric model and were fitted by GAM. We show that endpoint gain integrated in time, a GAM-derived efficacy metric, is equivalent to exponential growth rate, a metric we previously proposed and conveniently calculated by simple algebra. Using five studies on paclitaxel, anti-PD1 antibody, cetuximab, irinotecan, and sorafenib, we showed that exponential and exponential quadratic models achieve similar performance in uncovering drug mechanism and biomarkers. We also compared exponential growth rate-based association analysis and exponential modeling approach in biomarker discovery and found that they complement each other. Modeling methods herein are implemented in an open-source R package freely available at https://github.com/hjzhou988/TuGroMix. SIGNIFICANCE We present a general strategy for mathematically modeling tumor growth in mouse models using data from 30,000 mice and show that modeling and nonmodeling approaches are complementary in biomarker discovery and drug mechanism studies.
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Affiliation(s)
| | | | - Sheng Guo
- Crown Bioscience Inc., Suzhou, China
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15
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Singh D, Paquin D. Modeling free tumor growth: Discrete, continuum, and hybrid approaches to interpreting cancer development. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:6659-6693. [PMID: 39176414 DOI: 10.3934/mbe.2024292] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/24/2024]
Abstract
Tumor growth dynamics serve as a critical aspect of understanding cancer progression and treatment response to mitigate one of the most pressing challenges in healthcare. The in silico approach to understanding tumor behavior computationally provides an efficient, cost-effective alternative to wet-lab examinations and are adaptable to different environmental conditions, time scales, and unique patient parameters. As a result, this paper explored modeling of free tumor growth in cancer, surveying contemporary literature on continuum, discrete, and hybrid approaches. Factors like predictive power and high-resolution simulation competed against drawbacks like simulation load and parameter feasibility in these models. Understanding tumor behavior in different scenarios and contexts became the first step in advancing cancer research and revolutionizing clinical outcomes.
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Affiliation(s)
- Dashmi Singh
- Stanford University Online High School, 415 Broadway Academy Hall, Floor 2, 8853,415 Broadway, Redwood City, CA 94063, USA
| | - Dana Paquin
- Stanford University Online High School, 415 Broadway Academy Hall, Floor 2, 8853,415 Broadway, Redwood City, CA 94063, USA
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16
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Mahasa KJ, Ouifki R, de Pillis L, Eladdadi A. A Role of Effector CD 8 + T Cells Against Circulating Tumor Cells Cloaked with Platelets: Insights from a Mathematical Model. Bull Math Biol 2024; 86:89. [PMID: 38884815 DOI: 10.1007/s11538-024-01323-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2024] [Accepted: 05/31/2024] [Indexed: 06/18/2024]
Abstract
Cancer metastasis accounts for a majority of cancer-related deaths worldwide. Metastasis occurs when the primary tumor sheds cells into the blood and lymphatic circulation, thereby becoming circulating tumor cells (CTCs) that transverse through the circulatory system, extravasate the circulation and establish a secondary distant tumor. Accumulating evidence suggests that circulating effector CD 8 + T cells are able to recognize and attack arrested or extravasating CTCs, but this important antitumoral effect remains largely undefined. Recent studies highlighted the supporting role of activated platelets in CTCs's extravasation from the bloodstream, contributing to metastatic progression. In this work, a simple mathematical model describes how the primary tumor, CTCs, activated platelets and effector CD 8 + T cells participate in metastasis. The stability analysis reveals that for early dissemination of CTCs, effector CD 8 + T cells can present or keep secondary metastatic tumor burden at low equilibrium state. In contrast, for late dissemination of CTCs, effector CD 8 + T cells are unlikely to inhibit secondary tumor growth. Moreover, global sensitivity analysis demonstrates that the rate of the primary tumor growth, intravascular CTC proliferation, as well as the CD 8 + T cell proliferation, strongly affects the number of the secondary tumor cells. Additionally, model simulations indicate that an increase in CTC proliferation greatly contributes to tumor metastasis. Our simulations further illustrate that the higher the number of activated platelets on CTCs, the higher the probability of secondary tumor establishment. Intriguingly, from a mathematical immunology perspective, our simulations indicate that if the rate of effector CD 8 + T cell proliferation is high, then the secondary tumor formation can be considerably delayed, providing a window for adjuvant tumor control strategies. Collectively, our results suggest that the earlier the effector CD 8 + T cell response is enhanced the higher is the probability of preventing or delaying secondary tumor metastases.
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Affiliation(s)
- Khaphetsi Joseph Mahasa
- Department of Mathematics and Computer Science, National University of Lesotho, Roma, Maseru, Lesotho.
| | - Rachid Ouifki
- Department of Mathematics and Applied Mathematics, Mafikeng Campus, North-West University, Private Bag X2046, Mmabatho, 2735, South Africa
| | | | - Amina Eladdadi
- Division of Mathematical Sciences, The National Science Foundation, Alexandria, VA, USA
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17
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Castorina P, Castiglione F, Ferini G, Forte S, Martorana E, Giuffrida D. Mathematical modeling of the synergistic interplay of radiotherapy and immunotherapy in anti-cancer treatments. Front Immunol 2024; 15:1373738. [PMID: 38779678 PMCID: PMC11109403 DOI: 10.3389/fimmu.2024.1373738] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2024] [Accepted: 04/15/2024] [Indexed: 05/25/2024] Open
Abstract
Introduction While radiotherapy has long been recognized for its ability to directly ablate cancer cells through necrosis or apoptosis, radiotherapy-induced abscopal effect suggests that its impact extends beyond local tumor destruction thanks to immune response. Cellular proliferation and necrosis have been extensively studied using mathematical models that simulate tumor growth, such as Gompertz law, and the radiation effects, such as the linear-quadratic model. However, the effectiveness of radiotherapy-induced immune responses may vary among patients due to individual differences in radiation sensitivity and other factors. Methods We present a novel macroscopic approach designed to quantitatively analyze the intricate dynamics governing the interactions among the immune system, radiotherapy, and tumor progression. Building upon previous research demonstrating the synergistic effects of radiotherapy and immunotherapy in cancer treatment, we provide a comprehensive mathematical framework for understanding the underlying mechanisms driving these interactions. Results Our method leverages macroscopic observations and mathematical modeling to capture the overarching dynamics of this interplay, offering valuable insights for optimizing cancer treatment strategies. One shows that Gompertz law can describe therapy effects with two effective parameters. This result permits quantitative data analyses, which give useful indications for the disease progression and clinical decisions. Discussion Through validation against diverse data sets from the literature, we demonstrate the reliability and versatility of our approach in predicting the time evolution of the disease and assessing the potential efficacy of radiotherapy-immunotherapy combinations. This further supports the promising potential of the abscopal effect, suggesting that in select cases, depending on tumor size, it may confer full efficacy to radiotherapy.
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Affiliation(s)
- Paolo Castorina
- Genomics and molecular oncology unit, Istituto Oncologico del Mediterraneo, Viagrande, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Catania, Italy
- Faculty of Mathematics and Physics, Charles University, Prague, Czechia
| | - Filippo Castiglione
- Biotech Research Center, Technology Innovation Institute, Abu Dhabi, United Arab Emirates
- Institute for Applied Computing, National Research Council of Italy, Rome, Italy
| | - Gianluca Ferini
- Radiotherapy Unit, REM Radioterapia, Viagrande, Italy
- School of Medicine, University Kore of Enna, Enna, Italy
| | - Stefano Forte
- Genomics and molecular oncology unit, Istituto Oncologico del Mediterraneo, Viagrande, Italy
| | - Emanuele Martorana
- Genomics and molecular oncology unit, Istituto Oncologico del Mediterraneo, Viagrande, Italy
| | - Dario Giuffrida
- Genomics and molecular oncology unit, Istituto Oncologico del Mediterraneo, Viagrande, Italy
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18
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Dolan M, Shi Y, Mastri M, Long MD, McKenery A, Hill JW, Vaghi C, Benzekry S, Barbi J, Ebos JM. A senescence-mimicking (senomimetic) VEGFR TKI side-effect primes tumor immune responses via IFN/STING signaling. Mol Cancer Ther 2024; 23:745113. [PMID: 38690835 PMCID: PMC11527799 DOI: 10.1158/1535-7163.mct-24-0139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2024] [Revised: 04/18/2024] [Accepted: 04/19/2024] [Indexed: 05/03/2024]
Abstract
Tyrosine kinase inhibitors (TKIs) that block the vascular endothelial growth factor receptors (VEGFRs) disrupt tumor angiogenesis but also have many unexpected side-effects that impact tumor cells directly. This includes the induction of molecular markers associated with senescence, a form of cellular aging that typically involves growth arrest. We have shown that VEGFR TKIs can hijack these aging programs by transiently inducting senescence-markers (SMs) in tumor cells to activate senescence-associated secretory programs that fuel drug resistance. Here we show that these same senescence-mimicking ('senomimetic') VEGFR TKI effects drive an enhanced immunogenic signaling that, in turn, can alter tumor response to immunotherapy. Using a live-cell sorting method to detect beta-galactosidase, a commonly used SM, we found that subpopulations of SM-expressing (SM+) tumor cells have heightened interferon (IFN) signaling and increased expression of IFN-stimulated genes (ISGs). These ISG increases were under the control of the STimulator of INterferon Gene (STING) signaling pathway, which we found could be directly activated by several VEGFR TKIs. TKI-induced SM+ cells could stimulate or suppress CD8 T-cell activation depending on host:tumor cell contact while tumors grown from SM+ cells were more sensitive to PD-L1 inhibition in vivo, suggesting that offsetting immune-suppressive functions of SM+ cells can improve TKI efficacy overall. Our findings may explain why some (but not all) VEGFR TKIs improve outcomes when combined with immunotherapy and suggest that exploiting senomimetic drug side-effects may help identify TKIs that uniquely 'prime' tumors for enhanced sensitivity to PD-L1 targeted agents.
