Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment

Chemovirotherapy is a combination therapy with chemotherapy and oncolytic viruses. It is gaining more interest and attracting more attention in the clinical setting due to its effective therapy and potential synergistic interactions against cancer. In this paper, we develop and analyse a mathematical model in the form of parabolic non-linear partial differential equations to investigate the spatiotemporal dynamics of tumour cells under chemovirotherapy treatment. The proposed model consists of uninfected and infected tumour cells, a free virus, and a chemotherapeutic drug. The analysis of the model is carried out for both the temporal and spatiotemporal cases. Travelling wave solutions to the spatiotemporal model are used to determine the minimum wave speed of tumour invasion. A sensitivity analysis is performed on the model parameters to establish the key parameters that promote cancer remission during chemovirotherapy treatment. Model analysis of the temporal model suggests that virus burst size and virus infection rate determine the success of the virotherapy treatment, whereas travelling wave solutions to the spatiotemporal model show that tumour diffusivity and growth rate are critical during chemovirotherapy. Simulation results reveal that chemovirotherapy is more effective and a good alternative to either chemotherapy or virotherapy, which is in agreement with the recent experimental studies.     

Mathematical and Computational Modeling for Tumor Virotherapy with Mediated Immunity

We propose a new mathematical modeling framework based on partial differential equations to study tumor virotherapy with mediated immunity. The model incorporates both innate and adaptive immune responses and represents the complex interaction among tumor cells, oncolytic viruses, and immune systems on a domain with a moving boundary. Using carefully designed computational methods, we conduct extensive numerical simulation to the model. The results allow us to examine tumor development under a wide range of settings and provide insight into several important aspects of the virotherapy, including the dependence of the efficacy on a few key parameters and the delay in the adaptive immunity. Our findings also suggest possible ways to improve the virotherapy for tumor treatment.     

Kinetic Instability of Zero Steady State As a Fundamental Cause of Low Efficiency of Chemotherapy of Cancer

Using mathematical modeling of the process of cancer treatment by the classical chemotherapy methods and therapy with biological agents, the effect of the kinetic parameters of the model on the final outcome of treatment was studied. It is established that the complete cure (i.e., the formation of a stable steady state with a zero number of cancer cells) cannot be reached by means of only classical chemotherapy.     

Oncolytic virotherapy

Oncolytic virotherapy is an emerging treatment modality that uses replication-competent viruses to destroy cancers. Recent advances include preclinical proof of feasibility for a single-shot virotherapy cure, identification of drugs that accelerate intratumoral virus propagation, strategies to maximize the immunotherapeutic action of oncolytic viruses and clinical confirmation of a critical viremic threshold for vascular delivery and intratumoral virus replication. The primary clinical milestone has been completion of accrual in a phase 3 trial of intratumoral herpes simplex virus therapy using talimogene laherparepvec for metastatic melanoma. Key challenges for the field are to select 'winners' from a burgeoning number of oncolytic platforms and engineered derivatives, to transiently suppress but then unleash the power of the immune system to maximize both virus spread and anticancer immunity, to develop more meaningful preclinical virotherapy models and to manufacture viruses with orders-of-magnitude higher yields than is currently possible.     

Targeting gene-virotherapy of cancer and its prosperity

Gene and viral therapies for cancer have shown some therapeutic effects, but there has been a lack of real breakthrough. To achieve the goal of complete elimination of tumor xenograft in animal models, we have developed a new strategy called Targeting Gene-Virotherapy of Cancer, which aims to combine the advantages of both gene therapy and virotherapy. This new strategy has produced stronger anti-tumor effects than either gene or viral therapy alone. A tumorspecific replicative adenovirus vector, designated as ZD55, was constructed by deletion of the 55kDa E1B region of adenovirus. The resulting viral construct not only retains a similar function to ONYX-015 by specifically targeting p53 negative tumors, but also allows for the insertion of various therapeutic genes to form appropriate ZD55 derivatives due to the newly introduced cloning site, a task not feasible with the original ONYX-015 virus. We showed that the anti-tumor effect of one such derivative, ZD55-IL-24, is at least 100 times more potent than that of either ZD55 virotherapy or Ad-IL-24 gene therapy. Nevertheless, complete elimination of tumor mass by the use of ZD55-1L-24 was only observed in some but not all mice, indicating that one therapeutic gene was not sufficient to ＂cure＂ these mice. When genes with complementary or synergetic effects were separately cloned into the ZD55 vector and used in combination （designated as the Dual Gene Therapy strategy）, much better results were obtained; and it was possible to achieve complete elimination of all the xenograft tumor masses in all mice if two suitable genes were chosen. More comprehensive studies based on this new strategy will likely lead to a protocol for clinical trial. Finally, the concept of Double Controlled Targeting Virus-Dual Gene Therapy for cancer treatment, and the implication of the recent progress in cancer stem cells are also discussed.     

