The model muddle: in search of tumor growth laws

Learning Chemotherapy Drug Action via Universal Physics-Informed Neural Networks

OBJECTIVE

Quantitative systems pharmacology (QSP) is widely used to assess drug effects and toxicity before the drug goes to clinical trial. However, significant manual distillation of the literature is needed in order to construct a QSP model. Parameters may need to be fit, and simplifying assumptions of the model need to be made. In this work, we apply Universal Physics-Informed Neural Networks (UPINNs) to learn unknown components of various differential equations that model chemotherapy pharmacodynamics.

METHODS

Using UPINNs, we learn three commonly employed chemotherapeutic drug actions (log-kill, Norton-Simon, and E max ) from synthetic data. Then, we use the UPINN method to fit the parameters for several synthetic datasets simultaneously. Finally, we learn the net proliferation rate in a model of doxorubicin (a chemotherapeutic) pharmacodynamics.

RESULTS

We show that the UPINN can successfully learn the hidden terms and unknown parameters in a variety of differential equations (with differing time and variable scales) that model the effect of chemotherapeutics on cancer cells.

CONCLUSIONS

As the examples we study are only toy examples, we highlight the usefulness of UPINNs in learning unknown terms in pharmacodynamic and pharmacokinetic models. UPINNs can be used to find these terms and analyze them further to understand new chemotherapeutics and biological mechanisms that interact with them.

Identifiability and model selection frameworks for models of high-grade glioma response to chemoradiation

We have developed a family of biology-based mathematical models of high-grade glioma (HGG), capturing the key features of tumour growth and response to chemoradiation. We now seek to quantify the accuracy of parameter estimation and determine, when given a virtual patient cohort, which model was used to generate the tumours. In this way, we systematically test both the parameter and model identifiability. Virtual patients are generated from unique growth parameters whose growth dynamics are determined by the model family. We then assessed the ability to recover model parameters and select the model used to generate the tumour. We then evaluated the accuracy of predictions using the selected model at four weeks post-chemoradiation. We observed median parameter errors from 0.04% to 72.96%. Our model selection framework selected the model that was used to generate the data in 82% of the cases. Finally, we predicted the growth of the virtual tumours using the selected model resulting in low error at the voxel-level (concordance correlation coefficient (CCC) ranged from 0.66 to 0.99) and global level (percentage error in total tumour cellularity ranged from -12.35% to 0.07%). These results demonstrate the reliability of our framework to identify the most appropriate model under noisy conditions expected in the clinical setting.This article is part of the theme issue 'Uncertainty quantification for healthcare and biological systems (Part 2)'.

Exploring trade-offs in drug administration for cancer treatment: A multi-criteria optimisation approach

This study addresses the combination of immunotherapy and chemotherapy in cancer treatment, recognising its promising effectiveness but highlighting the challenges of complex interactions between these therapeutic modalities. The central objective is to determine guidelines for the optimal administration of drugs, using an optimal control model that considers interactions in tumour dynamics, including cancer cells, the immune system, and therapeutic agents. The optimal control model is transformed into a multi-objective optimisation problem with treatment constraints. This is achieved by introducing adjustable trade-offs, allowing personalised adaptations in drug administration to achieve an optimal balance between established objectives. Various optimisation problems are addressed, considering two and three simultaneous objectives, such as optimising the number of cancer cells and the density of effector cells at the final treatment time. The diverse combinations presented reflect the model's flexibility in the face of multi-objective optimisation, providing a range of approaches to meet specific medical needs. The analysis of Pareto optimal fronts in in silico investigation offers an additional resource for decision-makers, enabling a more effective determination of the optimal administration of cytotoxic and immunotherapeutic agents. By leveraging an optimal control model, we have demonstrated the effectiveness of considering interactions in tumour dynamics, including the integration of immunotherapy and chemotherapy. Our findings underscore the importance of tailored treatment plans to achieve optimal outcomes, showcasing the versatility of our approach in addressing individual patient needs. The insights gained from our analysis offer valuable guidance for future research and clinical practice, paving the way for more effective and personalised cancer therapies.

Predictive Factors for Oligometastatic Renal Cell Carcinoma Treated with Stereotactic Radiation: A Retrospective Study

BACKGROUND AND OBJECTIVE

Stereotactic ablative radiotherapy (SAbR) has shown promise in controlling oligometastatic renal cell carcinoma (omRCC). Careful patient selection is critical, and yet the selection criteria remain unknown for patients who will not be harmed by delayed systemic therapy using SAbR. Here, we analyzed long-term follow-up of omRCC patients treated with SAbR to derive the predictors of survival benefit.

METHODS

We retrospectively reviewed patients with up to five omRCC sites treated with sequential SAbR from November 2007 to July 2022. Overall survival (OS), progression-free survival (PFS), local control (LC), and toxicity were analyzed. The predictors of PFS were analyzed using a univariate analysis and a Cox proportional hazard (CPH) model-based machine learning approach.

KEY FINDINGS AND LIMITATIONS

We analyzed 153 patients who underwent SAbR to 337 metastases with a median follow-up of 27 mo. The median OS and PFS were 61.3 and 32 mo, respectively. The rate of grade ≥3 toxicity was 1.3%, and the 3-yr rate of LC was 98%. Patients with bone and brain metastases had lower PFS on the univariate analysis. When compared with historical controls, the delayed-onset PFS with first-line systemic therapy in this cohort was not compromised. The CPH model found bone, brain, and number of metastases at diagnosis to be the predictors of PFS, with a C-index of 0.66 and 1-yr area under the curve of 0.68.

CONCLUSIONS AND CLINICAL IMPLICATIONS

For selected patients, SAbR is effective in controlling omRCC for >2 yr and can delay systemic therapy without compromising patient outcome. Bone and brain metastases, as well as an increasing number of metastases are poor predictive factors for omRCC patients treated with sequential SAbR who may benefit from upfront systemic therapy. Prospective studies are required to verify these findings.

Impact of endocrine therapy regimens for early-stage ER+/HER2-breast cancer on contralateral breast cancer risk

Endocrine therapy for breast cancer may reduce the risk of contralateral breast cancer (CBC). However, there are no published estimates quantifying the lifetime outcomes by age at primary diagnosis, regimen, or duration. Here, we adapted an established Cancer Intervention and Surveillance Network (CISNET) model to simulate life histories of multiple US female birth-cohorts diagnosed with stage 0-III ER+/HER2- breast cancer receiving different durations (none, 2.5, 5, 10 years) of two endocrine therapy regimens (aromatase inhibitors or tamoxifen; including ovarian-function suppression for premenopausal women). As expected, greater duration of endocrine therapy led to more avoided CBC cases, as did aromatase inhibitors over tamoxifen, but the numbers varied greatly by the age of diagnosis. The maximum number of CBC were avoided using 10-year aromatase inhibitor regimens (6.0 vs. 11.2 for no adjuvant therapy, per 100 women with ER+/HER2- breast cancer). For the 5-year aromatase inhibitors therapy, women <45 years had the largest reduction in CBC cases (5.0/100), which dropped to 2.7/100 for women at 75+ years. Quantification of the lifetime risk of CBC for specific endocrine therapy types and duration is helpful for weighing therapeutic options. The risk of breast cancer death has a larger weight, but inclusion of the risk of CBC increases the separation between different therapy options.