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Affiliation(s)
- Melissa Dolan
- Department of Experimental Therapeutics, Roswell Park Comprehensive Cancer Center Buffalo, NY, 14263. USA
| | - Yuhao Shi
- Department of Experimental Therapeutics, Roswell Park Comprehensive Cancer Center Buffalo, NY, 14263. USA
| | - Michalis Mastri
- Department of Cancer Genetics and Genomics, Roswell Park Comprehensive Cancer Center, Buffalo, NY, 14263. USA
| | - Mark D. Long
- Department of Bioinformatics and Statistics, Roswell Park Comprehensive Cancer Center Buffalo, NY, 14263. USA
| | - Amber McKenery
- Department of Cancer Genetics and Genomics, Roswell Park Comprehensive Cancer Center, Buffalo, NY, 14263. USA
| | - James W. Hill
- Jacobs School of Medicine and Biomedical Sciences, SUNY at Buffalo, Buffalo, New York, 14263. USA
| | - Cristina Vaghi
- Inria Team MONC, Inria Bordeaux Sud-Ouest, Talence, France
- Computational Pharmacology and Clinical Oncology (COMPO), Inria Sophia Antipolis–Méditerranée, Cancer Research Center of Marseille, Inserm UMR1068, CNRS UMR7258, Aix Marseille University UM105, 13385 Marseille, France
| | - Sebastien Benzekry
- Inria Team MONC, Inria Bordeaux Sud-Ouest, Talence, France
- Computational Pharmacology and Clinical Oncology (COMPO), Inria Sophia Antipolis–Méditerranée, Cancer Research Center of Marseille, Inserm UMR1068, CNRS UMR7258, Aix Marseille University UM105, 13385 Marseille, France
| | - Joseph Barbi
- Department of Immunology, Roswell Park Comprehensive Cancer Center, Buffalo, NY, 14263. USA
| | - John M.L. Ebos
- Department of Experimental Therapeutics, Roswell Park Comprehensive Cancer Center Buffalo, NY, 14263. USA
- Department of Cancer Genetics and Genomics, Roswell Park Comprehensive Cancer Center, Buffalo, NY, 14263. USA
- Department of Medicine, Roswell Park Comprehensive Cancer Center Buffalo, NY, 14263. USA
- Lead Contact
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19
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Castorina P, Castiglione F, Ferini G, Forte S, Martorana E. Computational Approach for Spatially Fractionated Radiation Therapy (SFRT) and Immunological Response in Precision Radiation Therapy. J Pers Med 2024; 14:436. [PMID: 38673063 PMCID: PMC11051362 DOI: 10.3390/jpm14040436] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2024] [Revised: 04/08/2024] [Accepted: 04/14/2024] [Indexed: 04/28/2024] Open
Abstract
The field of precision radiation therapy has seen remarkable advancements in both experimental and computational methods. Recent literature has introduced various approaches such as Spatially Fractionated Radiation Therapy (SFRT). This unconventional treatment, demanding high-precision radiotherapy, has shown promising clinical outcomes. A comprehensive computational scheme for SFRT, extrapolated from a case report, is proposed. This framework exhibits exceptional flexibility, accommodating diverse initial conditions (shape, inhomogeneity, etc.) and enabling specific choices for sub-volume selection with administrated higher radiation doses. The approach integrates the standard linear quadratic model and, significantly, considers the activation of the immune system due to radiotherapy. This activation enhances the immune response in comparison to the untreated case. We delve into the distinct roles of the native immune system, immune activation by radiation, and post-radiotherapy immunotherapy, discussing their implications for either complete recovery or disease regrowth.
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Affiliation(s)
- Paolo Castorina
- Istituto Oncologico del Mediterraneo, Via Penninazzo, 7, 95029 Viagrande, Italy; (S.F.); (E.M.)
- INFN, Sezione di Catania, Via Santa Sofia, 64, 95123 Catania, Italy
- Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000 Prague, Czech Republic
| | - Filippo Castiglione
- Biotechnology Research Center, Technology Innovation Institute, Abu Dhabi P.O. Box 9639, United Arab Emirates;
- Institute for Applied Computing, National Research Council of Italy, Via dei Taurini, 19, 00185 Rome, Italy
| | - Gianluca Ferini
- REM Radioterapia, Via Penninazzo, 11, 95029 Viagrande, Italy;
| | - Stefano Forte
- Istituto Oncologico del Mediterraneo, Via Penninazzo, 7, 95029 Viagrande, Italy; (S.F.); (E.M.)
| | - Emanuele Martorana
- Istituto Oncologico del Mediterraneo, Via Penninazzo, 7, 95029 Viagrande, Italy; (S.F.); (E.M.)
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20
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Huber HJ, Mistry HB. Explaining in-vitro to in-vivo efficacy correlations in oncology pre-clinical development via a semi-mechanistic mathematical model. J Pharmacokinet Pharmacodyn 2024; 51:169-185. [PMID: 37930506 PMCID: PMC10982099 DOI: 10.1007/s10928-023-09891-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2023] [Accepted: 10/03/2023] [Indexed: 11/07/2023]
Abstract
In-vitro to in-vivo correlations (IVIVC), relating in-vitro parameters like IC50 to in-vivo drug exposure in plasma and tumour growth, are widely used in oncology for experimental design and dose decisions. However, they lack a deeper understanding of the underlying mechanisms. Our paper therefore focuses on linking empirical IVIVC relations for small-molecule kinase inhibitors with a semi-mechanistic tumour-growth model. We develop an approach incorporating parameters like the compound's peak-trough ratio (PTR), Hill coefficient of in-vitro dose-response curves, and xenograft-specific properties. This leads to formulas for determining efficacious doses for tumor stasis under linear pharmacokinetics equivalent to traditional empirical IVIVC relations, but enabling more systematic analysis. Our findings reveal that in-vivo xenograft-specific parameters, specifically the growth rate (g) and decay rate (d), along with the average exposure, are generally more significant determinants of tumor stasis and effective dose than the compound's peak-trough ratio. However, as the Hill coefficient increases, the dependency of tumor stasis on the PTR becomes more pronounced, indicating that the compound is more influenced by its maximum or trough values rather than the average exposure. Furthermore, we discuss the translation of our method to predict population dose ranges in clinical studies and propose a resistance mechanism that solely relies on specific in-vivo xenograft parameters instead of IC50 exposure coverage. In summary, our study aims to provide a more mechanistic understanding of IVIVC relations, emphasizing the importance of xenograft-specific parameters and PTR on tumor stasis.
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Affiliation(s)
- Heinrich J Huber
- Drug Discovery Sciences, Boehringer Ingelheim RCV GmbH & Co KG, Dr. Boehringer-Gasse 5-11, Vienna, 1120, Austria.
| | - Hitesh B Mistry
- Department, SEDA Pharmaceutical Development Services, Oakfield Road Cheadle Royal Business Park, Cheadle, SK8 3GX, United Kingdom
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21
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Schultz L, Gondim A, Ruan S. Gompertz models with periodical treatment and applications to prostate cancer. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:4104-4116. [PMID: 38549320 DOI: 10.3934/mbe.2024181] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/02/2024]
Abstract
In this paper, Gompertz type models are proposed to understand the temporal tumor volume behavior of prostate cancer when a periodical treatment is provided. Existence, uniqueness, and stability of periodic solutions are established. The models are used to fit the data and to forecast the tumor growth behavior based on prostate cancer treatments using capsaicin and docetaxel anticancer drugs. Numerical simulations show that the combination of capsaicin and docetaxel is the most efficient treatment of prostate cancer.
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Affiliation(s)
- Leonardo Schultz
- Department of Mathematics, University of Miami, 1365 Memorial Drive, Coral Gables, FL 33146, USA
| | - Antonio Gondim
- Department of Mathematics, University of Miami, 1365 Memorial Drive, Coral Gables, FL 33146, USA
| | - Shigui Ruan
- Department of Mathematics, University of Miami, 1365 Memorial Drive, Coral Gables, FL 33146, USA
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22
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Benzekry S, Schlicke P, Mogenet A, Greillier L, Tomasini P, Simon E. Computational markers for personalized prediction of outcomes in non-small cell lung cancer patients with brain metastases. Clin Exp Metastasis 2024; 41:55-68. [PMID: 38117432 DOI: 10.1007/s10585-023-10245-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 11/07/2023] [Indexed: 12/21/2023]
Abstract
Intracranial progression after curative treatment of early-stage non-small cell lung cancer (NSCLC) occurs from 10 to 50% and is difficult to manage, given the heterogeneity of clinical presentations and the variability of treatments available. The objective of this study was to develop a mechanistic model of intracranial progression to predict survival following a first brain metastasis (BM) event occurring at a time [Formula: see text]. Data included early-stage NSCLC patients treated with a curative intent who had a BM as the first and single relapse site (N = 31). We propose a mechanistic mathematical model able to derive computational markers from primary tumor and BM data at [Formula: see text] and estimate the amount and sizes of (visible and invisible) BMs, as well as their future behavior. These two key computational markers are [Formula: see text], the proliferation rate of a single tumor cell; and [Formula: see text], the per day, per cell, probability to metastasize. The predictive value of these individual computational biomarkers was evaluated. The model was able to correctly describe the number and size of metastases at [Formula: see text] for 20 patients. Parameters [Formula: see text] and [Formula: see text] were significantly associated with overall survival (OS) (HR 1.65 (1.07-2.53) p = 0.0029 and HR 1.95 (1.31-2.91) p = 0.0109, respectively). Adding the computational markers to the clinical ones significantly improved the predictive value of OS (c-index increased from 0.585 (95% CI 0.569-0.602) to 0.713 (95% CI 0.700-0.726), p < 0.0001). We demonstrated that our model was applicable to brain oligoprogressive patients in NSCLC and that the resulting computational markers had predictive potential. This may help lung cancer physicians to guide and personalize the management of NSCLC patients with intracranial oligoprogression.