BCG-Mediated Bladder Cancer Immunotherapy: Identifying Determinants of Treatment Response Using a Calibrated Mathematical Model

Intravesical Bacillus Calmette Guérin (BCG) immunotherapy is considered the standard of care for treatment of non-muscle invasive bladder cancer; however the treatment parameters were established empirically. In order to evaluate potential optimization of clinical parameters of BCG induction therapy, we constructed and queried a new mathematical model. Specifically, we assessed the impact of (1) duration between resection and the first instillation; (2) BCG dose; (3) indwelling time; and (4) treatment interval of induction therapy – using cure rate as the primary endpoint. Based on available clinical and in vitro experimental data, we constructed and parameterized a stochastic mathematical model describing the interactions between BCG, the immune system, the bladder mucosa and tumor cells. The primary endpoint of the model was the probability of tumor extinction following BCG induction therapy in patients with high risk for tumor recurrence. We theoretically demonstrate that extending the duration between the resection and the first BCG instillation negatively influences treatment outcome. Simulations of higher BCG doses and longer indwelling times both improved the probability of tumor extinction. A remarkable finding was that an inter-instillation interval two times longer than the seven-day interval used in the current standard of care would substantially improve treatment outcome. We provide insight into relevant clinical questions using a novel mathematical model of BCG immunotherapy. Our model predicts an altered regimen that may decrease side effects of treatment while improving response to therapy.     

Optimization of Virotherapy for Cancer

Several viruses preferentially infect and replicate in cancer cells by usurping pathways that are defective in the tumor cell population. Such viruses have a potential as oncolytic agents. The aim of tumor virotherapy is that after injection of the replicating virus, it propagates in the tumor cell population with amplification. As a result, the oncolytic virus spreads to eradicate the tumor. The outcome of tumor virotherapy is determined by population dynamics and different from standard cancer therapy. Several models have been developed that provided considerable insights on the potential therapeutic scenarios. However, virotherapy is potentially risky since large amounts of a replicating virus are injected in the host with a risk of adverse effects. Therefore, the optimal dose, number of doses, and timing are expected to play an important role on the outcome both for the tumor and the host. In the current work, we combine a model of the dynamics of tumor virotherapy that was validated with experimental data with optimization theory to illustrate how we can improve the outcome of tumor therapy. In this first report, we demonstrate that (i) in most circumstances, anything more than two administrations of a vector is not helpful, (ii) correctly timed delivery of the virus provides superior results compared to regularly scheduled therapy or continuous infusion, (iii) a second dose of virus that is not properly timed leads to a worse outcome compared to a single dose of virus, and (iv) it is less costly to treat larger tumors.     

一类带有肝炎B病毒感染的数学模型的全局稳定性分析（英文）

本文主要分析了一类具有肝炎B病毒感染且带有治愈率的典型的数学模型（HBV）.通过稳定性分析,得到了该模型的无病平衡点与地方病平衡点全局稳定的充分条件,并且证明了当基本再生数R0〈1, HBV感染消失;当R0〉1,HBV感染持续.     

Mathematical Modelling of the Interaction Between Cancer Cells and an Oncolytic Virus: Insights into the Effects of Treatment Protocols

Oncolytic virotherapy is an experimental cancer treatment that uses genetically engineered viruses to target and kill cancer cells. One major limitation of this treatment is that virus particles are rapidly cleared by the immune system, preventing them from arriving at the tumour site. To improve virus survival and infectivity Kim et al. (Biomaterials 32(9):2314–2326, 2011) modified virus particles with the polymer polyethylene glycol (PEG) and the monoclonal antibody herceptin. Whilst PEG modification appeared to improve plasma retention and initial infectivity, it also increased the virus particle arrival time. We derive a mathematical model that describes the interaction between tumour cells and an oncolytic virus. We tune our model to represent the experimental data by Kim et al. (2011) and obtain optimised parameters. Our model provides a platform from which predictions may be made about the response of cancer growth to other treatment protocols beyond those in the experiments. Through model simulations, we find that the treatment protocol affects the outcome dramatically. We quantify the effects of dosage strategy as a function of tumour cell replication and tumour carrying capacity on the outcome of oncolytic virotherapy as a treatment. The relative significance of the modification of the virus and the crucial role it plays in optimising treatment efficacy are explored.     