Proper likelihood functions for parameter estimation in S-shaped models of unperturbed tumor growth

The analysis of unperturbed tumor growth kinetics, particularly the estimation of parameters for S-shaped equations used to describe growth, requires an appropriate likelihood function that accounts for the increasing error in solid tumor measurements as tumor size grows over time. This study aims to propose suitable likelihood functions for parameter estimation in S-shaped models of unperturbed tumor growth. Five different likelihood functions are evaluated and compared using three Bayesian criteria (the Bayesian Information Criterion, Deviance Information Criterion, and Bayes Factor) along with hypothesis tests on residuals. These functions are applied to fit data from unperturbed Ehrlich, fibrosarcoma Sa-37, and F3II tumors using the Gompertz equation, though they are generalizable to other S-shaped growth models for solid tumors or analogous systems (e.g., microorganisms, viruses). Results indicate that error models with tumor volume-dependent dispersion outperform standard constant-variance models in capturing the variability of tumor measurements, particularly the Thres model, which provides interpretable parameters for tumor growth. Additionally, constant-variance models, such as those assuming a normal error distribution, remain valuable as complementary benchmarks in analysis. It is concluded that models incorporating volume-dependent dispersion are preferred for accurate and clinically meaningful tumor growth modeling, whereas constant-dispersion models serve as useful complements for consistency and historical comparability.

Negligible Long-Term Impact of Nonlinear Growth Dynamics on Heterogeneity in Models of Cancer Cell Populations

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.

Choroidal nevi and melanoma doubling times and implications for delays in treatment: A systematic review and meta-analysis

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.

Spatiotemporal spread of oncolytic virus in a heterogeneous cell population

Oncolytic (cancer-killing) virus treatment is a promising new therapy for cancer, with many viruses currently being tested for their ability to eradicate tumors. One of the major stumbling blocks to the development of this treatment modality has been preventing spread of the virus to non-cancerous cells. Our recent ability to manipulate RNA and DNA now allows for the possibility of creating designer viruses specifically targeted to cancer cells, thereby significantly reducing unwanted side effects in patients. In this study, we use a partial differential equation model to determine the characteristics of a virus needed to contain spread of an oncolytic virus within a spherical tumor and prevent it from spreading to non-cancerous cells outside the tumor. We find that oncolytic viruses that have different infection rates or different cell death rates in cancer and non-cancerous cells can be made to stay within the tumor. We find that there is a minimum difference in infection rates or cell death rates that will contain the virus and that this threshold value depends on the growth rate of the cancer. Identification of these types of thresholds can help researchers develop safer strains of oncolytic viruses allowing further development of this promising treatment.

CT- and MRI-based Factors Associated with Rapid Growth in Early-Stage Hepatocellular Carcinoma

Background Prediction of the tumor growth rates is clinically important in patients with hepatocellular carcinoma (HCC), but previous studies have presented conflicting results and generally lacked radiologic evaluations. Purpose To evaluate the percentage of rapidly growing early-stage HCCs in each Liver Imaging Reporting and Data System (LI-RADS) category and to identify prognostic factors associated with rapid growth. Materials and Methods Retrospective study of patients with risk factors for HCC and those with surgically proven early-stage HCC who underwent two or more preoperative multiphasic CT or MRI examinations between January 2016 and December 2020. LI-RADS categories were assigned according to the baseline CT or MRI results. The tumor volume doubling time (TVDT) was calculated from the tumor volumes measured at the two examinations. The growth rate was classified as rapid (TVDT < 3 months), intermediate (TVDT = 3-9 months), or indolent (TVDT > 9 months). The percentage of rapidly growing HCCs was compared among the LI-RADS categories, and multivariable logistic regression was used to identify factors associated with rapidly growing HCC. Results In 322 patients (mean age, 61 years ± 9 [SD]; 249 men) with 345 HCCs (30 LR-3, 64 LR-4, 221 LR-5, and 30 LR-M category), the median TVDT of HCC was 131 days (IQR, 87-233) and 27.0% of HCCs showed rapid growth. The growth rates differed among the LI-RADS categories, with a higher percentage of rapidly growing HCCs observed for LR-M HCCs than for LR-3 (70.0% vs 3.3%, P < .001), LR-4 (70.0% vs 12.5%, P < .001), or LR-5 (70.0% vs 28.5%, P < .001) HCCs. An α-fetoprotein level greater than 400 ng/mL (adjusted odds ratio [OR], 2.54; 95% CI: 1.16, 5.54; P = .02), baseline tumor diameter (adjusted OR, 0.65; 95% CI: 0.48, 0.87; P = .004), and LR-M category (adjusted OR, 9.26; 95% CI: 3.70, 23.16; P < .001) were independently associated with higher odds of rapid growth. Conclusion Among early-stage HCCs, LR-M category was an independent factor for rapid growth, observed in 70% of HCCs. © RSNA, 2024 Supplemental material is available for this article.

Harnessing Flex Point Symmetry to Estimate Logistic Tumor Population Growth

The observed time evolution of a population is well approximated by a logistic growth function in many research fields, including oncology, ecology, chemistry, demography, economy, linguistics, and artificial neural networks. Initial growth is exponential, then decelerates as the population approaches its limit size, i.e., the carrying capacity. In mathematical oncology, the tumor carrying capacity has been postulated to be dynamically evolving as the tumor overcomes several evolutionary bottlenecks and, thus, to be patient specific. As the relative tumor-over-carrying capacity ratio may be predictive and prognostic for tumor growth and treatment response dynamics, it is paramount to estimate it from limited clinical data. We show that exploiting the logistic function's rotation symmetry can help estimate the population's growth rate and carry capacity from fewer data points than conventional regression approaches. We test this novel approach against published pan-cancer animal and human breast cancer data, achieving a 30% to 40% reduction in the time at which subsequent data collection is necessary to estimate the logistic growth rate and carrying capacity correctly. These results could improve tumor dynamics forecasting and augment the clinical decision-making process.

A mathematical framework for the statistical interpretation of biological growth models

Biological entities are inherently dynamic. As such, various ecological disciplines use mathematical models to describe temporal evolution. Typically, growth curves are modelled as sigmoids, with the evolution modelled by ordinary differential equations. Among the various sigmoid models, the logistic, Gompertz and Richards equations are well-established and widely used for the purpose of fitting growth data in the fields of biology and ecology. The present paper puts forth a mathematical framework for the statistical analysis of population growth models. The analysis is based on a mathematical model of the population-environment relationship, the theoretical foundations of which are discussed in detail. By applying this theory, stochastic evolutionary equations are obtained, for which the logistic, Gompertz, Richards and Birch equations represent a limiting case. To substantiate the models of population growth dynamics, the results of numerical simulations are presented. It is demonstrated that a variety of population growth models can be addressed in a comparable manner. It is suggested that the discussed mathematical framework for statistical interpretation of the joint population-environment evolution represents a promising avenue for further research.