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Affiliation(s)
- Sébastien Benzekry
- COMPutational Pharmacology and Clinical Oncology Department, Inria Sophia Antipolis - Méditerranée, Faculté de Pharmacie, Cancer Research Center of Marseille, Inserm UMR1068, CNRS UMR7258, Aix Marseille University UM105, 27 Boulevard Jean Moulin, 13005, Marseille, France.
| | - Pirmin Schlicke
- Department of Mathematics, TUM School of Computation, Information and Technology, Technical University of Munich, Garching (Munich), Germany
| | - Alice Mogenet
- Multidisciplinary Oncology and Therapeutic Innovations Department, Assistance Publique - Hôpitaux de Marseille, Aix Marseille University, Marseille, France
| | - Laurent Greillier
- Multidisciplinary Oncology and Therapeutic Innovations Department, Assistance Publique - Hôpitaux de Marseille, Aix Marseille University, Marseille, France
- Aix Marseille University, CNRS, INSERM, CRCM, Marseille, France
| | - Pascale Tomasini
- Multidisciplinary Oncology and Therapeutic Innovations Department, Assistance Publique - Hôpitaux de Marseille, Aix Marseille University, Marseille, France
- Aix Marseille University, CNRS, INSERM, CRCM, Marseille, France
| | - Eléonore Simon
- Multidisciplinary Oncology and Therapeutic Innovations Department, Assistance Publique - Hôpitaux de Marseille, Aix Marseille University, Marseille, France
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23
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Otunuga OM. Tumor growth and population modeling in a toxicant-stressed random environment. J Math Biol 2024; 88:18. [PMID: 38245595 DOI: 10.1007/s00285-023-02035-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/25/2022] [Revised: 11/30/2023] [Accepted: 12/05/2023] [Indexed: 01/22/2024]
Abstract
When examining some factors that contribute to the growth or decline of a population or tumor, it is essential to consider a random hypothesis. By analyzing the effects of stress on a population (or volume of tumor growth) in a random environment, we develop stochastic models describing the dynamics of the population (or tumor growth) based on random adjustments to the population's intrinsic growth rate, carrying capacity, and harvesting efforts (or tumor treatments). Apart from the models' ability to capture fluctuations, the availability of a shape parameter in the models gives it the flexibility to describe a variety of population/tumor data with different shapes. The distribution of the stressed population size with or without harvesting (or treatments) is derived and used to calculate the maximum expected amount of harvests that can be taken from the population without depleting resources in the long run (or the minimum amount of chemotherapy needed to cause shrinkage or eradication of a tumor). The work done is applied to analyze tumor growth using published data comprising of the volume of breast tumor obtained by orthotopically implanting LM2-[Formula: see text] cells into the right inguinal mammary fat pads of 6- to 8-week-old female Severe Combined Immuno-Deficient mice.
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24
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Pierce L, Anderson H, Sarkar S, Bauer SR, Sarkar S. Experimental and computational approach to establish fit-for-purpose cell viability assays. Regen Med 2024; 19:27-45. [PMID: 38247346 DOI: 10.2217/rme-2023-0154] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2024] Open
Abstract
Aim: Cell viability assays are critical for cell-based products. Here, we demonstrate a combined experimental and computational approach to identify fit-for-purpose cell assays that can predict changes in cell proliferation, a critical biological response in cell expansion. Materials & methods: Jurkat cells were systematically injured using heat (45 ± 1°C). Cell viability was measured at 0 h and 24 h after treatment using assays for membrane integrity, metabolic function and apoptosis. Proliferation kinetics for longer term cultures were modeled using the Gompertz distribution to establish predictive models between cell viability results and proliferation. Results & conclusion: We demonstrate an approach for ranking these assays as predictors of cell proliferation and for setting cell viability specifications when a particular proliferation response is required.
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Affiliation(s)
- Laura Pierce
- Biosystems & Biomaterials Division, National Institute of Standards & Technology, Gaithersburg, MD 20899, USA
| | - Hidayah Anderson
- Division of Cellular & Gene Therapies, CBER, FDA, Silver Spring, MD 20993, USA
| | - Swarnavo Sarkar
- Biosystems & Biomaterials Division, National Institute of Standards & Technology, Gaithersburg, MD 20899, USA
| | - Steven R Bauer
- Division of Cellular & Gene Therapies, CBER, FDA, Silver Spring, MD 20993, USA
| | - Sumona Sarkar
- Biosystems & Biomaterials Division, National Institute of Standards & Technology, Gaithersburg, MD 20899, USA
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25
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Fang J, Wang J, Li A, Yan Y, Liu H, Li J, Yang H, Hou Y, Yang X, Yang M, Liu J. Parameterized Gompertz-Guided Morphological AutoEncoder for Predicting Pulmonary Nodule Growth. IEEE TRANSACTIONS ON MEDICAL IMAGING 2023; 42:3602-3613. [PMID: 37471191 DOI: 10.1109/tmi.2023.3297209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/22/2023]
Abstract
The growth rate of pulmonary nodules is a critical clue to the cancerous diagnosis. It is essential to monitor their dynamic progressions during pulmonary nodule management. To facilitate the prosperity of research on nodule growth prediction, we organized and published a temporal dataset called NLSTt with consecutive computed tomography (CT) scans. Based on the self-built dataset, we develop a visual learner to predict the growth for the following CT scan qualitatively and further propose a model to predict the growth rate of pulmonary nodules quantitatively, so that better diagnosis can be achieved with the help of our predicted results. To this end, in this work, we propose a parameterized Gempertz-guided morphological autoencoder (GM-AE) to generate any future-time-span high-quality visual appearances of pulmonary nodules from the baseline CT scan. Specifically, we parameterize a popular mathematical model for tumor growth kinetics, Gompertz, to predict future masses and volumes of pulmonary nodules. Then, we exploit the expected growth rate on the mass and volume to guide decoders generating future shape and texture of pulmonary nodules. We introduce two branches in an autoencoder to encourage shape-aware and textural-aware representation learning and integrate the generated shape into the textural-aware branch to simulate the future morphology of pulmonary nodules. We conduct extensive experiments on the self-built NLSTt dataset to demonstrate the superiority of our GM-AE to its competitive counterparts. Experiment results also reveal the learnable Gompertz function enjoys promising descriptive power in accounting for inter-subject variability of the growth rate for pulmonary nodules. Besides, we evaluate our GM-AE model on an in-house dataset to validate its generalizability and practicality. We make its code publicly available along with the published NLSTt dataset.
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26
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Hutson AD, Yu H, Attwood K. Leveraging homologous hypotheses for increased efficiency in tumor growth curve testing. Sci Rep 2023; 13:19890. [PMID: 37963974 PMCID: PMC10646053 DOI: 10.1038/s41598-023-47202-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2023] [Accepted: 11/10/2023] [Indexed: 11/16/2023] Open
Abstract
In this note, we present an innovative approach called "homologous hypothesis tests" that focuses on cross-sectional comparisons of average tumor volumes at different time-points. By leveraging the correlation structure between time-points, our method enables highly efficient per time-point comparisons, providing inferences that are highly efficient as compared to those obtained from a standard two-sample t test. The key advantage of this approach lies in its user-friendliness and accessibility, as it can be easily employed by the broader scientific community through standard statistical software packages.
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Affiliation(s)
- Alan D Hutson
- Department of Biostatistics and Bioinformatics, Roswell Park Comprehensive Cancer Center, Elm and Carlton Streets, Buffalo, NY, 14623, USA.
| | - Han Yu
- Department of Biostatistics and Bioinformatics, Roswell Park Comprehensive Cancer Center, Elm and Carlton Streets, Buffalo, NY, 14623, USA
| | - Kristopher Attwood
- Department of Biostatistics and Bioinformatics, Roswell Park Comprehensive Cancer Center, Elm and Carlton Streets, Buffalo, NY, 14623, USA
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27
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Sancho-Araiz A, Parra-Guillen ZP, Bragard J, Ardanza S, Mangas-Sanjuan V, Trocóniz IF. Mechanistic characterization of oscillatory patterns in unperturbed tumor growth dynamics: The interplay between cancer cells and components of tumor microenvironment. PLoS Comput Biol 2023; 19:e1011507. [PMID: 37792732 PMCID: PMC10550146 DOI: 10.1371/journal.pcbi.1011507] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Accepted: 09/11/2023] [Indexed: 10/06/2023] Open
Abstract
Mathematical modeling of unperturbed and perturbed tumor growth dynamics (TGD) in preclinical experiments provides an opportunity to establish translational frameworks. The most commonly used unperturbed tumor growth models (i.e. linear, exponential, Gompertz and Simeoni) describe a monotonic increase and although they capture the mean trend of the data reasonably well, systematic model misspecifications can be identified. This represents an opportunity to investigate possible underlying mechanisms controlling tumor growth dynamics through a mathematical framework. The overall goal of this work is to develop a data-driven semi-mechanistic model describing non-monotonic tumor growth in untreated mice. For this purpose, longitudinal tumor volume profiles from different tumor types and cell lines were pooled together and analyzed using the population approach. After characterizing the oscillatory patterns (oscillator half-periods between 8-11 days) and confirming that they were systematically observed across the different preclinical experiments available (p<10-9), a tumor growth model was built including the interplay between resources (i.e. oxygen or nutrients), angiogenesis and cancer cells. The new structure, in addition to improving the model diagnostic compared to the previously used tumor growth models (i.e. AIC reduction of 71.48 and absence of autocorrelation in the residuals (p>0.05)), allows the evaluation of the different oncologic treatments in a mechanistic way. Drug effects can potentially, be included in relevant processes taking place during tumor growth. In brief, the new model, in addition to describing non-monotonic tumor growth and the interaction between biological factors of the tumor microenvironment, can be used to explore different drug scenarios in monotherapy or combination during preclinical drug development.
