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Dobrovolny HM. How do viruses get around? A review of mathematical modeling of in-host viral transmission. Virology 2025; 604:110444. [PMID: 39908773 DOI: 10.1016/j.virol.2025.110444] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2024] [Revised: 01/21/2025] [Accepted: 01/29/2025] [Indexed: 02/07/2025]
Abstract
Mathematical models of within host viral infections have provided important insights into the dynamics of viral infections. There has been much progress in adding more detailed biological processes to these models, such as incorporating the immune response, drug resistance, and viral coinfections. Unfortunately, the default assumption for the majority of these models is that virus is released from infected cells, travels through extracellular space, and deposits on another cell. This mode of transmission is known as cell-free infection. However, virus can also tunnel directly from one cell to another or cause neighboring cells to fuse, processes that also pass the infection to new cells. Additionally, most models do not explicitly include the transport of virus from one cell to another when describing cell-free transmission. In this review, we examine the current state of mathematical modeling that explicitly examines transmission beyond the cell-free assumption. While mathematical models have been developed to examine these processes, there are further improvements that can be made to better capture known viral dynamics.
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Affiliation(s)
- Hana M Dobrovolny
- Department of Physics & Astronomy, Texas Christian University, United States.
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2
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Macarie AC, Suveges S, Okasha M, Hossain-Ibrahim K, Steele JD, Trucu D. Post-operative glioblastoma cancer cell distribution in the peritumoural oedema. Front Oncol 2024; 14:1447010. [PMID: 39726706 PMCID: PMC11669604 DOI: 10.3389/fonc.2024.1447010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2024] [Accepted: 09/20/2024] [Indexed: 12/28/2024] Open
Abstract
Glioblastoma multiforme (GBM), the most aggressive primary brain tumour, exhibits low survival rates due to its rapid growth, infiltrates surrounding brain tissue, and is highly resistant to treatment. One major challenge is oedema infiltration, a fluid build-up that provides a path for cancer cells to invade other areas. MRI resolution is insufficient to detect these infiltrating cells, leading to relapses despite chemotherapy and radiotherapy. In this work, we propose a new multiscale mathematical modelling method, to explore the oedema infiltration and predict tumour relapses. To address tumour relapses, we investigated several possible scenarios for the distribution of remaining GBM cells within the oedema after surgery. Furthermore, in this computational modelling investigation on tumour relapse scenarios were investigated assuming the presence of clinically relevant chemo-radio therapy, numerical results suggest that a higher concentration of GBM cells near the surgical cavity edge led to limited spread and slower progression of tumour relapse. Finally, we explore mathematical and computational avenues for reconstructing relevant shapes for the initial distributions of GBM cells within the oedema from available MRI scans. The results obtained show good overlap between our simulation and the patient's serial MRI scans taken 881 days into the treatment. While still under analytical investigation, this work paves the way for robust reconstruction of tumour relapses from available clinical data.
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Affiliation(s)
- Andrei Ciprian Macarie
- Division of Mathematics, University of Dundee, Dundee, United Kingdom
- Division of Neuroscience, School of Medicine, University of Dundee, Dundee, United Kingdom
| | - Szabolcs Suveges
- Division of Neuroscience, School of Medicine, University of Dundee, Dundee, United Kingdom
| | - Mohamed Okasha
- Department of Neurosurgery, Ninewells Hospital and School of Medicine, National Health Service (NHS) Tayside, Dundee, United Kingdom
| | - Kismet Hossain-Ibrahim
- Department of Neurosurgery, Ninewells Hospital and School of Medicine, National Health Service (NHS) Tayside, Dundee, United Kingdom
| | - J. Douglas Steele
- Division of Neuroscience, School of Medicine, University of Dundee, Dundee, United Kingdom
| | - Dumitru Trucu
- Division of Mathematics, University of Dundee, Dundee, United Kingdom
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3
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Glaschke S, Dobrovolny HM. Spatiotemporal spread of oncolytic virus in a heterogeneous cell population. Comput Biol Med 2024; 183:109235. [PMID: 39369544 DOI: 10.1016/j.compbiomed.2024.109235] [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: 07/12/2024] [Revised: 09/27/2024] [Accepted: 09/30/2024] [Indexed: 10/08/2024]
Abstract
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.