Quantitative evaluation of DNA damage repair dynamics to elucidate predictors of autism vs. cancer in individuals with germline PTEN variants

Persons with germline variants in the tumor suppressor gene phosphatase and tensin homolog, PTEN, are molecularly diagnosed with PTEN hamartoma tumor syndrome (PHTS). PHTS confers high risks of specific malignancies, and up to 23% of the patients are diagnosed with autism spectrum disorder (ASD) and/or developmental delay (DD). The accurate prediction of these two seemingly disparate phenotypes (cancer vs. ASD/DD) for PHTS at the individual level remains elusive despite the available statistical prevalence of specific phenotypes of the syndrome at the population level. The pleiotropy of the syndrome may, in part, be due to the alterations of the key multi-functions of PTEN. Maintenance of genome integrity is one of the key biological functions of PTEN, but no integrative studies have been conducted to quantify the DNA damage response (DDR) in individuals with PHTS and to relate to phenotypes and genotypes. In this study, we used 43 PHTS patient-derived lymphoblastoid cell lines (LCLs) to investigate the associations between DDR and PTEN genotypes and/or clinical phenotypes ASD/DD vs. cancer. The dynamics of DDR of γ-irradiated LCLs were analyzed using the exponential decay mathematical model to fit temporal changes in γH2AX levels which report the degree of DNA damage. We found that PTEN nonsense variants are associated with less efficient DNA damage repair ability resulting in higher DNA damage levels at 24 hours after irradiation compared to PTEN missense variants. Regarding PHTS phenotypes, LCLs from PHTS individuals with ASD/DD showed faster DNA damage repairing rate than those from patients without ASD/DD or cancer. We also applied the reaction-diffusion partial differential equation (PDE) mathematical model, a cell growth model with a DNA damage term, to accurately describe the DDR process in the LCLs. For each LCL, we can derive parameters of the PDE. Then we averaged the numerical results by PHTS phenotypes. By performing simple subtraction of two subgroup average results, we found that PHTS-ASD/DD is associated with higher live cell density at lower DNA damage level but lower cell density level at higher DNA damage level compared to LCLs from individuals with PHTS-cancer and PHTS-neither.

Spatial interactions modulate tumor growth and immune infiltration

Direct observation of tumor-immune interactions is unlikely in tumors with currently available technology, but computational simulations based on clinical data can provide insight to test hypotheses. It is hypothesized that patterns of collagen evolve as a mechanism of immune escape, but the exact nature of immune-collagen interactions is poorly understood. Spatial data quantifying collagen fiber alignment in squamous cell carcinomas indicates that late-stage disease is associated with highly aligned fibers. Our computational modeling framework discriminates between two hypotheses: immune cell migration that moves (1) parallel or (2) perpendicular to collagen fiber orientation. The modeling recapitulates immune-extracellular matrix interactions where collagen patterns provide immune protection, leading to an emergent inverse relationship between disease stage and immune coverage. Here, computational modeling provides important mechanistic insights by defining a kernel cell-cell interaction function that considers a spectrum of local (cell-scale) to global (tumor-scale) spatial interactions. Short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects, while asymmetric tumor-immune interaction kernels lead to poor immune response. Thus, the length scale of tumor-immune interaction kernels drives tumor growth and infiltration.

Error-induced extinction in a multi-type critical birth-death process

Extreme mutation rates in microbes and cancer cells can result in error-induced extinction (EEX), where every descendant cell eventually acquires a lethal mutation. In this work, we investigate critical birth-death processes with n distinct types as a birth-death model of EEX in a growing population. Each type-i cell divides independently ( i ) → ( i ) + ( i ) or mutates ( i ) → ( i + 1 ) at the same rate. The total number of cells grows exponentially as a Yule process until a cell of type-n appears, which cell type can only divide or die at rate one. This makes the whole process critical and hence after the exponentially growing phase eventually all cells die with probability one. We present large-time asymptotic results for the general n-type critical birth-death process. We find that the mass function of the number of cells of type-k has algebraic and stationary tail( size ) - 1 - χ k , withχ k = 2 1 - k , for k = 2 , ⋯ , n , in sharp contrast to the exponential tail of the first type. The same exponents describe the tail of the asymptotic survival probability( time ) - ξ k . We present applications of the results for studying extinction due to intolerable mutation rates in biological populations.

Practical parameter identifiability and handling of censored data with Bayesian inference in mathematical tumour models

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.

Modeling free tumor growth: Discrete, continuum, and hybrid approaches to interpreting cancer development

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.

Tumor Doubling Time and Screening Interval

The goal of screening is to detect breast cancers when still curable to decrease breast cancer-specific mortality. Breast cancer screening in the United States is routinely performed with digital mammography and digital breast tomosynthesis. This article reviews breast cancer doubling time by tumor subtype and examines the impact of doubling time on breast cancer screening intervals. By the article's end, the reader will be better equipped to have informed discussions with patients and medical professionals regarding the benefits and disadvantages of the currently recommended screening mammography intervals.

Making Predictions Using Poorly Identified Mathematical Models

Many commonly used mathematical models in the field of mathematical biology involve challenges of parameter non-identifiability. Practical non-identifiability, where the quality and quantity of data does not provide sufficiently precise parameter estimates is often encountered, even with relatively simple models. In particular, the situation where some parameters are identifiable and others are not is often encountered. In this work we apply a recent likelihood-based workflow, called Profile-Wise Analysis (PWA), to non-identifiable models for the first time. The PWA workflow addresses identifiability, parameter estimation, and prediction in a unified framework that is simple to implement and interpret. Previous implementations of the workflow have dealt with idealised identifiable problems only. In this study we illustrate how the PWA workflow can be applied to both structurally non-identifiable and practically non-identifiable models in the context of simple population growth models. Dealing with simple mathematical models allows us to present the PWA workflow in a didactic, self-contained document that can be studied together with relatively straightforward Julia code provided on GitHub . Working with simple mathematical models allows the PWA workflow prediction intervals to be compared with gold standard full likelihood prediction intervals. Together, our examples illustrate how the PWA workflow provides us with a systematic way of dealing with non-identifiability, especially compared to other approaches, such as seeking ad hoc parameter combinations, or simply setting parameter values to some arbitrary default value. Importantly, we show that the PWA workflow provides insight into the commonly-encountered situation where some parameters are identifiable and others are not, allowing us to explore how uncertainty in some parameters, and combinations of parameters, regardless of their identifiability status, influences model predictions in a way that is insightful and interpretable.

A novel multiscale framework for delineating cancer evolution from subclonal compositions

OBJECTIVE

Owing to the heterogeneity in the evolution of cancer, distinguishing between diverse growth patterns and predicting long-term outcomes based on short-term measurements poses a great challenge.

METHODS

A novel multiscale framework is proposed to unravel the connections between the population dynamics of cancer growth (i.e., aggressive, bounded, and indolent) and the cellular-subclonal dynamics of cancer evolution. This framework employs the non-negative lasso (NN-LASSO) algorithm to forge a link between an ordinary differential equation (ODE)-based population model and a cellular evolution model.

RESULTS

The findings of our current work not only affirm the impact of subclonal composition on growth dynamics but also identify two significant subclones within heterogeneous growth patterns. Moreover, the subclonal compositions at the initial time are able to accurately discriminate diverse growth patterns through a machine learning algorithm.