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Affiliation(s)
- Aymara Sancho-Araiz
- Pharmacometrics & Systems Pharmacology Group, Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain
- IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
| | - Zinnia P. Parra-Guillen
- Pharmacometrics & Systems Pharmacology Group, Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain
- IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
| | - Jean Bragard
- Department of Physics and Applied Math. University of Navarra, Pamplona, Spain
- Institute of Data Science and Artificial Intelligence, DATAI, University of Navarra, Pamplona, Spain
| | - Sergio Ardanza
- Department of Physics and Applied Math. University of Navarra, Pamplona, Spain
- Institute of Data Science and Artificial Intelligence, DATAI, University of Navarra, Pamplona, Spain
| | - Victor Mangas-Sanjuan
- Department of Pharmacy and Pharmaceutical Technology and Parasitology, Faculty of Pharmacy, University of Valencia, Valencia, Spain
- Interuniversity Research Institute for Molecular Recognition and Technological Development, Valencia, Spain
| | - Iñaki F. Trocóniz
- Pharmacometrics & Systems Pharmacology Group, Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain
- IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
- Institute of Data Science and Artificial Intelligence, DATAI, University of Navarra, Pamplona, Spain
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Hutson AD, Yu H, Attwood K. Leveraging Homologous Hypotheses for Increased Efficiency in Tumor Growth Curve Testing. RESEARCH SQUARE 2023:rs.3.rs-3242375. [PMID: 37645958 PMCID: PMC10462185 DOI: 10.21203/rs.3.rs-3242375/v1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
In this note, we present an innovative approach called "homologous hypothesis tests" that focuses on cross-sectional comparisons of average tumor volumes at different time-points. By leveraging the correlation structure between time-points, our method enables highly efficient per time-point comparisons, providing inferences that are highly efficient as compared to those obtained from a standard two-sample t-test. The key advantage of this approach lies in its user-friendliness and accessibility, as it can be easily employed by the broader scientific community through standard statistical software packages.
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Affiliation(s)
- Alan D Hutson
- Roswell Park Comprehensive Cancer Center, Department of Biostatistics and Bioinformatics, Elm and Carlton Streets, Buffalo, NY 14623
| | - Han Yu
- Roswell Park Comprehensive Cancer Center, Department of Biostatistics and Bioinformatics, Elm and Carlton Streets, Buffalo, NY 14623
| | - Kristopher Attwood
- Roswell Park Comprehensive Cancer Center, Department of Biostatistics and Bioinformatics, Elm and Carlton Streets, Buffalo, NY 14623
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Martorana E, Castorina P, Ferini G, Forte S, Mare M. Forecasting Individual Patients' Best Time for Surgery in Colon-Rectal Cancer by Tumor Regression during and after Neoadjuvant Radiochemotherapy. J Pers Med 2023; 13:jpm13050851. [PMID: 37241020 DOI: 10.3390/jpm13050851] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2023] [Revised: 04/24/2023] [Accepted: 05/12/2023] [Indexed: 05/28/2023] Open
Abstract
The standard treatment of locally advanced rectal cancer is neoadjuvant chemoradiotherapy before surgery. For those patients experiencing a complete clinical response after the treatment, a watch-and-wait strategy with close monitoring may be practicable. In this respect, the identification of biomarkers of the response to therapy is extremely important. Many mathematical models have been developed or used to describe tumor growth, such as Gompertz's Law and the Logistic Law. Here we show that the parameters of those macroscopic growth laws, obtained by fitting the tumor evolution during and immediately after therapy, are a useful tool for evaluating the best time for surgery in this type of cancer. A limited number of experimental observations of the tumor volume regression, during and after the neoadjuvant doses, permits a reliable evaluation of a specific patient response (partial or complete recovery) for a later time, and one can evaluate a modification of the scheduled treatment, following a watch-and-wait approach or an early or late surgery. Neoadjuvant chemoradiotherapy effects can be quantitatively described by applying Gompertz's Law and the Logistic Law to estimate tumor growth by monitoring patients at regular intervals. We show a quantitative difference in macroscopic parameters between partial and complete response patients, reliable for estimating the treatment effects and best time for surgery.
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Affiliation(s)
| | - Paolo Castorina
- Istituto Oncologico del Mediterraneo, 95029 Viagrande, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Catania, 95123 Catania, Italy
- Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000 Prague, Czech Republic
| | | | - Stefano Forte
- Istituto Oncologico del Mediterraneo, 95029 Viagrande, Italy
| | - Marzia Mare
- Istituto Oncologico del Mediterraneo, 95029 Viagrande, Italy
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30
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Bigarré C, Bertucci F, Finetti P, Macgrogan G, Muracciole X, Benzekry S. Mechanistic modeling of metastatic relapse in early breast cancer to investigate the biological impact of prognostic biomarkers. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2023; 231:107401. [PMID: 36804267 DOI: 10.1016/j.cmpb.2023.107401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Revised: 01/12/2023] [Accepted: 02/01/2023] [Indexed: 06/18/2023]
Abstract
BACKGROUND AND OBJECTIVE Estimating the risk of metastatic relapse is a major challenge to decide adjuvant treatment options in early-stage breast cancer (eBC). To date, distant metastasis-free survival (DMFS) analysis mainly relies on classical, agnostic, statistical models (e.g., Cox regression). Instead, we propose here to derive mechanistic models of DMFS. METHODS The present series consisted of eBC patients who did not receive adjuvant systemic therapy from three datasets, composed respectively of 692 (Bergonié Institute), 591 (Paoli-Calmettes Institute, IPC), and 163 (Public Hospital Marseille, AP-HM) patients with routine clinical annotations. The last dataset also contained expression of three non-routine biomarkers. Our mechanistic model of DMFS relies on two mathematical parameters that represent growth (α) and dissemination (μ). We identified their population distributions using mixed-effects modeling. Critically, we propose a novel variable selection procedure allowing to: (i) identify the association of biological parameters with either α, μ or both, and (ii) generate an optimal candidate model for DMFS prediction. RESULTS We found that Ki67 and Thymidine Kinase-1 were associated with α, and nodal status and Plasminogen Activator Inhibitor-1 with μ. The predictive performances of the model were excellent in calibration but moderate in discrimination, with c-indices of 0.72 (95% CI [0.48, 0.95], AP-HM), 0.63 ([0.44, 0.83], Bergonié) and 0.60 (95% CI [0.54, 0.80], IPC). CONCLUSIONS Overall, we demonstrate that our novel method combining mechanistic and advanced statistical modeling is able to unravel the biological roles of clinicopathological parameters from DMFS data.
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Affiliation(s)
- Célestin Bigarré
- COMPO, Inria Méditerranée, Cancer Research Center of Marseille, Inserm UMR1068, CNRS UMR7258, Aix Marseille University UM105, 13385 Marseille, France.
| | - François Bertucci
- Predictive Oncology Laboratory, Marseille Cancer Research Centre (CRCM), Inserm U1068, CNRS UMR7258, Institut Paoli-Calmettes, Equipe labellisée Ligue Nationale Contre Le Cancer, Aix-Marseille University, Marseille, France; Department of Medical Oncology, CRCM, Institut Paoli-Calmettes, CNRS, Inserm, Aix-Marseille University, Marseille, France
| | - Pascal Finetti
- Predictive Oncology Laboratory, Marseille Cancer Research Centre (CRCM), Inserm U1068, CNRS UMR7258, Institut Paoli-Calmettes, Equipe labellisée Ligue Nationale Contre Le Cancer, Aix-Marseille University, Marseille, France
| | - Gaëtan Macgrogan
- Department of Biopathology, Institut Bergonié, Regional Comprehensive Cancer Centre, Bordeaux, France; Inserm U1218, Bordeaux Public Health, University of Bordeaux, Bordeaux, France
| | - Xavier Muracciole
- COMPO, Inria Méditerranée, Cancer Research Center of Marseille, Inserm UMR1068, CNRS UMR7258, Aix Marseille University UM105, 13385 Marseille, France; Radiotherapy Department, Assistance Publique - Hôpitaux de Marseille, Aix Marseille University, Marseille, France
| | - Sébastien Benzekry
- COMPO, Inria Méditerranée, Cancer Research Center of Marseille, Inserm UMR1068, CNRS UMR7258, Aix Marseille University UM105, 13385 Marseille, France
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31
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Nakano H, Shiinoki T, Tanabe S, Nakano T, Takizawa T, Utsunomiya S, Sakai M, Tanabe S, Ohta A, Kaidu M, Nishio T, Ishikawa H. Multicomponent mathematical model for tumor volume calculation with setup error using single-isocenter stereotactic radiotherapy for multiple brain metastases. Phys Eng Sci Med 2023; 46:945-953. [PMID: 36940064 DOI: 10.1007/s13246-023-01241-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 03/06/2023] [Indexed: 03/21/2023]
Abstract
We evaluated the tumor residual volumes considering six degrees-of-freedom (6DoF) patient setup errors in stereotactic radiotherapy (SRT) with multicomponent mathematical model using single-isocenter irradiation for brain metastases. Simulated spherical gross tumor volumes (GTVs) with 1.0 (GTV 1), 2.0 (GTV 2), and 3.0 (GTV 3)-cm diameters were used. The distance between the GTV center and isocenter (d) was set at 0-10 cm. The GTV was simultaneously translated within 0-1.0 mm (T) and rotated within 0°-1.0° (R) in the three axis directions using affine transformation. We optimized the tumor growth model parameters using measurements of non-small cell lung cancer cell lines' (A549 and NCI-H460) growth. We calculated the GTV residual volume at the irradiation's end using the physical dose to the GTV when the GTV size, d, and 6DoF setup error varied. The d-values that satisfy tolerance values (10%, 35%, and 50%) of the GTV residual volume rate based on the pre-irradiation GTV volume were determined. The larger the tolerance value set for both cell lines, the longer the distance to satisfy the tolerance value. In GTV residual volume evaluations based on the multicomponent mathematical model on SRT with single-isocenter irradiation, the smaller the GTV size and the larger the distance and 6DoF setup error, the shorter the distance that satisfies the tolerance value might need to be.
