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Sánchez JF, Ramtani S, Boucetta A, Velasco MA, Vaca-González JJ, Duque-Daza CA, Garzón-Alvarado DA. Tumor growth for remodeling process: A 2D approach. J Theor Biol 2024; 585:111781. [PMID: 38432504 DOI: 10.1016/j.jtbi.2024.111781] [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: 11/01/2023] [Revised: 02/07/2024] [Accepted: 02/27/2024] [Indexed: 03/05/2024]
Abstract
This paper aims to present a comprehensive framework for coupling tumor-bone remodeling processes in a 2-dimensional geometry. This is achieved by introducing a bio-inspired damage that represents the growing tumor, which subsequently affects the main populations involved in the remodeling process, namely, osteoclasts, osteoblasts, and bone tissue. The model is constructed using a set of differential equations based on the Komarova's and Ayati's models, modified to incorporate the bio-inspired damage that may result in tumor mass formation. Three distinct models were developed. The first two models are based on the Komarova's governing equations, with one demonstrating an osteolytic behavior and the second one an osteoblastic model. The third model is a variation of Ayati's model, where the bio-inspired damage is induced through the paracrine and autocrine parameters, exhibiting an osteolytic behavior. The obtained results are consistent with existing literature, leading us to believe that our in-silico experiments will serve as a cornerstone for paving the way towards targeted interventions and personalized treatment strategies, ultimately improving the quality of life for those affected by these conditions.
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Affiliation(s)
| | - Salah Ramtani
- Laboratoire CSPBAT, equipe LBPS, CNRS (UMR 7244), Universit e Sorbonne Paris Nord, France.
| | - Abdelkader Boucetta
- Laboratoire CSPBAT, equipe LBPS, CNRS (UMR 7244), Universit e Sorbonne Paris Nord, France
| | | | - Juan Jairo Vaca-González
- Escuela de Pregrado - Direccion Académica, Universidad Nacional de Colombia, Sede de La Paz, Colombia.
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2
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Cook CV, Islam MA, Smith BJ, Versypt ANF. Mathematical modeling of the effects of Wnt-10b on bone metabolism. AIChE J 2022; 68:e17809. [PMID: 36567819 PMCID: PMC9788157 DOI: 10.1002/aic.17809] [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: 02/16/2022] [Accepted: 06/14/2022] [Indexed: 12/30/2022]
Abstract
Bone health is determined by factors including bone metabolism or remodeling. Wnt-10b alters osteoblastogenesis through pre-osteoblast proliferation and differentiation and osteoblast apoptosis rate, which collectively lead to the increase of bone density. To model this, we adapted a previously published model of bone remodeling. The resulting model for the bone compartment includes differential equations for active osteoclasts, pre-osteoblasts, osteoblasts, osteocytes, and the amount of bone present at the remodeling site. Our alterations to the original model consist of extending it past a single remodeling cycle and implementing a direct relationship to Wnt-10b. Four new parameters were estimated and validated using normalized data from mice. The model connects Wnt-10b to bone metabolism and predicts the change in trabecular bone volume caused by a change in Wnt-10b input. We find that this model predicts the expected increase in pre-osteoblasts and osteoblasts while also pointing to a decrease in osteoclasts when Wnt-10b is increased.