CONCLUSION

The proposed multiscale framework successfully delineates the intricate landscape of cancer evolution, bridging the gap between long-term growth dynamics and short-term measurements, both in simulated and real-world data. This methodology provides a novel avenue for thorough exploration into the realm of cancer evolution.

Spatial interactions modulate tumor growth and immune infiltration

Direct observation of immune cell trafficking patterns and tumor-immune interactions is unlikely in human tumors with currently available technology, but computational simulations based on clinical data can provide insight to test hypotheses. It is hypothesized that patterns of collagen formation evolve as a mechanism of immune escape, but the exact nature of the interaction between immune cells and collagen is poorly understood. Spatial data quantifying the degree of collagen fiber alignment in squamous cell carcinomas indicates that late stage disease is associated with highly aligned fibers. Here, we introduce a computational modeling framework (called Lenia) to discriminate between two hypotheses: immune cell migration that moves 1) parallel or 2) perpendicular to collagen fiber orientation. The modeling recapitulates immune-ECM interactions where collagen patterns provide immune protection, leading to an emergent inverse relationship between disease stage and immune coverage. We also illustrate the capabilities of Lenia to model the evolution of tumor progression and immune predation. Lenia provides a flexible framework for considering a spectrum of local (cell-scale) to global (tumor-scale) dynamics by defining a kernel cell-cell interaction function that governs tumor growth dynamics under immune predation with immune cell migration. Mathematical modeling provides important mechanistic insights into cell interactions. Short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects, while asymmetric tumor-immune interaction kernels lead to poor immune response. Thus, the length scale of tumor-immune interactions drives tumor growth and infiltration.

Modelling count data with partial differential equation models in biology

Partial differential equation (PDE) models are often used to study biological phenomena involving movement-birth-death processes, including ecological population dynamics and the invasion of populations of biological cells. Count data, by definition, is non-negative, and count data relating to biological populations is often bounded above by some carrying capacity that arises through biological competition for space or nutrients. Parameter estimation, parameter identifiability, and making model predictions usually involves working with a measurement error model that explicitly relating experimental measurements with the solution of a mathematical model. In many biological applications, a typical approach is to assume the data are normally distributed about the solution of the mathematical model. Despite the widespread use of the standard additive Gaussian measurement error model, the assumptions inherent in this approach are rarely explicitly considered or compared with other options. Here, we interpret scratch assay data, involving migration, proliferation and delays in a population of cancer cells using a reaction-diffusion PDE model. We consider relating experimental measurements to the PDE solution using a standard additive Gaussian measurement error model alongside a comparison to a more biologically realistic binomial measurement error model. While estimates of model parameters are relatively insensitive to the choice of measurement error model, model predictions for data realisations are very sensitive. The standard additive Gaussian measurement error model leads to biologically inconsistent predictions, such as negative counts and counts that exceed the carrying capacity across a relatively large spatial region within the experiment. Furthermore, the standard additive Gaussian measurement error model requires estimating an additional parameter compared to the binomial measurement error model. In contrast, the binomial measurement error model leads to biologically plausible predictions and is simpler to implement. We provide open source Julia software on GitHub to replicate all calculations in this work, and we explain how to generalise our approach to deal with coupled PDE models with several dependent variables through a multinomial measurement error model, as well as pointing out other potential generalisations by linking our work with established practices in the field of generalised linear models.

Tumor containment: a more general mathematical analysis

Clinical and pre-clinical data suggest that treating some tumors at a mild, patient-specific dose might delay resistance to treatment and increase survival time. A recent mathematical model with sensitive and resistant tumor cells identified conditions under which a treatment aiming at tumor containment rather than eradication is indeed optimal. This model however neglected mutations from sensitive to resistant cells, and assumed that the growth-rate of sensitive cells is non-increasing in the size of the resistant population. The latter is not true in standard models of chemotherapy. This article shows how to dispense with this assumption and allow for mutations from sensitive to resistant cells. This is achieved by a novel mathematical analysis comparing tumor sizes across treatments not as a function of time, but as a function of the resistant population size.

Simulating tumor volume dynamics in response to radiotherapy: Implications of model selection

From the beginning of the usage of radiotherapy (RT) for cancer treatment, mathematical modeling has been integral to understanding radiobiology and for designing treatment approaches and schedules. There has been extensive modeling of response to RT with the inclusion of various degrees of biological complexity. In this study, we compare three models of tumor volume dynamics: (1) exponential growth with RT directly reducing tumor volume, (2) logistic growth with direct tumor volume reduction, and (3) logistic growth with RT reducing the tumor carrying capacity with the objective of understanding the implications of model selection and informing the process of model calibration and parameterization. For all three models, we: examined the rates of change in tumor volume during and RT treatment course; performed parameter sensitivity and identifiability analyses; and investigated the impact of the parameter sensitivity on the tumor volume trajectories. In examining the tumor volume dynamics trends, we coined a new metric - the point of maximum reduction of tumor volume (MRV) - to quantify the magnitude and timing of the expected largest impact of RT during a treatment course. We found distinct timing differences in MRV, dependent on model selection. The parameter identifiability and sensitivity analyses revealed the interdependence of the different model parameters and that it is only possible to independently identify tumor growth and radiation response parameters if the underlying tumor growth rate is sufficiently large. Ultimately, the results of these analyses help us to better understand the implications of model selection while simultaneously generating falsifiable hypotheses about MRV timing that can be tested on longitudinal measurements of tumor volume from pre-clinical or clinical data with high acquisition frequency. Although, our study only compares three particular models, the results demonstrate that caution is necessary in selecting models of response to RT, given the artifacts imposed by each model.

Focused ultrasound ablation of melanoma with boiling histotripsy yields abscopal tumor control and antigen-dependent dendritic cell activation

Background

Boiling histotripsy (BH), a mechanical focused ultrasound ablation strategy, can elicit intriguing signatures of anti-tumor immunity. However, the influence of BH on dendritic cell function is unknown, compromising our ability to optimally combine BH with immunotherapies to control metastatic disease.

Methods

BH was applied using a sparse scan (1 mm spacing between sonications) protocol to B16F10-ZsGreen melanoma in bilateral and unilateral settings. Ipsilateral and contralateral tumor growth was measured. Flow cytometry was used to track ZsGreen antigen and assess how BH drives dendritic cell behavior.

Results

BH monotherapy elicited ipsilateral and abscopal tumor control in this highly aggressive model. Tumor antigen presence in immune cells in the tumor-draining lymph nodes (TDLNs) was ~3-fold greater at 24h after BH, but this abated by 96h. B cells, macrophages, monocytes, granulocytes, and both conventional dendritic cell subsets (i.e. cDC1s and cDC2s) acquired markedly more antigen with BH. BH drove activation of both cDC subsets, with activation being dependent upon tumor antigen acquisition. Our data also suggest that BH-liberated tumor antigen is complexed with damage-associated molecular patterns (DAMPs) and that cDCs do not traffic to the TDLN with antigen. Rather, they acquire antigen as it flows through afferent lymph vessels into the TDLN.

Conclusion

When applied with a sparse scan protocol, BH monotherapy elicits abscopal melanoma control and shapes dendritic cell function through several previously unappreciated mechanisms. These results offer new insight into how to best combine BH with immunotherapies for the treatment of metastatic melanoma.