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Affiliation(s)
- Hisashi Nakano
- Department of Radiation Oncology, Niigata University Medical and Dental Hospital, 1-757 Asahimachi-Dori, Chuo-Ku, Niigata-Shi, Niigata, Japan. .,Department of Medical Physics and Engineering, Osaka University Graduate School of Medicine, 1-7 Yamadaoka, Suita-Shi, Osaka, Japan.
| | - Takehiro Shiinoki
- Department of Radiation Oncology, Yamaguchi University, Minamikogushi 1-1-1 Ube, Yamaguchi, Japan
| | - Satoshi Tanabe
- Department of Radiation Oncology, Niigata University Medical and Dental Hospital, 1-757 Asahimachi-Dori, Chuo-Ku, Niigata-Shi, Niigata, Japan
| | - Toshimichi Nakano
- Department of Radiology and Radiation Oncology, Niigata University Graduate School of Medical and Dental Sciences, 1-757 Asahimachi-Dori, Chuo-Ku, Niigata-Shi, Niigata, Japan
| | - Takeshi Takizawa
- Department of Radiology and Radiation Oncology, Niigata University Graduate School of Medical and Dental Sciences, 1-757 Asahimachi-Dori, Chuo-Ku, Niigata-Shi, Niigata, Japan.,Department of Radiation Oncology, Niigata Neurosurgical Hospital, 3057 Yamada, Nishi-Ku, Niigata-Shi, Niigata, Japan
| | - Satoru Utsunomiya
- Department of Radiological Technology, Niigata University Graduate School of Health Sciences, 2-746 Asahimachi-Dori, Chuo-Ku, Niigata-Shi, Niigata, Japan
| | - Madoka Sakai
- Department of Radiation Oncology, Niigata University Medical and Dental Hospital, 1-757 Asahimachi-Dori, Chuo-Ku, Niigata-Shi, Niigata, Japan
| | - Shunpei Tanabe
- Department of Radiation Oncology, Niigata University Medical and Dental Hospital, 1-757 Asahimachi-Dori, Chuo-Ku, Niigata-Shi, Niigata, Japan
| | - Atsushi Ohta
- Department of Radiation Oncology, Niigata University Medical and Dental Hospital, 1-757 Asahimachi-Dori, Chuo-Ku, Niigata-Shi, Niigata, Japan
| | - Motoki Kaidu
- Department of Radiology and Radiation Oncology, Niigata University Graduate School of Medical and Dental Sciences, 1-757 Asahimachi-Dori, Chuo-Ku, Niigata-Shi, Niigata, Japan
| | - Teiji Nishio
- Department of Medical Physics and Engineering, Osaka University Graduate School of Medicine, 1-7 Yamadaoka, Suita-Shi, Osaka, Japan
| | - Hiroyuki Ishikawa
- Department of Radiology and Radiation Oncology, Niigata University Graduate School of Medical and Dental Sciences, 1-757 Asahimachi-Dori, Chuo-Ku, Niigata-Shi, Niigata, Japan
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32
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Bukkuri A, Pienta KJ, Hockett I, Austin RH, Hammarlund EU, Amend SR, Brown JS. Modeling cancer's ecological and evolutionary dynamics. Med Oncol 2023; 40:109. [PMID: 36853375 PMCID: PMC9974726 DOI: 10.1007/s12032-023-01968-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Accepted: 02/05/2023] [Indexed: 03/01/2023]
Abstract
In this didactic paper, we present a theoretical modeling framework, called the G-function, that integrates both the ecology and evolution of cancer to understand oncogenesis. The G-function has been used in evolutionary ecology, but has not been widely applied to problems in cancer. Here, we build the G-function framework from fundamental Darwinian principles and discuss how cancer can be seen through the lens of ecology, evolution, and game theory. We begin with a simple model of cancer growth and add on components of cancer cell competition and drug resistance. To aid in exploration of eco-evolutionary modeling with this approach, we also present a user-friendly software tool. By the end of this paper, we hope that readers will be able to construct basic G function models and grasp the usefulness of the framework to understand the games cancer plays in a biologically mechanistic fashion.
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Affiliation(s)
- Anuraag Bukkuri
- Cancer Biology and Evolution Program and Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, USA.
- Tissue Development and Evolution Research Group, Department of Laboratory Medicine, Lund University, Lund, Sweden.
| | - Kenneth J Pienta
- The Brady Urological Institute, Johns Hopkins School of Medicine, Baltimore, USA
| | - Ian Hockett
- The Brady Urological Institute, Johns Hopkins School of Medicine, Baltimore, USA
| | | | - Emma U Hammarlund
- Tissue Development and Evolution Research Group, Department of Laboratory Medicine, Lund University, Lund, Sweden
| | - Sarah R Amend
- The Brady Urological Institute, Johns Hopkins School of Medicine, Baltimore, USA
| | - Joel S Brown
- Cancer Biology and Evolution Program and Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, USA
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33
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Gonçalves IG, García-Aznar JM. Hybrid computational models of multicellular tumour growth considering glucose metabolism. Comput Struct Biotechnol J 2023; 21:1262-1271. [PMID: 36814723 PMCID: PMC9939553 DOI: 10.1016/j.csbj.2023.01.044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2022] [Revised: 01/30/2023] [Accepted: 01/30/2023] [Indexed: 02/04/2023] Open
Abstract
Cancer cells metabolize glucose through metabolic pathways that differ from those used by healthy and differentiated cells. In particular, tumours have been shown to consume more glucose than their healthy counterparts and to use anaerobic metabolic pathways, even under aerobic conditions. Nevertheless, scientists have still not been able to explain why cancer cells evolved to present an altered metabolism and what evolutionary advantage this might provide them. Experimental and computational models have been increasingly used in recent years to understand some of these biological questions. Multicellular tumour spheroids are effective experimental models as they replicate the initial stages of avascular solid tumour growth. Furthermore, these experiments generate data which can be used to calibrate and validate computational studies that aim to simulate tumour growth. Hybrid models are of particular relevance in this field of research because they model cells as individual agents while also incorporating continuum representations of the substances present in the surrounding microenvironment that may participate in intracellular metabolic networks as concentration or density distributions. Henceforth, in this review, we explore the potential of computational modelling to reveal the role of metabolic reprogramming in tumour growth.
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Key Words
- ABM, agent-based model
- ATP, adenosine triphosphate
- CA, cellular automata
- CPM, cellular Potts model
- ECM, extracellular matrix
- FBA, Flux Balance Analysis
- FDG-PET, [18F]-fluorodeoxyglucose-positron emission tomography
- MCTS, multicellular tumour spheroids
- ODEs, ordinary differential equations
- PDEs, partial differential equations
- SBML, Systems Biology Markup Language
- Warburg effect
- agent-based models
- glucose metabolism
- hybrid modelling
- multicellular simulations
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Affiliation(s)
- Inês G. Gonçalves
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, Aragon Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza 50018, Aragon, Spain
| | - José Manuel García-Aznar
- Multiscale in Mechanical and Biological Engineering, Department of Mechanical Engineering, Aragon Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza 50018, Aragon, Spain
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34
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Castorina P, Martorana E, Forte S. Dynamical Synergy of Drug Combinations during Cancer Chemotherapy. J Pers Med 2022; 12:jpm12111873. [PMID: 36579581 PMCID: PMC9695902 DOI: 10.3390/jpm12111873] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2022] [Revised: 11/03/2022] [Accepted: 11/07/2022] [Indexed: 11/11/2022] Open
Abstract
Synergistic drug combinations often provide effective strategies to increase treatment efficacy and, during therapy, it is a time-dependent process. Data for colorectal and lung cancer in vivo were used for the phenomenological study of dynamical synergy during treatments. The proposed approach takes into consideration tumor regrowth by macroscopic laws. The time dependencies of synergistic drug combinations are analyzed by different parametric indicators. The cumulative effects of the single therapy and drug combinations are quantitatively well described and related to the cumulative doses. In conclusion, the analysis of dynamical synergy during chemotherapy has to take into account the effects of the drug doses and the tumor regrowth, which can provide a reliable description of the synergistic time dependence.
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Affiliation(s)
- Paolo Castorina
- INFN, Sezione di Catania, I-95123 Catania, Italy
- Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000 Prague, Czech Republic
- Correspondence:
| | | | - Stefano Forte
- Istituto Oncologico del Mediterraneo, 95029 Viagrande, Italy
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35
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Lee ND, Bozic I. Inferring parameters of cancer evolution in chronic lymphocytic leukemia. PLoS Comput Biol 2022; 18:e1010677. [PMID: 36331987 PMCID: PMC9668150 DOI: 10.1371/journal.pcbi.1010677] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2022] [Revised: 11/16/2022] [Accepted: 10/24/2022] [Indexed: 11/06/2022] Open
Abstract
As a cancer develops, its cells accrue new mutations, resulting in a heterogeneous, complex genomic profile. We make use of this heterogeneity to derive simple, analytic estimates of parameters driving carcinogenesis and reconstruct the timeline of selective events following initiation of an individual cancer, where two longitudinal samples are available for sequencing. Using stochastic computer simulations of cancer growth, we show that we can accurately estimate mutation rate, time before and after a driver event occurred, and growth rates of both initiated cancer cells and subsequently appearing subclones. We demonstrate that in order to obtain accurate estimates of mutation rate and timing of events, observed mutation counts should be corrected to account for clonal mutations that occurred after the founding of the tumor, as well as sequencing coverage. Chronic lymphocytic leukemia (CLL), which often does not require treatment for years after diagnosis, presents an optimal system to study the untreated, natural evolution of cancer cell populations. When we apply our methodology to reconstruct the individual evolutionary histories of CLL patients, we find that the parental leukemic clone typically appears within the first fifteen years of life.