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Affiliation(s)
- Sabrina Glaschke
- Institute of Physics, Universitat Kassel, Kassel, Germany; Department of Physics & Astronomy, Texas Christian University, Fort Worth, TX, USA
| | - Hana M Dobrovolny
- Department of Physics & Astronomy, Texas Christian University, Fort Worth, TX, USA.
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4
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Buntval K, Dobrovolny HM. Modeling of oncolytic viruses in a heterogeneous cell population to predict spread into non-cancerous cells. Comput Biol Med 2023; 165:107362. [PMID: 37633084 DOI: 10.1016/j.compbiomed.2023.107362] [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: 11/11/2022] [Revised: 08/06/2023] [Accepted: 08/12/2023] [Indexed: 08/28/2023]
Abstract
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.
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Affiliation(s)
- Karan Buntval
- SUNY Upstate Medical University, Syracuse, NY, United States of America; Department of Physics and Astronomy, Texas Christian University, Fort Worth, TX, United States of America
| | - Hana M Dobrovolny
- Department of Physics and Astronomy, Texas Christian University, Fort Worth, TX, United States of America.
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5
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Parra-Guillen ZP, Sancho-Araiz A, Mayawala K, Zalba S, Garrido MJ, de Alwis D, Troconiz IF, Freshwater T. Assessment of Clinical Response to V937 Oncolytic Virus After Intravenous or Intratumoral Administration Using Physiologically-Based Modeling. Clin Pharmacol Ther 2023; 114:623-632. [PMID: 37170933 DOI: 10.1002/cpt.2937] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Accepted: 05/03/2023] [Indexed: 05/13/2023]
Abstract
Oncolytic viruses (OVs) represent a potential therapeutic strategy in cancer treatment. However, there is currently a lack of comprehensive quantitative models characterizing clinical OV kinetics and distribution to the tumor. In this work, we present a mechanistic modeling framework for V937 OV, after intratumoral (i.t.) or intravascular (i.v.) administration in patients with cancer. A minimal physiologically-based pharmacokinetic model was built to characterize biodistribution of OVs in humans. Viral dynamics was incorporated at the i.t. cellular level and linked to tumor response, enabling the characterization of a direct OV killing triggered by the death of infected tumor cells and an indirect killing induced by the immune response. The model provided an adequate description of changes in V937 mRNA levels and tumor size obtained from phase I/II clinical trials after V937 administration. The model showed prominent role of viral clearance from systemic circulation and infectivity in addition to known tumor aggressiveness on clinical response. After i.v. administration, i.t. exposure of V937 was predicted to be several orders of magnitude lower compared with i.t. administration. These differences could be overcome if there is high virus infectivity and/or replication. Unfortunately, the latter process could not be identified at the current clinical setting. This work provides insights on selecting optimal OV considering replication rate and infectivity.
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Affiliation(s)
- Zinnia P Parra-Guillen
- Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain
- IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
| | - Aymara Sancho-Araiz
- Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain
- IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
| | - Kapil Mayawala
- Quantitative Pharmacology and Pharmacometrics Immune/Oncology (QP2-I/O), Merck & Co., Inc., Rahway, New Jersey, USA
| | - Sara Zalba
- Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain
- IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
| | - Maria J Garrido
- Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain
- IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
| | - Dinesh de Alwis
- Quantitative Pharmacology and Pharmacometrics Immune/Oncology (QP2-I/O), Merck & Co., Inc., Rahway, New Jersey, USA
| | - Iñaki F Troconiz
- Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain
- IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
| | - Tomoko Freshwater
- Quantitative Pharmacology and Pharmacometrics Immune/Oncology (QP2-I/O), Merck & Co., Inc., Rahway, New Jersey, USA
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6
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Iqbal J, Ahmad S, Marwan M, Rafiq A. Control analysis of virotherapy chaotic system. JOURNAL OF BIOLOGICAL DYNAMICS 2022; 16:585-595. [PMID: 35894929 DOI: 10.1080/17513758.2022.2104391] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2021] [Accepted: 07/18/2022] [Indexed: 06/15/2023]
Abstract
In this work, we consider a chaotic system that plays a vital role in the treatment of cancer by injection of a virus externally. Due to the sensitivity of this disease, most of its treatments are highly risky. Therefore, we have designed control inputs using adaptive and passive control techniques for virotherapy. Both controllers are designed to bring global stability to the cancer system with the aid of a quadratic Lyapunov function. Furthermore, we use simulations to verify our controllers. Moreover, we show that our adaptive control technique gives better results in comparison.