Modeling tumor growth using fractal calculus: Insights into tumor dynamics

Important concepts like fractal calculus and fractal analysis, the sum of squared residuals, and Aikaike's information criterion must be thoroughly understood in order to correctly fit cancer-related data using the proposed models. The fractal growth models employed in this work are classified in three main categories: Sigmoidal growth models (Logistic, Gompertz, and Richards models), Power Law growth model, and Exponential growth models (Exponential and Exponential-Lineal models)". We fitted the data, computed the sum of squared residuals, and determined Aikaike's information criteria using Matlab and the web tool WebPlotDigitizer. In addition, the research investigates "double-size cancer" in the fractal temporal dimension with respect to various mathematical models.

Formation and Growth of Co-Culture Tumour Spheroids: New Compartment-Based Mathematical Models and Experiments

Co-culture tumour spheroid experiments are routinely performed to investigate cancer progression and test anti-cancer therapies. Therefore, methods to quantitatively characterise and interpret co-culture spheroid growth are of great interest. However, co-culture spheroid growth is complex. Multiple biological processes occur on overlapping timescales and different cell types within the spheroid may have different characteristics, such as differing proliferation rates or responses to nutrient availability. At present there is no standard, widely-accepted mathematical model of such complex spatio-temporal growth processes. Typical approaches to analyse these experiments focus on the late-time temporal evolution of spheroid size and overlook early-time spheroid formation, spheroid structure and geometry. Here, using a range of ordinary differential equation-based mathematical models and parameter estimation, we interpret new co-culture experimental data. We provide new biological insights about spheroid formation, growth, and structure. As part of this analysis we connect Greenspan's seminal mathematical model to co-culture data for the first time. Furthermore, we generalise a class of compartment-based spheroid mathematical models that have previously been restricted to one population so they can be applied to multiple populations. As special cases of the general model, we explore multiple natural two population extensions to Greenspan's seminal model and reveal biological mechanisms that can describe the internal dynamics of growing co-culture spheroids and those that cannot. This mathematical and statistical modelling-based framework is well-suited to analyse spheroids grown with multiple different cell types and the new class of mathematical models provide opportunities for further mathematical and biological insights.

Simulating Interclonal Interactions in Diffuse Large B-Cell Lymphoma

Diffuse large B-cell lymphoma (DLBCL) is one of the most common types of cancers, accounting for 37% of B-cell tumor cases globally. DLBCL is known to be a heterogeneous disease, resulting in variable clinical presentations and the development of drug resistance. One underexplored aspect of drug resistance is the evolving dynamics between parental and drug-resistant clones within the same microenvironment. In this work, the effects of interclonal interactions between two cell populations-one sensitive to treatment and the other resistant to treatment-on tumor growth behaviors were explored through a mathematical model. In vitro cultures of mixed DLBCL populations demonstrated cooperative interactions and revealed the need for modifying the model to account for complex interactions. Multiple best-fit models derived from in vitro data indicated a difference in steady-state behaviors based on therapy administrations in simulations. The model and methods may serve as a tool for understanding the behaviors of heterogeneous tumors and identifying the optimal therapeutic regimen to eliminate cancer cell populations using computer-guided simulations.

Comparative Epidemiological Assessment of Monkeypox Infections on a Global and Continental Scale Using Logistic and Gompertz Mathematical Models

The monkeypox virus (MPXV) has caused an unusual epidemiological scenario-an epidemic within a pandemic (COVID-19). Despite the inherent evolutionary and adaptive capacity of poxviruses, one of the potential triggers for the emergence of this epidemic was the change in the status of orthopoxvirus vaccination and eradication programs. This epidemic outbreak of HMPX spread worldwide, with a notable frequency in Europe, North America, and South America. Due to these particularities, the objective of the present study was to assess and compare cases of HMPX in these geographical regions through logistic and Gompertz mathematical modeling over one year since its inception. We estimated the highest contagion rates (people per day) of 690, 230, 278, and 206 for the world, Europe, North America, and South America, respectively, in the logistic model. The equivalent values for the Gompertz model were 696, 268, 308, and 202 for the highest contagion rates. The Kruskal-Wallis Test indicated different means among the geographical regions affected by HMPX regarding case velocity, and the Wilcoxon pairwise test indicated the absence of significant differences between the case velocity means between Europe and South America. The coefficient of determination (R2) values in the logistic model varied from 0.8720 to 0.9023, and in the Gompertz model, they ranged from 0.9881 to 0.9988, indicating a better fit to the actual data when using the Gompertz model. The estimated basic reproduction numbers (R0) were more consistent in the logistic model, varying from 1.71 to 1.94 in the graphical method and from 1.75 to 1.95 in the analytical method. The comparative assessment of these mathematical modeling approaches permitted the establishment of the Gompertz model as the better-fitting model for the data and the logistic model for the R0. However, both models successfully represented the actual HMPX case data. The present study estimated relevant epidemiological data to understand better the geographic similarities and differences in the dynamics of HMPX.

Mathematical modeling of radiotherapy: impact of model selection on estimating minimum radiation dose for tumor control

Introduction

Radiation therapy (RT) is one of the most common anticancer therapies. Yet, current radiation oncology practice does not adapt RT dose for individual patients, despite wide interpatient variability in radiosensitivity and accompanying treatment response. We have previously shown that mechanistic mathematical modeling of tumor volume dynamics can simulate volumetric response to RT for individual patients and estimation personalized RT dose for optimal tumor volume reduction. However, understanding the implications of the choice of the underlying RT response model is critical when calculating personalized RT dose.

Methods

In this study, we evaluate the mathematical implications and biological effects of 2 models of RT response on dose personalization: (1) cytotoxicity to cancer cells that lead to direct tumor volume reduction (DVR) and (2) radiation responses to the tumor microenvironment that lead to tumor carrying capacity reduction (CCR) and subsequent tumor shrinkage. Tumor growth was simulated as logistic growth with pre-treatment dynamics being described in the proliferation saturation index (PSI). The effect of RT was simulated according to each respective model for a standard schedule of fractionated RT with 2 Gy weekday fractions. Parameter sweeps were evaluated for the intrinsic tumor growth rate and the radiosensitivity parameter for both models to observe the qualitative impact of each model parameter. We then calculated the minimum RT dose required for locoregional tumor control (LRC) across all combinations of the full range of radiosensitvity and proliferation saturation values.

Results

Both models estimate that patients with higher radiosensitivity will require a lower RT dose to achieve LRC. However, the two models make opposite estimates on the impact of PSI on the minimum RT dose for LRC: the DVR model estimates that tumors with higher PSI values will require a higher RT dose to achieve LRC, while the CCR model estimates that higher PSI values will require a lower RT dose to achieve LRC.

Discussion

Ultimately, these results show the importance of understanding which model best describes tumor growth and treatment response in a particular setting, before using any such model to make estimates for personalized treatment recommendations.