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Affiliation(s)
- Nathan D. Lee
- Department of Applied Mathematics, University of Washington, Seattle, Washington, United States of America
| | - Ivana Bozic
- Department of Applied Mathematics, University of Washington, Seattle, Washington, United States of America
- Herbold Computational Biology Program, Fred Hutchinson Cancer Research Center, Seattle, Washington, United States of America
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36
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Rodallec A, Vaghi C, Ciccolini J, Fanciullino R, Benzekry S. Tumor growth monitoring in breast cancer xenografts: A good technique for a strong ethic. PLoS One 2022; 17:e0274886. [PMID: 36178898 PMCID: PMC9524649 DOI: 10.1371/journal.pone.0274886] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Accepted: 09/06/2022] [Indexed: 11/19/2022] Open
Abstract
Purpose Although recent regulations improved conditions of laboratory animals, their use remains essential in cancer research to determine treatment efficacy. In most cases, such experiments are performed on xenografted animals for which tumor volume is mostly estimated from caliper measurements. However, many formulas have been employed for this estimation and no standardization is available yet. Methods Using previous animal studies, we compared all formulas used by the scientific community in 2019. Data were collected from 93 mice orthotopically xenografted with human breast cancer cells. All formulas were evaluated and ranked based on correlation and lower mean relative error. They were then used in a Gompertz quantitative model of tumor growth. Results Seven formulas for tumor volume estimation were identified and a statistically significant difference was observed among them (ANOVA test, p < 2.10−16), with the ellipsoid formula (1/6 π × L × W × (L + W)/2) being the most accurate (mean relative error = 0.272 ± 0.201). This was confirmed by the mathematical modeling analysis where this formula resulted in the smallest estimated residual variability. Interestingly, such result was no longer valid for tumors over 1968 ± 425 mg, for which a cubic formula (L x W x H) should be preferred. Main findings When considering that tumor volume remains under 1500mm3, to limit animal stress, improve tumor growth monitoring and go toward mathematic models, the following formula 1/6 π × L × W x (L + W)/2 should be preferred.
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Affiliation(s)
- Anne Rodallec
- COMPO, CRCM, INRIA Sophia Antipolis, INSERM UMR1068, CNRS UMR7258, AMU U105, IPC, Marseille, France
- SMARTc, CRCM, INSERM UMR1068, CNRS UMR7258, AMU U105, IPC, Marseille, France
- * E-mail:
| | | | - Joseph Ciccolini
- COMPO, CRCM, INRIA Sophia Antipolis, INSERM UMR1068, CNRS UMR7258, AMU U105, IPC, Marseille, France
- SMARTc, CRCM, INSERM UMR1068, CNRS UMR7258, AMU U105, IPC, Marseille, France
| | - Raphaelle Fanciullino
- COMPO, CRCM, INRIA Sophia Antipolis, INSERM UMR1068, CNRS UMR7258, AMU U105, IPC, Marseille, France
- SMARTc, CRCM, INSERM UMR1068, CNRS UMR7258, AMU U105, IPC, Marseille, France
| | - Sebastien Benzekry
- COMPO, CRCM, INRIA Sophia Antipolis, INSERM UMR1068, CNRS UMR7258, AMU U105, IPC, Marseille, France
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37
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Can the Kuznetsov Model Replicate and Predict Cancer Growth in Humans? Bull Math Biol 2022; 84:130. [PMID: 36175705 PMCID: PMC9522842 DOI: 10.1007/s11538-022-01075-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2022] [Accepted: 08/29/2022] [Indexed: 11/17/2022]
Abstract
Several mathematical models to predict tumor growth over time have been developed in the last decades. A central aspect of such models is the interaction of tumor cells with immune effector cells. The Kuznetsov model (Kuznetsov et al. in Bull Math Biol 56(2):295–321, 1994) is the most prominent of these models and has been used as a basis for many other related models and theoretical studies. However, none of these models have been validated with large-scale real-world data of human patients treated with cancer immunotherapy. In addition, parameter estimation of these models remains a major bottleneck on the way to model-based and data-driven medical treatment. In this study, we quantitatively fit Kuznetsov’s model to a large dataset of 1472 patients, of which 210 patients have more than six data points, by estimating the model parameters of each patient individually. We also conduct a global practical identifiability analysis for the estimated parameters. We thus demonstrate that several combinations of parameter values could lead to accurate data fitting. This opens the potential for global parameter estimation of the model, in which the values of all or some parameters are fixed for all patients. Furthermore, by omitting the last two or three data points, we show that the model can be extrapolated and predict future tumor dynamics. This paves the way for a more clinically relevant application of mathematical tumor modeling, in which the treatment strategy could be adjusted in advance according to the model’s future predictions.
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38
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A Mathematical Study of the Role of tBregs in Breast Cancer. Bull Math Biol 2022; 84:112. [PMID: 36048369 DOI: 10.1007/s11538-022-01054-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Accepted: 07/12/2022] [Indexed: 12/24/2022]
Abstract
A model for the mathematical study of immune response to breast cancer is proposed and studied, both analytically and numerically. It is a simplification of a complex one, recently introduced by two of the present authors. It serves for a compact study of the dynamical role in cancer promotion of a relatively recently described subgroup of regulatory B cells, which are evoked by the tumour.
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39
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Isheden G, Humphreys K. A unifying framework for continuous tumour growth modelling of breast cancer screening data. Math Biosci 2022; 353:108897. [PMID: 36037859 DOI: 10.1016/j.mbs.2022.108897] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2022] [Revised: 08/22/2022] [Accepted: 08/22/2022] [Indexed: 11/19/2022]
Abstract
The aim of the current article is to present theory that can help unify continuous growth approaches for modelling breast cancer tumour growth based on human data. We present a framework that has three main features: a general likelihood function to account for patient specific screening regiments; stable disease assumptions describing tumour population dynamics; and mathematical models describing tumour growth, individual variation in tumour growth, a hazard for symptomatic detection, and screening test sensitivity. The framework is able to incorporate any random effects distributions for the tumour growth rate parameter, any hazard functions for symptomatic tumour detection, as well as any monotonously increasing function for the tumour growth model. Based on a sample of 1902 incident breast cancer cases with data on mammography screening, we show how the framework can be used to estimate tumour growth based on different growth functions.
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40
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Álvarez-Arenas A, Souleyreau W, Emanuelli A, Cooley LS, Bernhard JC, Bikfalvi A, Benzekry S. Practical identifiability analysis of a mechanistic model for the time to distant metastatic relapse and its application to renal cell carcinoma. PLoS Comput Biol 2022; 18:e1010444. [PMID: 36007057 PMCID: PMC9451098 DOI: 10.1371/journal.pcbi.1010444] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2021] [Revised: 09/07/2022] [Accepted: 07/27/2022] [Indexed: 12/02/2022] Open
Abstract
Distant metastasis-free survival (DMFS) curves are widely used in oncology. They are classically analyzed using the Kaplan-Meier estimator or agnostic statistical models from survival analysis. Here we report on a method to extract more information from DMFS curves using a mathematical model of primary tumor growth and metastatic dissemination. The model depends on two parameters, α and μ, respectively quantifying tumor growth and dissemination. We assumed these to be lognormally distributed in a patient population. We propose a method for identification of the parameters of these distributions based on least-squares minimization between the data and the simulated survival curve. We studied the practical identifiability of these parameters and found that including the percentage of patients with metastasis at diagnosis was critical to ensure robust estimation. We also studied the impact and identifiability of covariates and their coefficients in α and μ, either categorical or continuous, including various functional forms for the latter (threshold, linear or a combination of both). We found that both the functional form and the coefficients could be determined from DMFS curves. We then applied our model to a clinical dataset of metastatic relapse from kidney cancer with individual data of 105 patients. We show that the model was able to describe the data and illustrate our method to disentangle the impact of three covariates on DMFS: a categorical one (Führman grade) and two continuous ones (gene expressions of the macrophage mannose receptor 1 (MMR) and the G Protein-Coupled Receptor Class C Group 5 Member A (GPRC5a) gene). We found that all had an influence in metastasis dissemination (μ), but not on growth (α). Understanding biological mechanisms leading to metastasis development is a major challenge in order to prevent distant relapse of cancer. Classical methods to study associations of biomarkers with subsequent metastatic relapse rely on the analysis of metastasis free survival curves by means of statistical models such as proportional hazards Cox regression. These models act as black boxes and don’t provide detailed information about the specific mechanism involved. In our study, we propose to use a method based on mechanistic modeling of the metastatic development, that is, a mathematical model that simulates the biological process. The main challenge for these models is to implement the right level of complexity, because if too many parameters are included, these cannot be precisely identified from the data. We reduced the metastatic process to two main aspects: growth and dissemination. We then proposed a theoretical study of the identifiability of the two associated parameters from metastasis-free survival curves. Eventually, we applied our method to a clinical dataset in kidney cancer and illustrated how we could gain biological insights about the role of some diagnosis markers.
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Affiliation(s)
| | | | - Andrea Emanuelli
- University of Bordeaux, LAMC, Pessac, France
- Inserm U1029, Pessac, France
| | - Lindsay S. Cooley
- University of Bordeaux, LAMC, Pessac, France
- Inserm U1029, Pessac, France
| | | | - Andreas Bikfalvi
- University of Bordeaux, LAMC, Pessac, France
- Inserm U1029, Pessac, France
| | - Sebastien Benzekry
- COMPO, COMPutational pharmacology and clinical Oncology, Centre Inria Sophia Antipolis - Méditerranée, Centre de Recherches en Cancérologie de Marseille, Inserm U1068, CNRS UMR7258, Institut Paoli-Calmettes, Aix-Marseille University
- * E-mail:
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41
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Blee JA, Liu X, Harland AJ, Fatania K, Currie S, Kurian KM, Hauert S. Liquid biopsies for early diagnosis of brain tumours: in silico mathematical biomarker modelling. J R Soc Interface 2022; 19:20220180. [PMID: 35919979 PMCID: PMC9346349 DOI: 10.1098/rsif.2022.0180] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Accepted: 07/07/2022] [Indexed: 11/12/2022] Open
Abstract
Brain tumours are the biggest cancer killer in those under 40 and reduce life expectancy more than any other cancer. Blood-based liquid biopsies may aid early diagnosis, prediction and prognosis for brain tumours. It remains unclear whether known blood-based biomarkers, such as glial fibrillary acidic protein (GFAP), have the required sensitivity and selectivity. We have developed a novel in silico model which can be used to assess and compare blood-based liquid biopsies. We focused on GFAP, a putative biomarker for astrocytic tumours and glioblastoma multi-formes (GBMs). In silico modelling was paired with experimental measurement of cell GFAP concentrations and used to predict the tumour volumes and identify key parameters which limit detection. The average GBM volumes of 449 patients at Leeds Teaching Hospitals NHS Trust were also measured and used as a benchmark. Our model predicts that the currently proposed GFAP threshold of 0.12 ng ml-1 may not be suitable for early detection of GBMs, but that lower thresholds may be used. We found that the levels of GFAP in the blood are related to tumour characteristics, such as vasculature damage and rate of necrosis, which are biological markers of tumour aggressiveness. We also demonstrate how these models could be used to provide clinical insight.