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Affiliation(s)
- Carley V. Cook
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260, USA
- School of Chemical Engineering, Oklahoma State University, Stillwater, OK 74078, USA
| | - Mohammad Aminul Islam
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260, USA
- School of Chemical Engineering, Oklahoma State University, Stillwater, OK 74078, USA
| | - Brenda J. Smith
- Department of Nutritional Sciences, Oklahoma State University, Stillwater, OK 74078, USA
| | - Ashlee N. Ford Versypt
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260, USA
- School of Chemical Engineering, Oklahoma State University, Stillwater, OK 74078, USA
- Institute for Computational and Data Sciences, University at Buffalo, The State University of New York, Buffalo, NY 14260, USA
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3
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Lorenzo G, di Muzio N, Deantoni CL, Cozzarini C, Fodor A, Briganti A, Montorsi F, Pérez-García VM, Gomez H, Reali A. Patient-specific forecasting of postradiotherapy prostate-specific antigen kinetics enables early prediction of biochemical relapse. iScience 2022; 25:105430. [DOI: 10.1016/j.isci.2022.105430] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2022] [Revised: 09/04/2022] [Accepted: 10/19/2022] [Indexed: 11/06/2022] Open
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4
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Ait Oumghar I, Barkaoui A, Chabrand P, Ghazi AE, Jeanneau C, Guenoun D, Pivonka P. Experimental-based mechanobiological modeling of the anabolic and catabolic effects of breast cancer on bone remodeling. Biomech Model Mechanobiol 2022; 21:1841-1856. [PMID: 36001274 DOI: 10.1007/s10237-022-01623-z] [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: 05/23/2022] [Accepted: 08/02/2022] [Indexed: 11/02/2022]
Abstract
Bone is a biological tissue characterized by its hierarchical organization. This material has the ability to be continually renewed, which makes it highly adaptative to external loadings. Bone renewing is managed by a dynamic biological process called bone remodeling (BR), where continuous resorption of old bone and formation of new bone permits to change the bone composition and microstructure. Unfortunately, because of several factors, such as age, hormonal imbalance, and a variety of pathologies including cancer metastases, this process can be disturbed leading to various bone diseases. In this study, we have investigated the effect of breast cancer (BC) metastases causing osteolytic bone loss. BC has the ability to affect bone quantity in different ways in each of its primary and secondary stages. Based on a BR mathematical model, we modeled the BC cells' interaction with bone cells to assess their effect on bone volume fraction (BV/TV) evolution during the remodeling process. Some of the parameters used in our model have been determined experimentally using the enzyme-linked immune-sorbent assay (ELISA) and the MTT assay. Our numerical simulations show that primary BC plays a significant role in enhancing bone-forming cells' activity leading to a 6.22% increase in BV/TV over 1 year. On the other hand, secondary BC causes a noticeable decrease in BV/TV reaching 15.74% over 2 years.
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Affiliation(s)
- Imane Ait Oumghar
- LERMA Lab, Université Internationale de Rabat, Rocade Rabat Salé 11100, Rabat-Sala El Jadida, Morocco.,Université Aix-Marseille, ISM, 163 av. de Luminy, 13288, Marseille Cedex 09, France
| | - Abdelwahed Barkaoui
- LERMA Lab, Université Internationale de Rabat, Rocade Rabat Salé 11100, Rabat-Sala El Jadida, Morocco.
| | - Patrick Chabrand
- Université Aix-Marseille, ISM, 163 av. de Luminy, 13288, Marseille Cedex 09, France
| | - Abdellatif El Ghazi
- TIC Lab, Université Internationale de Rabat, Rocade Rabat Salé 11100, Rabat-Sala El Jadida, Morocco
| | - Charlotte Jeanneau
- Université Aix-Marseille, ISM, 163 av. de Luminy, 13288, Marseille Cedex 09, France
| | - Daphne Guenoun
- Université Aix-Marseille, ISM, 163 av. de Luminy, 13288, Marseille Cedex 09, France
| | - Peter Pivonka
- Biomechanics and Spine Research Group, Queensland University of Technology at the Centre for Children's Health Research, South Brisbane, 4101, QLD, Australia
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5
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Antigen receptor therapy in bone metastasis via optimal control for different human life stages. J Math Biol 2021; 83:44. [PMID: 34596800 DOI: 10.1007/s00285-021-01673-4] [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: 09/25/2020] [Revised: 08/23/2021] [Accepted: 09/08/2021] [Indexed: 10/20/2022]
Abstract
In this work we propose a bone metastasis model using power law growth functions in order to describe the biochemical interactions between bone cells and cancer cells. Experimental studies indicate that bone remodeling cycles are different for human life stages: childhood, young adulthood, and adulthood. In order to include such differences in our study, we estimate the model parameter values for each human life stage via bifurcation analysis. Results reveal an intrinsic relationship between the active period of remodeling cycles and the proliferation of cancer cells. Subsequently, using optimal control theory we analyze a possible antigen receptor therapy as a new treatment for bone metastasis. Theoretical results such as existence of optimal solutions are proved. Numerical simulations for late stages of bone metastasis are presented and a discussion of our results is carried out.