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Affiliation(s)
- Javaria Iqbal
- Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabd, Pakistan
| | - Salman Ahmad
- Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabd, Pakistan
| | - Muhammad Marwan
- College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, People's Republic of China
| | - Ayesha Rafiq
- Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabd, Pakistan
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7
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Stochastic Analysis of Nonlinear Cancer Disease Model through Virotherapy and Computational Methods. MATHEMATICS 2022. [DOI: 10.3390/math10030368] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Cancer is a common term for many diseases that can affect anybody. A worldwide leading cause of death is cancer, according to the World Health Organization (WHO) report. In 2020, ten million people died from cancer. This model identifies the interaction of cancer cells, viral therapy, and immune response. In this model, the cell population has four parts, namely uninfected cells (x), infected cells (y), virus-free cells (v), and immune cells (z). This study presents the analysis of the stochastic cancer virotherapy model in the cell population dynamics. The model results have restored the properties of the biological problem, such as dynamical consistency, positivity, and boundedness, which are the considerable requirements of the models in these fields. The existing computational methods, such as the Euler Maruyama, Stochastic Euler, and Stochastic Runge Kutta, fail to restore the abovementioned properties. The proposed stochastic nonstandard finite difference method is efficient, cost-effective, and accommodates all the desired feasible properties. The existing standard stochastic methods converge conditionally or diverge in the long run. The solution by the nonstandard finite difference method is stable and convergent over all time steps.
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8
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Loyinmi AC, Akinfe TK, Ojo AA. Qualitative analysis and dynamical behavior of a Lassa haemorrhagic fever model with exposed rodents and saturated incidence rate. SCIENTIFIC AFRICAN 2021. [DOI: 10.1016/j.sciaf.2021.e01028] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022] Open
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9
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Parra-Guillen ZP, Freshwater T, Cao Y, Mayawala K, Zalba S, Garrido MJ, de Alwis D, Troconiz IF. Mechanistic Modeling of a Novel Oncolytic Virus, V937, to Describe Viral Kinetic and Dynamic Processes Following Intratumoral and Intravenous Administration. Front Pharmacol 2021; 12:705443. [PMID: 34366859 PMCID: PMC8343024 DOI: 10.3389/fphar.2021.705443] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Accepted: 07/07/2021] [Indexed: 12/28/2022] Open
Abstract
V937 is an investigational novel oncolytic non-genetically modified Kuykendall strain of Coxsackievirus A21 which is in clinical development for the treatment of advanced solid tumor malignancies. V937 infects and lyses tumor cells expressing the intercellular adhesion molecule I (ICAM-I) receptor. We integrated in vitro and in vivo data from six different preclinical studies to build a mechanistic model that allowed a quantitative analysis of the biological processes of V937 viral kinetics and dynamics, viral distribution to tumor, and anti-tumor response elicited by V937 in human xenograft models in immunodeficient mice following intratumoral and intravenous administration. Estimates of viral infection and replication which were calculated from in vitro experiments were successfully used to describe the tumor response in vivo under various experimental conditions. Despite the predicted high clearance rate of V937 in systemic circulation (t1/2 = 4.3 min), high viral replication was observed in immunodeficient mice which resulted in tumor shrinkage with both intratumoral and intravenous administration. The described framework represents a step towards the quantitative characterization of viral distribution, replication, and oncolytic effect of a novel oncolytic virus following intratumoral and intravenous administrations in the absence of an immune response. This model may further be expanded to integrate the role of the immune system on viral and tumor dynamics to support the clinical development of oncolytic viruses.