Treatment of evolving cancers will require dynamic decision support

Cancer research has traditionally focused on developing new agents, but an underexplored question is that of the dose and frequency of existing drugs. Based on the modus operandi established in the early days of chemotherapies, most drugs are administered according to predetermined schedules that seek to deliver the maximum tolerated dose and are only adjusted for toxicity. However, we believe that the complex, evolving nature of cancer requires a more dynamic and personalized approach. Chronicling the milestones of the field, we show that the impact of schedule choice crucially depends on processes driving treatment response and failure. As such, cancer heterogeneity and evolution dictate that a one-size-fits-all solution is unlikely-instead, each patient should be mapped to the strategy that best matches their current disease characteristics and treatment objectives (i.e. their 'tumorscape'). To achieve this level of personalization, we need mathematical modeling. In this perspective, we propose a five-step 'Adaptive Dosing Adjusted for Personalized Tumorscapes (ADAPT)' paradigm to integrate data and understanding across scales and derive dynamic and personalized schedules. We conclude with promising examples of model-guided schedule personalization and a call to action to address key outstanding challenges surrounding data collection, model development, and integration.

Modeling of oncolytic viruses in a heterogeneous cell population to predict spread into non-cancerous cells

New cancer treatment modalities that limit patient discomfort need to be developed. One possible new therapy is the use of oncolytic (cancer-killing) viruses. It is only recently that our ability to manipulate viral genomes has allowed us to consider deliberately infecting cancer patients with viruses. One key consideration is to ensure that the virus exclusively targets cancer cells and does not harm nearby non-cancerous cells. Here, we use a mathematical model of viral infection to determine the characteristics a virus would need to have in order to eradicate a tumor, but leave non-cancerous cells untouched. We conclude that the virus must differ in its ability to infect the two different cell types, with the infection rate of non-cancerous cells needing to be less than one hundredth of the infection rate of cancer cells. Differences in viral production rate or infectious cell death rate alone are not sufficient to protect non-cancerous cells.

Logistic tumor-population growth and ghost-points symmetry

The observed time evolution of a population is well approximated by a logistic function in many research fields, including oncology, ecology, chemistry, demography, economy, linguistics, and artificial neural networks. Initial growth is exponential at a constant rate and capped at a limit size, i.e., the carrying capacity. In mathematical oncology, the carrying capacity has been postulated to be co-evolving and thus patient-specific. As the relative tumor-over-carrying capacity ratio may be predictive and prognostic for tumor growth and treatment response dynamics, it is paramount to estimate it from limited clinical data. We show that exploiting the logistic function's rotation symmetry can help estimate the population's growth rate and carry capacity from fewer data points than conventional regression approaches. We test this novel approach against a classic oncology database of logistic tumor growth, achieving a 30% to 40% reduction in the time necessary to correctly estimate the logistic growth rate and carrying capacity. Our results will improve tumor dynamics forecasting and augment the clinical decision-making process.

Radio-immune response modelling for spatially fractionated radiotherapy

Objective.Radiation-induced cell death is a complex process influenced by physical, chemical and biological phenomena. Although consensus on the nature and the mechanism of the bystander effect were not yet made, the immune process presumably plays an important role in many aspects of the radiotherapy including the bystander effect. A mathematical model of immune response during and after radiation therapy is presented.Approach.Immune response of host body and immune suppression of tumor cells are modelled with four compartments in this study; viable tumor cells, T cell lymphocytes, immune triggering cells, and doomed cells. The growth of tumor was analyzed in two distinctive modes of tumor status (immune limited and immune escape) and its bifurcation condition.Main results.Tumors in the immune limited mode can grow only up to a finite size, named as terminal tumor volume analytically calculated from the model. The dynamics of the tumor growth in the immune escape mode is much more complex than the tumors in the immune limited mode especially when the status of tumor is close to the bifurcation condition. Radiation can kill tumor cells not only by radiation damage but also by boosting immune reaction.Significance.The model demonstrated that the highly heterogeneous dose distribution in spatially fractionated radiotherapy (SFRT) can make a drastic difference in tumor cell killing compared to the homogeneous dose distribution. SFRT cannot only enhance but also moderate the cell killing depending on the immune response triggered by many factors such as dose prescription parameters, tumor volume at the time of treatment and tumor characteristics. The model was applied to the lifted data of 67NR tumors on mice and a sarcoma patient treated multiple times over 1200 days for the treatment of tumor recurrence as a demonstration.

Growth exponents reflect evolutionary processes and treatment response in brain metastases

Tumor growth is the result of the interplay of complex biological processes in huge numbers of individual cells living in changing environments. Effective simple mathematical laws have been shown to describe tumor growth in vitro, or simple animal models with bounded-growth dynamics accurately. However, results for the growth of human cancers in patients are scarce. Our study mined a large dataset of 1133 brain metastases (BMs) with longitudinal imaging follow-up to find growth laws for untreated BMs and recurrent treated BMs. Untreated BMs showed high growth exponents, most likely related to the underlying evolutionary dynamics, with experimental tumors in mice resembling accurately the disease. Recurrent BMs growth exponents were smaller, most probably due to a reduction in tumor heterogeneity after treatment, which may limit the tumor evolutionary capabilities. In silico simulations using a stochastic discrete mesoscopic model with basic evolutionary dynamics led to results in line with the observed data.

Mathematical Modeling of Clonal Interference by Density-Dependent Selection in Heterogeneous Cancer Cell Lines

Many cancer cell lines are aneuploid and heterogeneous, with multiple karyotypes co-existing within the same cell line. Karyotype heterogeneity has been shown to manifest phenotypically, thus affecting how cells respond to drugs or to minor differences in culture media. Knowing how to interpret karyotype heterogeneity phenotypically would give insights into cellular phenotypes before they unfold temporally. Here, we re-analyzed single cell RNA (scRNA) and scDNA sequencing data from eight stomach cancer cell lines by placing gene expression programs into a phenotypic context. Using live cell imaging, we quantified differences in the growth rate and contact inhibition between the eight cell lines and used these differences to prioritize the transcriptomic biomarkers of the growth rate and carrying capacity. Using these biomarkers, we found significant differences in the predicted growth rate or carrying capacity between multiple karyotypes detected within the same cell line. We used these predictions to simulate how the clonal composition of a cell line would change depending on density conditions during in-vitro experiments. Once validated, these models can aid in the design of experiments that steer evolution with density-dependent selection.

Inferring density-dependent population dynamics mechanisms through rate disambiguation for logistic birth-death processes

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can manifest in birth processes, death processes, or both. Therefore, we utilize the mean and variance of cell number fluctuations to separately identify birth and death rates from time series that follow stochastic birth-death processes with logistic growth. Our nonparametric method provides a novel perspective on stochastic parameter identifiability, which we validate by analyzing the accuracy in terms of the discretization bin size. We apply our method to the scenario where a homogeneous cell population goes through three stages: (1) grows naturally to its carrying capacity, (2) is treated with a drug that reduces its carrying capacity, and (3) overcomes the drug effect to restore its original carrying capacity. In each stage, we disambiguate whether the dynamics occur through the birth process, death process, or some combination of the two, which contributes to understanding drug resistance mechanisms. In the case of limited sample sizes, we provide an alternative method based on maximum likelihood and solve a constrained nonlinear optimization problem to identify the most likely density dependence parameter for a given cell number time series. Our methods can be applied to other biological systems at different scales to disambiguate density-dependent mechanisms underlying the same net growth rate.