Targeting gene-virotherapy of cancer

Our purpose is to completely elimination of xenograft tumor in animal tumor model in order to work out a protocal for the cure of patient. Gene therapy and viral therapy for cancer have got some therapeutic effects, but both have no great breakthrough. Therefore, we worked out a new strategy called Targeting Gene-Virotherapy of Cancer which is a combination of the advantage of gene therapy and virotherapy. This new strategy has stronger antitumor effect than either of them alone. A tumor specific replicative adenovirus vector ZD55 (E1B 55KD deleted Adv.) which is similar to ONYX-015 in targeting fuction but significant different in construction was produced and various single therapeutic gene was inserted into ZD55. Now such a conception as Targeting Gene-Virotherapy of Cancer was raised and systemically studied before, although there are some works on ONYX-015-tk, -cd or cd/-tk etc. separately. The antitumor effect of ZD55-Gene (for example IL-24 gene) is much better than ZD55 (virotherapy) alone and hundred fold high than that of Ad-IL-24 (gene therapy) alone. ZD55-IL-24 was in preclinal studying in the ZD55-IL-24 therapy, completely elimination of tumor mass was occurred in some mice but not in all mice, that means one gene was not effictive enough to eliminate all the tumor mass in all mice. Therefore two genes with compensative or synergetic effect were inserted into ZD55 separately and used in combination. This strategy was called Targeting Dual Gene-Virotherapy of Cancer (with PCT patent). Then much better results were obtained and all the xenograft tumor masses were completely eliminated in all mice, if two suitable genes were chosen. On the basis of the initiation of two gene results, it was thought about that using two tumors promoter to control the virus vector will be better for the targeting effect and the safty of the drugs. Then double tumor controlled virus vector harboring two genes for cancer therapy was worked out. Better results have been obtained and another patent has been applied. This antitumor strategy could be used to kill all the tumor cells completely in all mice with minimum damage to normal cells.     

Dynamics and potential impact of the immune response to chronic myelogenous leukemia

Recent mathematical models have been developed to study the dynamics of chronic myelogenous leukemia (CML) under imatinib treatment. None of these models incorporates the anti-leukemia immune response. Recent experimental data show that imatinib treatment may promote the development of anti-leukemia immune responses as patients enter remission. Using these experimental data we develop a mathematical model to gain insights into the dynamics and potential impact of the resulting anti-leukemia immune response on CML. We model the immune response using a system of delay differential equations, where the delay term accounts for the duration of cell division. The mathematical model suggests that anti-leukemia T cell responses may play a critical role in maintaining CML patients in remission under imatinib therapy. Furthermore, it proposes a novel concept of an “optimal load zone” for leukemic cells in which the anti-leukemia immune response is most effective. Imatinib therapy may drive leukemic cell populations to enter and fall below this optimal load zone too rapidly to sustain the anti-leukemia T cell response. As a potential therapeutic strategy, the model shows that vaccination approaches in combination with imatinib therapy may optimally sustain the anti-leukemia T cell response to potentially eradicate residual leukemic cells for a durable cure of CML. The approach presented in this paper accounts for the role of the anti-leukemia specific immune response in the dynamics of CML. By combining experimental data and mathematical models, we demonstrate that persistence of anti-leukemia T cells even at low levels seems to prevent the leukemia from relapsing (for at least 50 months). As a consequence, we hypothesize that anti-leukemia T cell responses may help maintain remission under imatinib therapy. The mathematical model together with the new experimental data imply that there may be a feasible, low-risk, clinical approach to enhancing the effects of imatinib treatment.     