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Affiliation(s)
- Zinnia P Parra-Guillen
- Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain.,IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
| | | | - Youfang Cao
- Merck & Co., Inc., Kenilworth, NJ, United States
| | | | - Sara Zalba
- Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain.,IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
| | - Maria J Garrido
- Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain.,IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
| | | | - Iñaki F Troconiz
- Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain.,IdiSNA, Navarra Institute for Health Research, Pamplona, Spain
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10
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Costa A, Vale N. Strategies for the treatment of breast cancer: from classical drugs to mathematical models. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:6328-6385. [PMID: 34517536 DOI: 10.3934/mbe.2021316] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Breast cancer is one of the most common cancers and generally affects women. It is a heterogeneous disease that presents different entities, different biological characteristics, and differentiated clinical behaviors. With this in mind, this literature review had as its main objective to analyze the path taken from the simple use of classical drugs to the application of mathematical models, which through the many ongoing studies, have been considered as one of the reliable strategies, explaining the reasons why chemotherapy is not always successful. Besides, the most commonly mentioned strategies are immunotherapy, which includes techniques and therapies such as the use of antibodies, cytokines, antitumor vaccines, oncolytic and genomic viruses, among others, and nanoparticles, including metallic, magnetic, polymeric, liposome, dendrimer, micelle, and others, as well as drug reuse, which is a process by which new therapeutic indications are found for existing and approved drugs. The most commonly used pharmacological categories are cardiac, antiparasitic, anthelmintic, antiviral, antibiotic, and others. For the efficient development of reused drugs, there must be a process of exchange of purposes, methods, and information already available, and for their better understanding, computational mathematical models are then used, of which the methods of blind search or screening, based on the target, knowledge, signature, pathway or network and the mechanism to which it is directed, stand out. To conclude it should be noted that these different strategies can be applied alone or in combination with each other always to improve breast cancer treatment.
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Affiliation(s)
- Ana Costa
- OncoPharma Research Group, Center for Health Technology and Services Research (CINTESIS), Rua Dr. Plácido da Costa, 4200-450 Porto, Portugal
| | - Nuno Vale
- OncoPharma Research Group, Center for Health Technology and Services Research (CINTESIS), Rua Dr. Plácido da Costa, 4200-450 Porto, Portugal
- Department of Community Medicine, Health Information and Decision (MEDCIDS), Faculty of Medicine, University of Porto, Al. Prof. Hernâni Monteiro, 4200-319 Porto, Portugal
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11
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Mobaraki M, Moradi H. Design of robust control strategy in drug and virus scheduling in nonlinear process of chemovirotherapy. Comput Chem Eng 2021. [DOI: 10.1016/j.compchemeng.2021.107318] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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12
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Cassidy T, Humphries AR. A mathematical model of viral oncology as an immuno-oncology instigator. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2021; 37:117-151. [PMID: 31329873 DOI: 10.1093/imammb/dqz008] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2018] [Revised: 02/15/2019] [Accepted: 03/26/2019] [Indexed: 12/14/2022]
Abstract
We develop and analyse a mathematical model of tumour-immune interaction that explicitly incorporates heterogeneity in tumour cell cycle duration by using a distributed delay differential equation. We derive a necessary and sufficient condition for local stability of the cancer-free equilibrium in which the amount of tumour-immune interaction completely characterizes disease progression. Consistent with the immunoediting hypothesis, we show that decreasing tumour-immune interaction leads to tumour expansion. Finally, by simulating the mathematical model, we show that the strength of tumour-immune interaction determines the long-term success or failure of viral therapy.