COVID-19 vaccine incentive scheduling using an optimally controlled reinforcement learning model

We model Covid-19 vaccine uptake as a reinforcement learning dynamic between two populations: the vaccine adopters, and the vaccine hesitant. Using data available from the Center for Disease Control (CDC), we estimate the payoff matrix governing the interaction between these two groups over time and show they are playing a Hawk-Dove evolutionary game with an internal evolutionarily stable Nash equilibrium (the asymptotic percentage of vaccinated in the population). We then ask whether vaccine adoption can be improved by implementing dynamic incentive schedules that reward/punish the vaccine hesitant, and if so, what schedules are optimal and how effective are they likely to be? When is the optimal time to start an incentive program, how large should the incentives be, and is there a point of diminishing returns? By using a tailored replicator dynamic reinforcement learning model together with optimal control theory, we show that well designed and timed incentive programs can improve vaccine uptake by shifting the Nash equilibrium upward in large populations, but only so much, and incentive sizes above a certain threshold show diminishing returns.

Designing experimental conditions to use the Lotka-Volterra model to infer tumor cell line interaction types

The Lotka-Volterra model is widely used to model interactions between two species. Here, we generate synthetic data mimicking competitive, mutualistic and antagonistic interactions between two tumor cell lines, and then use the Lotka-Volterra model to infer the interaction type. Structural identifiability of the Lotka-Volterra model is confirmed, and practical identifiability is assessed for three experimental designs: (a) use of a single data set, with a mixture of both cell lines observed over time, (b) a sequential design where growth rates and carrying capacities are estimated using data from experiments in which each cell line is grown in isolation, and then interaction parameters are estimated from an experiment involving a mixture of both cell lines, and (c) a parallel experimental design where all model parameters are fitted to data from two mixtures (containing both cell lines but with different initial ratios) simultaneously. Each design is tested on data generated from the Lotka-Volterra model with noise added, to determine efficacy in an ideal sense. In addition to assessing each design for practical identifiability, we investigate how the predictive power of the model - i.e., its ability to fit data for initial ratios other than those to which it was calibrated - is affected by the choice of experimental design. The parallel calibration procedure is found to be optimal and is further tested on in silico data generated from a spatially-resolved cellular automaton model, which accounts for oxygen consumption and allows for variation in the intensity level of the interaction between the two cell lines. We use this study to highlight the care that must be taken when interpreting parameter estimates for the spatially-averaged Lotka-Volterra model when it is calibrated against data produced by the spatially-resolved cellular automaton model, since baseline competition for space and resources in the CA model may contribute to a discrepancy between the type of interaction used to generate the CA data and the type of interaction inferred by the LV model.

Integration of quantitative methods and mathematical approaches for the modeling of cancer cell proliferation dynamics

Physiological processes rely on the control of cell proliferation, and the dysregulation of these processes underlies various pathological conditions, including cancer. Mathematical modeling can provide new insights into the complex regulation of cell proliferation dynamics. In this review, we first examine quantitative experimental approaches for measuring cell proliferation dynamics in vitro and compare the various types of data that can be obtained in these settings. We then explore the toolbox of common mathematical modeling frameworks that can describe cell behavior, dynamics, and interactions of proliferation. We discuss how these wet-laboratory studies may be integrated with different mathematical modeling approaches to aid the interpretation of the results and to enable the prediction of cell behaviors, specifically in the context of cancer.

Total coumarins of Pileostegia tomentella induces cell death in SCLC by reprogramming metabolic patterns, possibly through attenuating β-catenin/AMPK/SIRT1

BACKGROUND

Small-cell lung cancer (SCLC) is a high malignant and high energy-consuming type of lung cancer. Total coumarins of Pileostegia tomentella (TCPT) from a traditional folk medicine of Yao minority, is a potential anti-cancer mixture against SCLC, but the pharmacological and molecular mechanism of TCPT remains largely unknown.

METHODS

Screening of viability inhibition of TCPT among 7 cell lines were conducted by using CCK-8 assays. Anti-proliferative activities of TCPT in SCLC were observed by using colony formation and flow cytometry assays. Morphological changes were observed by transmission electron microscope and Mito-Tracker staining. High Throughput RNA-seq analysis and bio-informatics analysis were applied to find potential targeted biological and signaling pathways affected by TCPT. The mRNA expression of DEGs and protein expression of signalling proteins and metabolic enzymes were verified by qPCR and Western blot assays. Activity of rate-limiting enzymes and metabolite level were detected by corresponding enzyme activity and metabolites kits. Xenograft nude mice model of SCLC was established to observe the in vivo inhibition, metabolism reprogramming and mechanism of TCPT.

RESULTS

TCPT treatment shows the best inhibition in SCLC cell line H1688 rather than other 5 lung cancer cell lines. Ultrastructural investigation indicates TCPT induces mitochondria damage such as cytoplasm shrinkage, ridges concentration and early sight of autolysosome, as well as decrease of membrane potential. Results of RNA-seq combined bio-informatics analysis find out changes of metabolism progression affected the most by TCPT in SCLC cells, and these changes might be regulated by β-catenin/AMPK/SIRT1 axis. TCPT might mainly decline the activity and expression of rate-limiting enzymes, OGDH, PDHE1, and LDHA/B to reprogram aerobic oxidation pattern, resulting in reduction of ATP production in SCLC cells. Xenograft nude mice model demonstrates TCPT could induce cell death and inhibit growth in vivo. Assimilate to the results of in vitro model, TCPT reprograms metabolism by decreasing the activity and expression of rate-limiting enzymes (OGDH, PDHE1, and LDHA/B), and attenuates the expression of β-catenin, p-β-catenin, AMPK and SIRT1 accordance with in vitro data.

CONCLUSION

Our results demonstrated TCPT induces cell death of SCLC by reprograming metabolic patterns, possibly through attenuating master metabolic pathway axis β-catenin/AMPK/SIRT1.

Geometric analysis enables biological insight from complex non-identifiable models using simple surrogates

An enduring challenge in computational biology is to balance data quality and quantity with model complexity. Tools such as identifiability analysis and information criterion have been developed to harmonise this juxtaposition, yet cannot always resolve the mismatch between available data and the granularity required in mathematical models to answer important biological questions. Often, it is only simple phenomenological models, such as the logistic and Gompertz growth models, that are identifiable from standard experimental measurements. To draw insights from complex, non-identifiable models that incorporate key biological mechanisms of interest, we study the geometry of a map in parameter space from the complex model to a simple, identifiable, surrogate model. By studying how non-identifiable parameters in the complex model quantitatively relate to identifiable parameters in surrogate, we introduce and exploit a layer of interpretation between the set of non-identifiable parameters and the goodness-of-fit metric or likelihood studied in typical identifiability analysis. We demonstrate our approach by analysing a hierarchy of mathematical models for multicellular tumour spheroid growth experiments. Typical data from tumour spheroid experiments are limited and noisy, and corresponding mathematical models are very often made arbitrarily complex. Our geometric approach is able to predict non-identifiabilities, classify non-identifiable parameter spaces into identifiable parameter combinations that relate to features in the data characterised by parameters in a surrogate model, and overall provide additional biological insight from complex non-identifiable models.