Lung cancer and oncolytic virotherapy——enemy's enemy

Lung cancer is one of the malignant tumors that seriously threaten human health worldwide, while the covid-19 virus has become people's nightmare after the coronavirus pandemic. There are too many similarities between cancer cells and viruses, one of the most significant is that both of them are our enemies. The strategy to take the advantage of the virus to beat cancer cells is called Oncolytic virotherapy. When immunotherapy represented by immune checkpoint inhibitors has made remarkable breakthroughs in the clinical practice of lung cancer, the induction of antitumor immunity from immune cells gradually becomes a rapidly developing and promising strategy of cancer therapy. Oncolytic virotherapy is based on the same mechanisms that selectively kill tumor cells and induce systemic anti-tumor immunity, but still has a long way to go before it becomes a standard treatment for lung cancer. This article provides a comprehensive review of the latest progress in oncolytic virotherapy for lung cancer, including the specific mechanism of oncolytic virus therapy and the main types of oncolytic viruses, and the combination of oncolytic virotherapy and existing standard treatments. It aims to provide new insights and ideas on oncolytic virotherapy for lung cancer.     

Using adaptive model predictive control to customize maintenance therapy chemotherapeutic dosing for childhood acute lymphoblastic leukemia

Acute lymphoblastic leukemia (ALL) is a common childhood cancer in which nearly one-quarter of patients experience a disease relapse. However, it has been shown that individualizing therapy for childhood ALL patients by adjusting doses based on the blood concentration of active drug metabolite could significantly improve treatment outcome. An adaptive model predictive control (MPC) strategy is presented in which maintenance therapy for childhood ALL is personalized using routine patient measurements of red blood cell mean corpuscular volume as a surrogate for the active drug metabolite concentration. A clinically relevant mathematical model is developed and used to describe the patient response to the chemotherapeutic drug 6-mercaptopurine, with some model parameters being patient-specific. During the course of treatment, the patient-specific parameters are adaptively identified using recurrent complete blood count measurements, which sufficiently constrain the patient parameter uncertainty to support customized adjustments of the drug dose. While this work represents only a first step toward a quantitative tool for clinical use, the simulated treatment results indicate that the proposed mathematical model and adaptive MPC approach could serve as valuable resources to the oncologist toward creating a personalized treatment strategy that is both safe and effective.     

Theoretical evaluation of the parameters of glucose metabolism on the basis of continuous glycemia monitoring data using mathematical modeling

The aim of this paper is to construct a mathematical model that takes the main physiological parameters of blood-glucose regulation into account, in order to identify these parameters for an individual patient according to continuous glucose-monitoring data. The constructed mathematical model consists of six ordinary differential equations that describe the dynamics of changes in glucose concentrations, as well as insulin and anti-insulin factors in the blood. Estimation of the parameters of the equations was performed using an evolutionary programming method. The model predictions were fitted to the continuous glucosemonitoring data. As a result of the identification of the model parameters for two patients with type 1 diabetes mellitus, the estimated insulin secretion was close to zero and the estimated glucose utilization and insulin clearance were increased in comparison with the data for healthy donors. Here, we present a personalized model of the regulation of blood glucose, which can be used to predict the results of continuous glucose monitoring depending on modification of the prescribed glucose-lowering therapy. This approach can significantly reduce the number of iterations of the selection of medical hypoglycemic therapy and therefore increase the effectiveness of treatment according to glucose-monitoring data.

     

Handling of the Cotton Rat in Studies for the Pre-clinical Evaluation of Oncolytic Viruses

Oncolytic viruses are a novel anticancer therapy with the ability to target tumor cells, while leaving healthy cells intact. For this strategy to be successful, recent studies have shown that involvement of the host immune system is essential. Therefore, oncolytic virotherapy should be evaluated within the context of an immunocompetent model. Furthermore, the study of antitumor therapies in tolerized animal models may better recapitulate results seen in clinical trials. Cotton rats, commonly used to study respiratory viruses, are an attractive model to study oncolytic virotherapy as syngeneic models of mammary carcinoma and osteosarcoma are well established. However, there is a lack of published information on the proper handling procedure for these highly excitable rodents. The handling and capture approach outlined minimizes animal stress to facilitate experimentation. This technique hinges upon the ability of the researcher to keep calm during handling and perform procedures in a timely fashion. Finally, we describe how to prepare cotton rat mammary tumor cells for consistent subcutaneous tumor formation, and how to perform intratumoral and intraperitoneal injections. These methods can be applied to a wide range of studies furthering the development of the cotton rat as a relevant pre-clinical model to study antitumor therapy.     