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Affiliation(s)
- Tyler Cassidy
- Department of Mathematics and Statistics, McGill University, Montreal, Canada
| | - Antony R Humphries
- Department of Mathematics and Statistics, McGill University, Montreal, Canada.,Department of Physiology, McGill University, Montreal, Canada
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13
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Mathematical modelling of the dynamics of prostate cancer with a curative vaccine. SCIENTIFIC AFRICAN 2021. [DOI: 10.1016/j.sciaf.2021.e00715] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
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14
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Malinzi J, Basita KB, Padidar S, Adeola HA. Prospect for application of mathematical models in combination cancer treatments. INFORMATICS IN MEDICINE UNLOCKED 2021. [DOI: 10.1016/j.imu.2021.100534] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023] Open
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15
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Pooladvand P, Yun CO, Yoon AR, Kim PS, Frascoli F. The role of viral infectivity in oncolytic virotherapy outcomes: A mathematical study. Math Biosci 2020; 334:108520. [PMID: 33290764 DOI: 10.1016/j.mbs.2020.108520] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2020] [Revised: 10/15/2020] [Accepted: 12/01/2020] [Indexed: 10/22/2022]
Abstract
A model capturing the dynamics between virus and tumour cells in the context of oncolytic virotherapy is presented and analysed. The ability of the virus to be internalised by uninfected cells is described by an infectivity parameter, which is inferred from available experimental data. The parameter is also able to describe the effects of changes in the tumour environment that affect viral uptake from tumour cells. Results show that when a virus is inoculated inside a growing tumour, strategies for enhancing infectivity do not lead to a complete eradication of the tumour. Within typical times of experiments and treatments, we observe the onset of oscillations, which always prevent a full destruction of the tumour mass. These findings are in good agreement with available laboratory results. Further analysis shows why a fully successful therapy cannot exist for the proposed model and that care must be taken when designing and engineering viral vectors with enhanced features. In particular, bifurcation analysis reveals that creating longer lasting virus particles or using strategies for reducing infected cell lifespan can cause unexpected and unwanted surges in the overall tumour load over time. Our findings suggest that virotherapy alone seems unlikely to be effective in clinical settings unless adjuvant strategies are included.
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Affiliation(s)
- Pantea Pooladvand
- School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia.
| | - Chae-Ok Yun
- Department of Bioengineering, Collage of Engineering, Hanyang University, Seoul, South Korea; Institute of Nano Science and Technology (INST), Hanyang University, Seoul, South Korea
| | - A-Rum Yoon
- Department of Bioengineering, Collage of Engineering, Hanyang University, Seoul, South Korea; Institute of Nano Science and Technology (INST), Hanyang University, Seoul, South Korea
| | - Peter S Kim
- School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia
| | - Federico Frascoli
- Department of Mathematics, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne, VIC 3122, Australia
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16
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Multidirectional Strategies for Targeted Delivery of Oncolytic Viruses by Tumor Infiltrating Immune Cells. Pharmacol Res 2020; 161:105094. [PMID: 32795509 DOI: 10.1016/j.phrs.2020.105094] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/31/2020] [Revised: 07/18/2020] [Accepted: 07/20/2020] [Indexed: 02/07/2023]
Abstract
Oncolytic virus (OV) immunotherapy has demonstrated to be a promising approach in cancer treatment due to tumor-specific oncolysis. However, their clinical use so far has been largely limited due to the lack of suitable delivery strategies with high efficacy. Direct 'intratumoral' injection is the way to cross the hurdles of systemic toxicity, while providing local effects. Progress in this field has enabled the development of alternative way using 'systemic' oncolytic virotherapy for producing better results. One major potential roadblock to systemic OV delivery is the low virus persistence in the face of hostile immune system. The delivery challenge is even greater when attempting to target the oncolytic viruses into the entire tumor mass, where not all tumor cells are equally exposed to exactly the same microenvironment. The microenvironment of many tumors is known to be massively infiltrated with various types of leucocytes in both primary and metastatic sites. Interestingly, this intratumoral immune cell heterogeneity exhibits a degree of organized distribution inside the tumor bed as evidenced, for example, by the hypoxic tumor microenviroment where predominantly recruits tumor-associated macrophages. Although in vivo OV delivery seems complicated and challenging, recent results are encouraging for decreasing the limitations of systemically administered oncolytic viruses and an improved efficiency of oncolytic viral therapy in targeting cancerous tissues in vitro. Here, we review the latest developments of carrier cell-based oncolytic virus delivery using tumor-infiltrating immune cells with a focus on the main features of each cellular vehicle.