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6
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Barkaoui A, Ait Oumghar I, Ben Kahla R. Review on the use of medical imaging in orthopedic biomechanics: finite element studies. COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING: IMAGING & VISUALIZATION 2021. [DOI: 10.1080/21681163.2021.1888317] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Abdelwahed Barkaoui
- Laboratoire des Énergies Renouvelables et Matériaux Avancés, Université Internationale de Rabat, Sala Al Jadida Morocco
| | - Imane Ait Oumghar
- Laboratoire des Énergies Renouvelables et Matériaux Avancés, Université Internationale de Rabat, Sala Al Jadida Morocco
- Aix Marseille Univ, CNRS, ISM, Inst Movement Sci, Marseille, France
| | - Rabeb Ben Kahla
- Laboratoire de Systémes et de Mécanique Appliquée, Ecole Polytechnique de Tunis, Université de Carthage, Tunis, Tunisia
- Ecole Nationale d’Ingénieurs de Tunis, Université de Tunis el Manar, Campus Universitaire, Tunis, Tunisia
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7
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Alishzadeh Khoei A, Zakerzadeh M, Ayati M, Soleimani N. Developing and studying the dynamical behavior of a nonlinear mathematical model for cancers with tumor by considering immune system role. INT J BIOMATH 2021. [DOI: 10.1142/s1793524520500564] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We are constrained by widespread cancerous diseases to improve treatment methods which save patients and provide better living conditions during and after the treatment period. Because of the complexity of the treatment process, mathematical models need to be used in order to have a better understanding of the process. However, deriving an adequate complex model that can capture the disease pattern which could be confirmed by simulations and experiments has its own barriers. In this paper, a new mathematical model is developed concerning immune system effect on cancer. The model is introduced using nonlinear ordinary differential equations. Also, the qualitative behavior of the proposed system is studied in order to examine the extent of the model with respect to the nature of tumor evolution. Thus, number and status of equilibria points in line with the existence of limit cycles are obtained for sub-systems and the whole system. Meanwhile, possible bifurcations are mentioned, and the consequent evolutions are described. It is shown that the model conforms well to natural possibilities, cancer growth or remission. Thus, the model would be fit for further studies for prediction and contemplating treatment method, especially for immune stimulating drugs and immunotherapy.
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Affiliation(s)
- Amir Alishzadeh Khoei
- School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
| | - Mohammadreza Zakerzadeh
- School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
| | - Moosa Ayati
- School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
| | - Neda Soleimani
- Department of Microbiology and Microbial Biotechnology, Faculty of Life Sciences and Biotechnology, Shahid Beheshti University, Tehran, Iran
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Ait Oumghar I, Barkaoui A, Chabrand P. Toward a Mathematical Modeling of Diseases' Impact on Bone Remodeling: Technical Review. Front Bioeng Biotechnol 2020; 8:584198. [PMID: 33224935 PMCID: PMC7667152 DOI: 10.3389/fbioe.2020.584198] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2020] [Accepted: 09/30/2020] [Indexed: 12/18/2022] Open
Abstract
A wide variety of bone diseases have hitherto been discovered, such as osteoporosis, Paget's disease, osteopetrosis, and metastatic bone disease, which are not well defined in terms of changes in biochemical and mechanobiological regulatory factors. Some of these diseases are secondary to other pathologies, including cancer, or to some clinical treatments. To better understand bone behavior and prevent its deterioration, bone biomechanics have been the subject of mathematical modeling that exponentially increased over the last years. These models are becoming increasingly complex. The current paper provides a timely and critical analysis of previously developed bone remodeling mathematical models, particularly those addressing bone diseases. Besides, mechanistic pharmacokinetic/pharmacodynamic (PK/PD) models, which englobe bone disease and its treatment's effect on bone health. Therefore, the review starts by presenting bone remodeling cycle and mathematical models describing this process, followed by introducing some bone diseases and discussing models of pathological mechanisms affecting bone, and concludes with exhibiting the available bone treatment procedures considered in the PK/PD models.