The joint modeling of a longitudinal disease progression marker and the failure time process in the presence of cure

In this paper we present an extension of cure models: to incorporate a longitudinal disease progression marker. The model is motivated by studies of patients with prostate cancer undergoing radiation therapy. The patients are followed until recurrence of the prostate cancer or censoring, with the PSA marker measured intermittently. Some patients are cured by the treatment and are immune from recurrence. A joint-cure model is developed for this type of data, in which the longitudinal marker and the failure time process are modeled jointly, with a fraction of patients assumed to be immune from the endpoint. A hierarchical nonlinear mixed-effects model is assumed for the marker and a time-dependent Cox proportional hazards model is used to model the time to endpoint. The probability of cure is modeled by a logistic link. The parameters are estimated using a Monte Carlo EM algorithm. Importance sampling with an adaptively chosen t-distribution and variable Monte Carlo sample size is used. We apply the method to data from prostate cancer and perform a simulation study. We show that by incorporating the longitudinal disease progression marker into the cure model, we obtain parameter estimates with better statistical properties. The classification of the censored patients into the cure group and the susceptible group based on the estimated conditional recurrence probability from the joint-cure model has a higher sensitivity and specificity, and a lower misclassification probability compared with the standard cure model. The addition of the longitudinal data has the effect of reducing the impact of the identifiability problems in a standard cure model and can help overcome biases due to informative censoring.     

Mathematical Modeling of the Effects of Tumor Heterogeneity on the Efficiency of Radiation Treatment Schedule

Radiotherapy uses high doses of energy to eradicate cancer cells and control tumors. Various treatment schedules have been developed and tried in clinical trials, yet significant obstacles remain to improving the radiotherapy fractionation. Genetic and non-genetic cellular diversity within tumors can lead to different radiosensitivity among cancer cells that can affect radiation treatment outcome. We propose a minimal mathematical model to study the effect of tumor heterogeneity and repair in different radiation treatment schedules. We perform stochastic and deterministic simulations to estimate model parameters using available experimental data. Our results suggest that gross tumor volume reduction is insufficient to control the disease if a fraction of radioresistant cells survives therapy. If cure cannot be achieved, protocols should balance volume reduction with minimal selection for radioresistant cells. We show that the most efficient treatment schedule is dependent on biology and model parameter values and, therefore, emphasize the need for careful tumor-specific model calibration before clinically actionable conclusions can be drawn.     

Dynamical properties of autoimmune disease models: tolerance, flare-up, dormancy

The mechanisms of autoimmune disease have remained puzzling for a long time. Here we construct a simple mathematical model for autoimmune disease based on the personal immune response function and the target cell growth function. We show that these two functions are sufficient to capture the essence of autoimmune disease and can explain characteristic symptom phases such as tolerance, repeated flare-ups and dormancy. Our results strongly suggest that a more complete understanding of these two functions will underlie the development of an effective therapy for autoimmune disease.     

人工心脏瓣膜置换术后近期死亡因素的Logistic回归模型与分析

主要研究人工心脏瓣膜置换手术中导致病人术后近期死亡的重要影响因素．目的是通过统计学方法分析病人身体状况与治疗手段的数据,探讨导致病人死亡的因素,为临床上改善治疗方法,减少或消除危险因素,降低手术的死亡率提供参考．通过Logistic回归模型,对所有变量作单因素分析和相关因素分析,在此基础上,结合医学背景知识,对入选因素进行多因素的逐步筛选;对所得模型作残差分析,用刀切法加以检验,保证了模型的正确性。     

Mathematical models of HIV pathogenesis and treatment

We review mathematical models of HIV dynamics, disease progression, and therapy. We start by introducing a basic model of virus infection and demonstrate how it was used to study HIV dynamics and to measure crucial parameters that lead to a new understanding of the disease process. We discuss the diversity threshold model as an example of the general principle that virus evolution can drive disease progression and the destruction of the immune system. Finally, we show how mathematical models can be used to understand correlates of long-term immunological control of HIV, and to design therapy regimes that convert a progressing patient into a state of long-term non-progression.