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17
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Chen J, Weihs D, Vermolen FJ. A Cellular Automata Model of Oncolytic Virotherapy in Pancreatic Cancer. Bull Math Biol 2020; 82:103. [PMID: 32737595 PMCID: PMC7395005 DOI: 10.1007/s11538-020-00780-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2020] [Accepted: 07/16/2020] [Indexed: 01/02/2023]
Abstract
Oncolytic virotherapy is known as a new treatment to employ less virulent viruses to specifically target and damage cancer cells. This work presents a cellular automata model of oncolytic virotherapy with an application to pancreatic cancer. The fundamental biomedical processes (like cell proliferation, mutation, apoptosis) are modeled by the use of probabilistic principles. The migration of injected viruses (as therapy) is modeled by diffusion through the tissue. The resulting diffusion–reaction equation with smoothed point viral sources is discretized by the finite difference method and integrated by the IMEX approach. Furthermore, Monte Carlo simulations are done to quantitatively evaluate the correlations between various input parameters and numerical results. As we expected, our model is able to simulate the pancreatic cancer growth at early stages, which is calibrated with experimental results. In addition, the model can be used to predict and evaluate the therapeutic effect of oncolytic virotherapy.
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Affiliation(s)
- J Chen
- Department of Biomedical Engineering and Physics, Amsterdam UMC, Amsterdam, The Netherlands.
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands.
| | - D Weihs
- Faculty of Biomedical Engineering, Technion-Israel Institute of Technology, Haifa, Israel
| | - F J Vermolen
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
- Division of Mathematics and Statistics, Faculty of Sciences, Hasselt University, Diepenbeek, Belgium
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18
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Heidbuechel JPW, Abate-Daga D, Engeland CE, Enderling H. Mathematical Modeling of Oncolytic Virotherapy. Methods Mol Biol 2020; 2058:307-320. [PMID: 31486048 DOI: 10.1007/978-1-4939-9794-7_21] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
Mathematical modeling in biology has a long history as it allows the analysis and simulation of complex dynamic biological systems at little cost. A mathematical model trained on experimental or clinical data can be used to generate and evaluate hypotheses, to ask "what if" questions, and to perform in silico experiments to guide future experimentation and validation. Such models may help identify and provide insights into the mechanisms that drive changes in dynamic systems. While a mathematical model may never replace actual experiments, it can synergize with experiments to save time and resources by identifying experimental conditions that are unlikely to yield favorable outcomes, and by using optimization principles to identify experiments that are most likely to be successful. Over the past decade, numerous models have also been developed for oncolytic virotherapy, ranging from merely theoretic frameworks to fully integrated studies that utilize experimental data to generate actionable hypotheses. Here we describe how to develop such models for specific oncolytic virotherapy experimental setups, and which questions can and cannot be answered using integrated mathematical oncology.
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Affiliation(s)
- Johannes P W Heidbuechel
- Research Group Mechanisms of Oncolytic Immunotherapy, Clinical Cooperation Unit Virotherapy, National Center for Tumor Diseases (NCT), German Cancer Research Center (DKFZ), University Hospital Heidelberg, Heidelberg, Germany.,Faculty of Biosciences, Heidelberg University, Heidelberg, Germany
| | - Daniel Abate-Daga
- Department of Immunology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, USA
| | - Christine E Engeland
- Research Group Mechanisms of Oncolytic Immunotherapy, Clinical Cooperation Unit Virotherapy, National Center for Tumor Diseases (NCT), German Cancer Research Center (DKFZ), University Hospital Heidelberg, Heidelberg, Germany
| | - Heiko Enderling
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, USA.