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Affiliation(s)
- Johanna A. Blee
- Department of Engineering Mathematics, University of Bristol, Ada Lovelace Building, Bristol BS8 1TW, UK
| | - Xia Liu
- Brain Tumour Research Centre, Bristol Medical School, Bristol BS2 8DZ, UK
| | - Abigail J. Harland
- Brain Tumour Research Centre, Bristol Medical School, Bristol BS2 8DZ, UK
| | - Kavi Fatania
- Department of Radiology, Leeds General Infirmary, Great George Street, Leeds LS1 3EX, UK
| | - Stuart Currie
- Department of Radiology, Leeds General Infirmary, Great George Street, Leeds LS1 3EX, UK
| | | | - Sabine Hauert
- Department of Engineering Mathematics, University of Bristol, Ada Lovelace Building, Bristol BS8 1TW, UK
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42
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Pham H. Analyzing the relationship between the vitamin D deficiency and COVID-19 mortality rate and modeling the time-delay interactions between body's immune healthy cells, infected cells, and virus particles with the effect of vitamin D levels. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:8975-9004. [PMID: 35942745 DOI: 10.3934/mbe.2022417] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
This paper presents some recent views on the aspects of vitamin D levels in relation to the COVID-19 infections and analyzes the relationship between the prevalence rates of vitamin D deficiency and COVID-19 death rates per million of various countries in Europe and Asia using the data from the PubMed database. The paper also discusses a new mathematical model of time-delay interactions between the body's immune healthy cells, infected cells, and virus particles with the effect of vitamin D levels. The model can be used to monitor the timely progression of healthy immune cells with the effects of the levels of vitamin D and probiotics supplement. It also can help to predict when the infected cells and virus particles free state can ever be reached as time progresses. The consideration of the time delay in the modeling due to effects of the infected cells or virus particles and the growth of healthy cells is also an important factor that can significantly change the outcomes of the body's immune cells as well as the infections.
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Affiliation(s)
- Hoang Pham
- Department of Industrial and Systems Engineering, Rutgers University, Piscataway, New Jersey 08854, USA
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43
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Cuchta T, Wintz N. Periodic functions related to the Gompertz difference equation. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:8774-8785. [PMID: 35942735 DOI: 10.3934/mbe.2022407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
We investigate periodicity of functions related to the Gompertz difference equation. In particular, we derive difference equations that must be satisfied to guarantee periodicity of the solution.
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Affiliation(s)
- Tom Cuchta
- Department of Computer Science and Mathematics, Fairmont State University, Fairmont, WV, USA
| | - Nick Wintz
- Department of Mathematics, Computer Science, and Information Technology, Lindenwood University, St. Charles, MO, USA
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44
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Vitos N, Gerlee P. Model-based inference of metastatic seeding rates in de novo metastatic breast cancer reveals the impact of secondary seeding and molecular subtype. Sci Rep 2022; 12:9455. [PMID: 35676303 PMCID: PMC9177582 DOI: 10.1038/s41598-022-12500-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2021] [Accepted: 03/08/2022] [Indexed: 11/25/2022] Open
Abstract
We present a stochastic network model of metastasis spread for de novo metastatic breast cancer, composed of tumor to metastasis (primary seeding) and metastasis to metastasis spread (secondary seeding), parameterized using the SEER (Surveillance, Epidemiology, and End Results) database. The model provides a quantification of tumor cell dissemination rates between the tumor and metastasis sites. These rates were used to estimate the probability of developing a metastasis for untreated patients. The model was validated using tenfold cross-validation. We also investigated the effect of HER2 (Human Epidermal Growth Factor Receptor 2) status, estrogen receptor (ER) status and progesterone receptor (PR) status on the probability of metastatic spread. We found that dissemination rate through secondary seeding is up to 300 times higher than through primary seeding. Hormone receptor positivity promotes seeding to the bone and reduces seeding to the lungs and primary seeding to the liver, while HER2 expression increases dissemination to the bone, lungs and primary seeding to the liver. Secondary seeding from the lungs to the liver seems to be hormone receptor-independent, while that from the lungs to the brain appears HER2-independent.
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Affiliation(s)
- Noemi Vitos
- Bla Kustens Halsocentral, 57251, Oskarshamn, Sweden
| | - Philip Gerlee
- Mathematical Sciences, Chalmers University of Technology, 41296, Gothenburg, Sweden. .,Mathematical Sciences, University of Gothenburg, 41296, Gothenburg, Sweden.
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45
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Aranda-Michel E, Serna-Gallegos D, Arnaoutakis G, Kilic A, Brown JA, Dai Y, Dunn-Lewis C, Sultan I. The Effect of COVID-19 on Cardiac Surgical Volume and its Associated Costs. Semin Thorac Cardiovasc Surg 2022; 35:508-515. [PMID: 35381354 PMCID: PMC8976579 DOI: 10.1053/j.semtcvs.2022.01.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2021] [Accepted: 01/20/2022] [Indexed: 11/11/2022]
Abstract
The COVID-19 pandemic significantly affected health care and in particular surgical volume. However, no data surrounding lost hospital revenue due to decreased cardiac surgical volume have been reported. The National Inpatient Sample database was used with decreases in cardiac surgery at a single center to generate a national estimate of decreased cardiac operative volume. Hospital charges and provided charge to cost ratios were used to create estimates of lost hospital revenue, adjusted for 2020 dollars. The COVID period was defined as January to May of 2020. A Gompertz function was used to model cardiac volume growth to pre-COVID levels. Single center cardiac case demographics were internally compared during January to May for 2019 and 2020 to create an estimate of volume reduction due to COVID. The maximum decrease in cardiac surgical volume was 28.3%. Cumulative case volume and hospital revenue loss during the COVID months as well as the recovery period totaled over 35 thousand cases and 2.5 billion dollars. Institutionally, patients during COVID months were younger, more frequently undergoing a CABG procedure, and had a longer length of stay. The pandemic caused a significant decrease in cardiac surgical volume and a subsequent decrease in hospital revenue. This data can be used to address the accumulated surgical backlog and programmatic changes for future occurrences.
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Affiliation(s)
- Edgar Aranda-Michel
- Division of Cardiac Surgery, Department of Cardiothoracic Surgery, University of Pittsburgh, Pittsburgh, Pennsylvania
| | - Derek Serna-Gallegos
- Division of Cardiac Surgery, Department of Cardiothoracic Surgery, University of Pittsburgh, Pittsburgh, Pennsylvania; Heart and Vascular Institute, University of Pittsburgh Medical Center, Pittsburgh, Pennsylvania
| | - George Arnaoutakis
- Department of Cardiothoracic Surgery, University of Florida, Gainesville, Florida
| | - Arman Kilic
- Division of Cardiac Surgery, Department of Cardiothoracic Surgery, University of Pittsburgh, Pittsburgh, Pennsylvania; Heart and Vascular Institute, University of Pittsburgh Medical Center, Pittsburgh, Pennsylvania
| | - James A Brown
- Division of Cardiac Surgery, Department of Cardiothoracic Surgery, University of Pittsburgh, Pittsburgh, Pennsylvania
| | - Yancheng Dai
- Division of Cardiac Surgery, Department of Cardiothoracic Surgery, University of Pittsburgh, Pittsburgh, Pennsylvania
| | - Courtenay Dunn-Lewis
- Heart and Vascular Institute, University of Pittsburgh Medical Center, Pittsburgh, Pennsylvania
| | - Ibrahim Sultan
- Division of Cardiac Surgery, Department of Cardiothoracic Surgery, University of Pittsburgh, Pittsburgh, Pennsylvania; Heart and Vascular Institute, University of Pittsburgh Medical Center, Pittsburgh, Pennsylvania.
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46
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Sharma M, Bakshi AK, Mittapelly N, Gautam S, Marwaha D, Rai N, Singh N, Tiwari P, Aggarwal N, Kumar A, Mishra PR. Recent updates on innovative approaches to overcome drug resistance for better outcomes in cancer. J Control Release 2022; 346:43-70. [PMID: 35405165 DOI: 10.1016/j.jconrel.2022.04.007] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Revised: 04/04/2022] [Accepted: 04/05/2022] [Indexed: 02/07/2023]
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47
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Tumor Volume Regression during and after Radiochemotherapy: A Macroscopic Description. J Pers Med 2022; 12:jpm12040530. [PMID: 35455646 PMCID: PMC9025192 DOI: 10.3390/jpm12040530] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Revised: 03/07/2022] [Accepted: 03/24/2022] [Indexed: 12/04/2022] Open
Abstract
Tumor volume regression during and after chemo and radio therapy is a useful information for clinical decisions. Indeed, a quantitative, patient oriented, description of the response to treatment can guide towards the modification of the scheduled doses or the evaluation of the best time for surgery. We propose a macroscopic algorithm which permits to follow quantitatively the time evolution of the tumor volume during and after radiochemotherapy. The method, initially validated with different cell-lines implanted in mice, is then successfully applied to the available data for partially responding and complete recovery patients.