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Affiliation(s)
- Imane Ait Oumghar
- Laboratoire des Energies Renouvelables et Matériaux Avancés (LERMA), Université Internationale de Rabat, Rabat-Sala El Jadida, Morocco
- Aix Marseille Univ, CNRS, ISM, Inst Movement Sci, Marseille, France
| | - Abdelwahed Barkaoui
- Laboratoire des Energies Renouvelables et Matériaux Avancés (LERMA), Université Internationale de Rabat, Rabat-Sala El Jadida, Morocco
| | - Patrick Chabrand
- Aix Marseille Univ, CNRS, ISM, Inst Movement Sci, Marseille, France
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9
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Review: Mathematical Modeling of Prostate Cancer and Clinical Application. APPLIED SCIENCES-BASEL 2020. [DOI: 10.3390/app10082721] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
We review and synthesize key findings and limitations of mathematical models for prostate cancer, both from theoretical work and data-validated approaches, especially concerning clinical applications. Our focus is on models of prostate cancer dynamics under treatment, particularly with a view toward optimizing hormone-based treatment schedules and estimating the onset of treatment resistance under various assumptions. Population models suggest that intermittent or adaptive therapy is more beneficial to delay cancer relapse as compared to the standard continuous therapy if treatment resistance comes at a competitive cost for cancer cells. Another consensus among existing work is that the standard biomarker for cancer growth, prostate-specific antigen, may not always correlate well with cancer progression. Instead, its doubling rate appears to be a better indicator of tumor growth. Much of the existing work utilizes simple ordinary differential equations due to difficulty in collecting spatial data and due to the early success of using prostate-specific antigen in mathematical modeling. However, a shift toward more complex and realistic models is taking place, which leaves many of the theoretical and mathematical questions unexplored. Furthermore, as adaptive therapy displays better potential than existing treatment protocols, an increasing number of studies incorporate this treatment into modeling efforts. Although existing modeling work has explored and yielded useful insights on the treatment of prostate cancer, the road to clinical application is still elusive. Among the pertinent issues needed to be addressed to bridge the gap from modeling work to clinical application are (1) real-time data validation and model identification, (2) sensitivity analysis and uncertainty quantification for model prediction, and (3) optimal treatment/schedule while considering drug properties, interactions, and toxicity. To address these issues, we suggest in-depth studies on various aspects of the parameters in dynamical models such as the evolution of parameters over time. We hope this review will assist future attempts at studying prostate cancer.
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10
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Mathematical modelling of the role of Endo180 network in the development of metastatic bone disease in prostate cancer. Comput Biol Med 2020; 117:103619. [PMID: 32072971 DOI: 10.1016/j.compbiomed.2020.103619] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2019] [Revised: 01/11/2020] [Accepted: 01/11/2020] [Indexed: 12/29/2022]
Abstract
Metastatic bone disease (MBD) is a common complication of advanced cancer and recent research suggests that Endo180 expression is dysregulated through the TGFβ-TGFβR-SMAD2/3 signalling pathway during the invasion of tumour cells in the development of MBD. We here provide a model for the dysregulation of the Endo180 network to demonstrate its vital contribution to bone destruction as well as tumour cell growth. The model consisted of a set of ordinary differential equations and reconstructed variations in the bone cells, resultant bone volume, and biochemical factors involved in the TGFβ-TGFβR-SMAD2/3 signalling pathway over time. The model also investigated the underlying mechanism in which the change of TGFβ affects the TGFβ-TGFβR-SMAD2/3 signalling pathway and the resultant Endo180 expression in osteoblastic and tumour cells. The model links the appearance of tumour cells with the inhibition of TGFβ binding to its receptors on osteoblastic cells, to affect TGFβ-TGFβR-SMAD2/3 signalling and Endo180 expression. Temporal variation in bone cells, bone volume, and the biochemical factors involved in the TGFβ-TGFβR-SMAD2/3 pathway as demonstrated in the model simulations agree with published experimental data. The model can be refined based on further discoveries but allows the influence of Endo180 network dysregulation on bone remodelling in MBD to be established. This model could aid in the development of Endo180 targeted therapies for MBD in the future.