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Investigating Macrophages Plasticity Following Tumour-Immune Interactions During Oncolytic Therapies. Acta Biotheor 2019; 67:321-359. [PMID: 31410657 PMCID: PMC6825040 DOI: 10.1007/s10441-019-09357-9] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2018] [Accepted: 08/02/2019] [Indexed: 12/22/2022]
Abstract
Over the last few years, oncolytic virus therapy has been recognised as a promising approach in cancer treatment, due to the potential of these viruses to induce systemic anti-tumour immunity and selectively killing tumour cells. However, the effectiveness of these viruses depends significantly on their interactions with the host immune responses, both innate (e.g., macrophages, which accumulate in high numbers inside solid tumours) and adaptive (e.g., \documentclass[12pt]{minimal}
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\begin{document}$$\hbox {CD8}^{+}$$\end{document}CD8+ T cells). In this article, we consider a mathematical approach to investigate the possible outcomes of the complex interactions between two extreme types of macrophages (M1 and M2 cells), effector \documentclass[12pt]{minimal}
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\begin{document}$$\hbox {CD8}^{+}$$\end{document}CD8+ T cells and an oncolytic Vesicular Stomatitis Virus (VSV), on the growth/elimination of B16F10 melanoma. We discuss, in terms of VSV, \documentclass[12pt]{minimal}
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\begin{document}$$\hbox {CD8}^{+}$$\end{document}CD8+ and macrophages levels, two different types of immune responses which could ensure tumour control and eventual elimination. We show that both innate and adaptive anti-tumour immune responses, as well as the oncolytic virus, could be very important in delaying tumour relapse and eventually eliminating the tumour. Overall this study supports the use mathematical modelling to increase our understanding of the complex immune interaction following oncolytic virotherapies. However, the complexity of the model combined with a lack of sufficient data for model parametrisation has an impact on the possibility of making quantitative predictions.
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Dynamics of Breast Cancer under Different Rates of Chemoradiotherapy. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2019; 2019:5216346. [PMID: 31611927 PMCID: PMC6755298 DOI: 10.1155/2019/5216346] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Accepted: 07/21/2019] [Indexed: 12/30/2022]
Abstract
A type of cancer which originates from the breast tissue is referred to as breast cancer. Globally, it is the most common cause of death in women. Treatments such as radiotherapy, chemotherapy, hormone therapy, immunotherapy, and gene therapy are the main strategies in the fight against breast cancer. The present study aims at investigating the effects of the combined radiotherapy and chemotherapy as a way to treat breast cancer, and different treatment approaches are incorporated into the model. Also, the model is fitted to data on patients with breast cancer in Tanzania. We determine new treatment strategies, and finally, we show that when sufficient amount of chemotherapy and radiotherapy with a low decay rate is used, the drug will be significantly more effective in combating the disease while health cells remain above the threshold.
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Alzahrani T, Eftimie R, Trucu D. Multiscale modelling of cancer response to oncolytic viral therapy. Math Biosci 2019; 310:76-95. [DOI: 10.1016/j.mbs.2018.12.018] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2018] [Revised: 12/29/2018] [Accepted: 12/29/2018] [Indexed: 12/29/2022]
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Mathematical Analysis of a Mathematical Model of Chemovirotherapy: Effect of Drug Infusion Method. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2019; 2019:7576591. [PMID: 30984283 PMCID: PMC6432739 DOI: 10.1155/2019/7576591] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/17/2018] [Revised: 01/14/2019] [Accepted: 01/28/2019] [Indexed: 12/31/2022]
Abstract
A mathematical model for the treatment of cancer using chemovirotherapy is developed with the aim of determining the efficacy of three drug infusion methods: constant, single bolus, and periodic treatments. The model is in the form of ODEs and is further extended into DDEs to account for delays as a result of the infection of tumor cells by the virus and chemotherapeutic drug responses. Analysis of the model is carried out for each of the three drug infusion methods. Analytic solutions are determined where possible and stability analysis of both steady state solutions for the ODEs and DDEs is presented. The results indicate that constant and periodic drug infusion methods are more efficient compared to a single bolus injection. Numerical simulations show that with a large virus burst size, irrespective of the drug infusion method, chemovirotherapy is highly effective compared to either treatments. The simulations further show that both delays increase the period within which a tumor can be cleared from body tissue.
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23
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Optimal Control Analysis of a Mathematical Model for Breast Cancer. MATHEMATICAL AND COMPUTATIONAL APPLICATIONS 2018. [DOI: 10.3390/mca23020021] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
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