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48
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Li M, Zhong X, Du F, Wu X, Li M, Chen Y, Zhao Y, Shen J, Yang Z, Xiao Z. Current Understanding and Future Perspectives on Hyperprogressive Disease Highlight the Tumor Microenvironment. J Clin Pharmacol 2022; 62:1059-1078. [PMID: 35303368 DOI: 10.1002/jcph.2048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2022] [Accepted: 03/14/2022] [Indexed: 11/09/2022]
Abstract
Cancer immunotherapy with immune checkpoint inhibitors has revolutionized traditional cancer therapy. Although many patients have achieved long-term survival benefits from immune checkpoint inhibitors treatment, there are still some patients who develop rapid tumor progression after immunotherapy, known as hyperprogressive disease. Here we summarize current knowledge on hyperprogressive disease after immune checkpoint inhibitors treatment to promote more thorough understanding of the disease. This review focuses on multiple aspects of hyperprogressive disease, especially the tumor microenvironment, with the hope that more reliable biomarkers and therapeutics could be established for hyperprogressive disease in the future. This article is protected by copyright. All rights reserved.
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Affiliation(s)
- Meiqi Li
- Laboratory of Molecular Pharmacology, Department of Pharmacology, School of Pharmacy, Southwest Medical University, Luzhou, Sichuan, 646000, P.R. China.,Cell Therapy & Cell Drugs of Luzhou Key Laboratory, Luzhou, Sichuan, 646000, P.R. China.,South Sichuan Institute of Translational Medicine, Luzhou, Sichuan, 646000, P.R. China
| | - Xianmei Zhong
- Laboratory of Molecular Pharmacology, Department of Pharmacology, School of Pharmacy, Southwest Medical University, Luzhou, Sichuan, 646000, P.R. China.,Cell Therapy & Cell Drugs of Luzhou Key Laboratory, Luzhou, Sichuan, 646000, P.R. China.,South Sichuan Institute of Translational Medicine, Luzhou, Sichuan, 646000, P.R. China
| | - Fukuan Du
- Laboratory of Molecular Pharmacology, Department of Pharmacology, School of Pharmacy, Southwest Medical University, Luzhou, Sichuan, 646000, P.R. China.,Cell Therapy & Cell Drugs of Luzhou Key Laboratory, Luzhou, Sichuan, 646000, P.R. China.,South Sichuan Institute of Translational Medicine, Luzhou, Sichuan, 646000, P.R. China
| | - Xu Wu
- Laboratory of Molecular Pharmacology, Department of Pharmacology, School of Pharmacy, Southwest Medical University, Luzhou, Sichuan, 646000, P.R. China.,Cell Therapy & Cell Drugs of Luzhou Key Laboratory, Luzhou, Sichuan, 646000, P.R. China.,South Sichuan Institute of Translational Medicine, Luzhou, Sichuan, 646000, P.R. China
| | - Mingxing Li
- Laboratory of Molecular Pharmacology, Department of Pharmacology, School of Pharmacy, Southwest Medical University, Luzhou, Sichuan, 646000, P.R. China.,Cell Therapy & Cell Drugs of Luzhou Key Laboratory, Luzhou, Sichuan, 646000, P.R. China.,South Sichuan Institute of Translational Medicine, Luzhou, Sichuan, 646000, P.R. China
| | - Yu Chen
- Laboratory of Molecular Pharmacology, Department of Pharmacology, School of Pharmacy, Southwest Medical University, Luzhou, Sichuan, 646000, P.R. China.,Cell Therapy & Cell Drugs of Luzhou Key Laboratory, Luzhou, Sichuan, 646000, P.R. China.,South Sichuan Institute of Translational Medicine, Luzhou, Sichuan, 646000, P.R. China
| | - Yueshui Zhao
- Laboratory of Molecular Pharmacology, Department of Pharmacology, School of Pharmacy, Southwest Medical University, Luzhou, Sichuan, 646000, P.R. China.,Cell Therapy & Cell Drugs of Luzhou Key Laboratory, Luzhou, Sichuan, 646000, P.R. China.,South Sichuan Institute of Translational Medicine, Luzhou, Sichuan, 646000, P.R. China
| | - Jing Shen
- Laboratory of Molecular Pharmacology, Department of Pharmacology, School of Pharmacy, Southwest Medical University, Luzhou, Sichuan, 646000, P.R. China.,Cell Therapy & Cell Drugs of Luzhou Key Laboratory, Luzhou, Sichuan, 646000, P.R. China.,South Sichuan Institute of Translational Medicine, Luzhou, Sichuan, 646000, P.R. China
| | - Zhongming Yang
- Department of Oncology and Hematology, The Affiliated Traditional Chinese Medicine Hospital of Southwest Medical University, Luzhou, Sichuan, 646000, China
| | - Zhangang Xiao
- Laboratory of Molecular Pharmacology, Department of Pharmacology, School of Pharmacy, Southwest Medical University, Luzhou, Sichuan, 646000, P.R. China.,Cell Therapy & Cell Drugs of Luzhou Key Laboratory, Luzhou, Sichuan, 646000, P.R. China.,South Sichuan Institute of Translational Medicine, Luzhou, Sichuan, 646000, P.R. China
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Mohammad Mirzaei N, Changizi N, Asadpoure A, Su S, Sofia D, Tatarova Z, Zervantonakis IK, Chang YH, Shahriyari L. Investigating key cell types and molecules dynamics in PyMT mice model of breast cancer through a mathematical model. PLoS Comput Biol 2022; 18:e1009953. [PMID: 35294447 PMCID: PMC8959189 DOI: 10.1371/journal.pcbi.1009953] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Revised: 03/28/2022] [Accepted: 02/22/2022] [Indexed: 02/07/2023] Open
Abstract
The most common kind of cancer among women is breast cancer. Understanding the tumor microenvironment and the interactions between individual cells and cytokines assists us in arriving at more effective treatments. Here, we develop a data-driven mathematical model to investigate the dynamics of key cell types and cytokines involved in breast cancer development. We use time-course gene expression profiles of a mouse model to estimate the relative abundance of cells and cytokines. We then employ a least-squares optimization method to evaluate the model's parameters based on the mice data. The resulting dynamics of the cells and cytokines obtained from the optimal set of parameters exhibit a decent agreement between the data and predictions. We perform a sensitivity analysis to identify the crucial parameters of the model and then perform a local bifurcation on them. The results reveal a strong connection between adipocytes, IL6, and the cancer population, suggesting them as potential targets for therapies.
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Affiliation(s)
- Navid Mohammad Mirzaei
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts, United States of America
| | - Navid Changizi
- Department of Civil and Environmental Engineering, University of Massachusetts, Dartmouth, Massachusetts, United States of America
| | - Alireza Asadpoure
- Department of Civil and Environmental Engineering, University of Massachusetts, Dartmouth, Massachusetts, United States of America
| | - Sumeyye Su
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts, United States of America
| | - Dilruba Sofia
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts, United States of America
| | - Zuzana Tatarova
- Department of Biomedical Engineering and OHSU Center for Spatial Systems Biomedicine (OCSSB), Oregon Health and Science University, Portland, Oregon, United States of America
| | - Ioannis K. Zervantonakis
- Department of Bioengineering, UPMC Hillman Cancer Center, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America
| | - Young Hwan Chang
- Department of Biomedical Engineering and OHSU Center for Spatial Systems Biomedicine (OCSSB), Oregon Health and Science University, Portland, Oregon, United States of America
| | - Leili Shahriyari
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts, United States of America
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Terranova N, French J, Dai H, Wiens M, Khandelwal A, Ruiz‐Garcia A, Manitz J, Heydebreck A, Ruisi M, Chin K, Girard P, Venkatakrishnan K. Pharmacometric modeling and machine learning analyses of prognostic and predictive factors in the JAVELIN Gastric 100 phase III trial of avelumab. CPT Pharmacometrics Syst Pharmacol 2022; 11:333-347. [PMID: 34971492 PMCID: PMC8923733 DOI: 10.1002/psp4.12754] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Revised: 11/24/2021] [Accepted: 11/25/2021] [Indexed: 12/23/2022] Open
Abstract
Avelumab (anti–PD‐L1) is an approved anticancer treatment for several indications. The JAVELIN Gastric 100 phase III trial did not meet its primary objective of demonstrating superior overall survival (OS) with avelumab maintenance versus continued chemotherapy in patients with advanced gastric cancer/gastroesophageal junction cancer; however, the OS rate was numerically higher with avelumab at timepoints after 12 months. Machine learning (random forests, SIDEScreen, and variable‐importance assessments) was used to build models to identify prognostic/predictive factors associated with long‐term OS and tumor growth dynamics (TGDs). Baseline, re‐baseline, and longitudinal variables were evaluated as covariates in a parametric time‐to‐event model for OS and Gompertzian population model for TGD. The final OS model incorporated a treatment effect on the log‐logistic shape parameter but did not identify a treatment effect on OS or TGD. Variables identified as prognostic for longer OS included older age; higher gamma‐glutamyl transferase (GGT) or albumin; absence of peritoneal carcinomatosis; lower neutrophil‐lymphocyte ratio, lactate dehydrogenase, or C‐reactive protein (CRP); response to induction chemotherapy; and Eastern Cooperative Oncology Group performance status of 0. Among baseline and time‐varying covariates, the largest effects were found for GGT and CRP, respectively. Liver metastasis at re‐baseline predicted higher tumor growth. Tumor size after induction chemotherapy was associated with number of metastatic sites and stable disease (vs. response). Asian region did not impact OS or TGD. Overall, an innovative workflow supporting pharmacometric modeling of OS and TGD was established. Consistent with the primary trial analysis, no treatment effect was identified. However, potential prognostic factors were identified.
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Affiliation(s)
- Nadia Terranova
- Merck Institute of Pharmacometrics (an affiliate of Merck KGaA, Darmstadt, Germany) Lausanne Switzerland
| | | | | | | | | | | | | | | | | | | | - Pascal Girard
- Merck Institute of Pharmacometrics (an affiliate of Merck KGaA, Darmstadt, Germany) Lausanne Switzerland
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