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11
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Lorenzo G, Pérez-García VM, Mariño A, Pérez-Romasanta LA, Reali A, Gomez H. Mechanistic modelling of prostate-specific antigen dynamics shows potential for personalized prediction of radiation therapy outcome. J R Soc Interface 2019; 16:20190195. [PMID: 31409240 DOI: 10.1098/rsif.2019.0195] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
External beam radiation therapy is a widespread treatment for prostate cancer. The ensuing patient follow-up is based on the evolution of the prostate-specific antigen (PSA). Serum levels of PSA decay due to the radiation-induced death of tumour cells and cancer recurrence usually manifest as a rising PSA. The current definition of biochemical relapse requires that PSA reaches nadir and starts increasing, which delays the use of further treatments. Also, these methods do not account for the post-radiation tumour dynamics that may contain early information on cancer recurrence. Here, we develop three mechanistic models of post-radiation PSA evolution. Our models render superior fits of PSA data in a patient cohort and provide a biological justification for the most common empirical formulation of PSA dynamics. We also found three model-based prognostic variables: the proliferation rate of the survival fraction, the ratio of radiation-induced cell death rate to the survival proliferation rate, and the time to PSA nadir since treatment termination. We argue that these markers may enable the early identification of biochemical relapse, which would permit physicians to subsequently adapt patient monitoring to optimize the detection and treatment of cancer recurrence.
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Affiliation(s)
- Guillermo Lorenzo
- Dipartimento di Ingegneria Civile e Architettura, Università degli Studi di Pavia, Via Ferrata 3, 27100 Pavia, Italy.,Departamento de Matemáticas, Universidade da Coruña, Campus de Elviña s/n, 15071 A Coruña, Spain
| | - Víctor M Pérez-García
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Edificio Politécnico, Avenida Camilo José Cela 3, 13071 Ciudad Real, Spain
| | - Alfonso Mariño
- Servicio de Oncología Radioterápica, Centro Oncológico de Galicia, Calle Doctor Camilo Veiras 1, 15009 A Coruña, Spain
| | - Luis A Pérez-Romasanta
- Servicio de Oncología Radioterápica, Hospital Universitario de Salamanca, Paseo de San Vicente 58-182, 37007 Salamanca, Spain
| | - Alessandro Reali
- Dipartimento di Ingegneria Civile e Architettura, Università degli Studi di Pavia, Via Ferrata 3, 27100 Pavia, Italy
| | - Hector Gomez
- School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907, USA.,Weldon School of Biomedical Engineering, Purdue University, 206 S. Martin Jischke Drive, West Lafayette, IN 47907, USA.,Purdue Center for Cancer Research, Purdue University, 201 S. University Street, West Lafayette, IN 47907, USA
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12
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Camacho A, Jerez S. Bone metastasis treatment modeling via optimal control. J Math Biol 2018; 78:497-526. [DOI: 10.1007/s00285-018-1281-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2017] [Revised: 07/29/2018] [Indexed: 12/14/2022]
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13
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López JI, Angulo JC. Pathological Bases and Clinical Impact of Intratumor Heterogeneity in Clear Cell Renal Cell Carcinoma. Curr Urol Rep 2018; 19:3. [PMID: 29374850 DOI: 10.1007/s11934-018-0754-7] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
PURPOSE OF REVIEW Intratumor heterogeneity is an inherent event in tumor development that is receiving much attention in the last years since it is responsible for most failures of current targeted therapies. The purpose of this review is to offer clinicians an updated insight of the multiple manifestations of a complex event that impacts significantly patient's life. RECENT FINDINGS Clear cell renal cell carcinoma is the most common renal tumor and a paradigmatic example of a heterogeneous neoplasm. Next-generation sequencing has demonstrated that intratumor heterogeneity encompasses genetic, epigenetic, and microenvironmental variability. Currently accepted protocols of tumor sampling seem insufficient in unveiling intratumor heterogeneity with reliability and need to be updated. This variability challenges the precise morphological diagnosis, its molecular characterization, and the selection of optimal personalized therapies in clear cell renal cell carcinoma, a neoplasm traditionally considered chemo- and radio-resistant. We review the state of the art of the different approaches to intratumor heterogeneity in clear cell renal cell carcinomas, from the simple morphology to the most sophisticated massive sequencing tools.
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Affiliation(s)
- José I López
- Department of Pathology, Cruces University Hospital, Biocruces Research Institute, University of the Basque Country (UPV/EHU), 48903, Barakaldo, Spain.
| | - Javier C Angulo
- Clinical Department, Urology, Hospital Universitario de Getafe, Universidad Europea de Madrid, 28905, Madrid, Spain
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