Profile likelihood-based parameter and predictive interval analysis guides model choice for ecological population dynamics

Calibrating mathematical models to describe ecological data provides important insight via parameter estimation that is not possible from analysing data alone. When we undertake a mathematical modelling study of ecological or biological data, we must deal with the trade-off between data availability and model complexity. Dealing with the nexus between data availability and model complexity is an ongoing challenge in mathematical modelling, particularly in mathematical biology and mathematical ecology where data collection is often not standardised, and more broad questions about model selection remain relatively open. Therefore, choosing an appropriate model almost always requires case-by-case consideration. In this work we present a straightforward approach to quantitatively explore this trade-off using a case study exploring mathematical models of coral reef regrowth after some ecological disturbance, such as damage caused by a tropical cyclone. In particular, we compare a simple single species ordinary differential equation (ODE) model approach with a more complicated two-species coupled ODE model. Univariate profile likelihood analysis suggests that the both models are practically identifiable. To provide additional insight we construct and compare approximate prediction intervals using a new parameter-wise prediction approximation, confirming both the simple and complex models perform similarly with regard to making predictions. Our approximate parameter-wise prediction interval analysis provides explicit information about how each parameter affects the predictions of each model. Comparing our approximate prediction intervals with a more rigorous and computationally expensive evaluation of the full likelihood shows that the new approximations are reasonable in this case. All algorithms and software to support this work are freely available as jupyter notebooks on GitHub so that they can be adapted to deal with any other ODE-based models.

Stochastic Fluctuations Drive Non-genetic Evolution of Proliferation in Clonal Cancer Cell Populations

Evolutionary dynamics allows us to understand many changes happening in a broad variety of biological systems, ranging from individuals to complete ecosystems. It is also behind a number of remarkable organizational changes that happen during the natural history of cancers. These reflect tumour heterogeneity, which is present at all cellular levels, including the genome, proteome and phenome, shaping its development and interrelation with its environment. An intriguing observation in different cohorts of oncological patients is that tumours exhibit an increased proliferation as the disease progresses, while the timescales involved are apparently too short for the fixation of sufficient driver mutations to promote explosive growth. Here, we discuss how phenotypic plasticity, emerging from a single genotype, may play a key role and provide a ground for a continuous acceleration of the proliferation rate of clonal populations with time. We address this question by combining the analysis of real-time growth of non-small-cell lung carcinoma cells (N-H460) together with stochastic and deterministic mathematical models that capture proliferation trait heterogeneity in clonal populations to elucidate the contribution of phenotypic transitions on tumour growth dynamics.

Computationally efficient framework for diagnosing, understanding and predicting biphasic population growth

Throughout the life sciences, biological populations undergo multiple phases of growth, often referred to as biphasic growth for the commonly encountered situation involving two phases. Biphasic population growth occurs over a massive range of spatial and temporal scales, ranging from microscopic growth of tumours over several days, to decades-long regrowth of corals in coral reefs that can extend for hundreds of kilometres. Different mathematical models and statistical methods are used to diagnose, understand and predict biphasic growth. Common approaches can lead to inaccurate predictions of future growth that may result in inappropriate management and intervention strategies being implemented. Here, we develop a very general computationally efficient framework, based on profile likelihood analysis, for diagnosing, understanding and predicting biphasic population growth. The two key components of the framework are as follows: (i) an efficient method to form approximate confidence intervals for the change point of the growth dynamics and model parameters and (ii) parameter-wise profile predictions that systematically reveal the influence of individual model parameters on predictions. To illustrate our framework we explore real-world case studies across the life sciences.

Inferring parameters of cancer evolution in chronic lymphocytic leukemia

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.

Occam's razor gets a new edge: the use of symmetries in model selection

We demonstrate the power of using symmetries for model selection in the context of mechanistic modelling. We analyse two different models called the power law model (PLM) and the immunological model (IM) describing the increase in cancer risk with age, due to mutation accumulation or immunosenescence, respectively. The IM fits several cancer types better than the PLM implying that it would be selected based on minimizing residuals. However, recently a symmetry-based method for model selection has been developed, which has been successfully used in an in silico setting to find the correct model when traditional model fitting has failed. Here, we apply this method in a real-world setting to investigate the mechanisms of carcinogenesis. First, we derive distinct symmetry transformations of the two models and then we select the model which not only fits the original data but is also invariant under transformations by its symmetry. Contrary to the initial conclusion, we conclude that the PLM realistically describes the mechanism underlying the colon cancer dataset. These conclusions agree with experimental knowledge, and this work demonstrates how a model selection criterion based on biological properties can be implemented using symmetries.

A Spatially Resolved Mechanistic Growth Law for Cancer Drug Development Predicting Tumor Growing Fractions

Mathematical models used in preclinical drug discovery tend to be empirical growth laws. Such models are well suited to fitting the data available, mostly longitudinal studies of tumor volume; however, they typically have little connection with the underlying physiologic processes. This lack of a mechanistic underpinning restricts their flexibility and potentially inhibits their translation across studies including from animal to human. Here we present a mathematical model describing tumor growth for the evaluation of single-agent cytotoxic compounds that is based on mechanistic principles. The model can predict spatial distributions of cell subpopulations and account for spatial drug distribution effects within tumors. Importantly, we demonstrate that the model can be reduced to a growth law similar in form to the ones currently implemented in pharmaceutical drug development for preclinical trials so that it can integrated into the current workflow. We validate this approach for both cell-derived xenograft and patient-derived xenograft (PDX) data. This shows that our theoretical model fits as well as the best performing and most widely used models. However, in addition, the model is also able to accurately predict the observed growing fraction of tumours. Our work opens up current preclinical modeling studies to also incorporating spatially resolved and multimodal data without significant added complexity and creates the opportunity to improve translation and tumor response predictions.

Significance

This theoretical model has the same mathematical structure as that currently used for drug development. However, its mechanistic basis enables prediction of growing fraction and spatial variations in drug distribution.

Tumour growth rate improves tumour assessment and first-line systemic treatment decision-making for immunotherapy in patients with liver metastatic uveal melanoma

BACKGROUND

The RECIST-based response variably matches the clinical benefit of systemic therapies for liver metastatic uveal melanoma (LMUM). The aims were to determine whether the tumour growth rate (TGR) can help predict the survival in patients with LMUM and to provide information for the management of first-line systemic treatment.

METHODS

This retrospective study included 147 (training: n = 110, validation: n = 37) patients with LMUM treated with first-line systemic treatment between 2010 and 2021. Two TGR-derived parameters were calculated, TGR0 and TGR3m. Multivariate Cox analyses identified independent predictors of progression-free survival (PFS) and overall survival (OS).

RESULTS

TGR3m was a strong independent prognostic factor of PFS and OS (p < 0.001). The RECIST-based response was no longer significant in the OS analyses. Only immunotherapy regimens correlated with higher OS (HR = 0.2; 95% CI, 0.1-0.5; p < 0.001) in the low-TGR3m (≤50%/m) subgroup. These findings were confirmed in the validation cohort. TGR0, disease-free interval (DFI), and the sum of target lesions at baseline were predictive factors of low TGR3m.

DISCUSSION

The use of TGR3m would improve tumour assessment by identifying patients who would benefit from first-line immunotherapy regimens despite PD. TGR0, DFI and the sum of target lesions were correlated with TGR3m, which can support first-line treatment decision-making for immunotherapy.