Introduction of Hypermatrix and Operator Notation into a Discrete Mathematics Simulation Model of Malignant Tumour Response to Therapeutic Schemes In Vivo. Some Operator Properties

The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code). However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the operators’ commutativity and outline the “summarize and jump” strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83–02, thus strengthening the reliability of the model developed

Applying a 4D multiscale in vivo tumor growth model to the exploration of radiotherapy scheduling: The effects of weekend treatment gaps and p53 gene status on the response of fast growing solid tumors

The present paper aims at demonstrating clinically oriented applications of the multiscale four dimensional in vivo tumor growth simulation model previously developed by our research group. To this end the effect of weekend radiotherapy treatment gaps and p53 gene status on two virtual glioblastoma tumors differing only in p53 gene status is investigated in silico. Tumor response predictions concerning two rather extreme dose fractionation schedules (daily dose of 4.5 Gy administered in 3 equal fractions) namely HART (Hyperfractionated Accelerated Radiotherapy weekend less) 54 Gy and CHART (Continuous HART) 54 Gy are presented and compared. The model predictions suggest that, for the same p53 status, HART 54 Gy and CHART 54 Gy have almost the same long term effects on locoregional tumor control. However, no data have been located in the literature concerning a comparison of HART and CHART radiotherapy schedules for glioblastoma. As non small cell lung carcinoma (NSCLC) may also be a fast growing and radiosensitive tumor, a comparison of the model predictions with the outcome of clinical studies concerning the response of NSCLC to HART 54 Gy and CHART 54 Gy is made. The model predictions are in accordance with corresponding clinical observations, thus strengthening the potential of the model

Numerical simulation of vascular tumour growth under antiangiogenic treatment: addressing the paradigm of single-agent bevacizumab therapy with the use of experimental data

Background: Antiangiogenic agents have been recently added to the oncological armamentarium with bevacizumab probably being the most popular representative in current clinical practice. The elucidation of the mode of action of these agents is a prerequisite for personalized prediction of antiangiogenic treatment response and selection of patients who may benefit from this kind of therapy. To this end, having used as a basis a preexisting continuous vascular tumour growth model which addresses the targeted nature of antiangiogenic treatment, we present a paper characterized by the following three features. First, the integration of a two-compartmental bevacizumab specific pharmacokinetic module into the core of the aforementioned preexisting model. Second, its mathematical modification in order to reproduce the asymptotic behaviour of tumour volume in the theoretical case of a total destruction of tumour neovasculature. Third, the exploitation of a range of published animal datasets pertaining to antitumour efficacy of bevacizumab on various tumour types (breast, lung, head and neck, colon).Results: Results for both the unperturbed growth and the treatment module reveal qualitative similarities with experimental observations establishing the biologically acceptable behaviour of the model. The dynamics of the untreated tumour has been studied via a parameter analysis, revealing the role of each relevant input parameter to tumour evolution. The combined effect of endogenous proangiogenic and antiangiogenic factors on the angiogenic potential of a tumour is also studied, in order to capture the dynamics of molecular competition between the two key-players of tumoural angiogenesis. The adopted methodology also allows accounting for the newly recognized direct antitumour effect of the specific agent.Conclusions: Interesting observations have been made, suggesting a potential size-dependent tumour response to different treatment modalities and determining the relative timing of cytotoxic versus antiangiogenic agents administration. Insight into the comparative effectiveness of different antiangiogenic treatment strategies is revealed. The results of a series of in vivo experiments in mice bearing diverse types of tumours (breast, lung, head and neck, colon) and treated with bevacizumab are successfully reproduced, supporting thus the validity of the underlying model.Reviewers: This article was reviewed by L. Hanin, T. Radivoyevitch and L. Edler

Exploiting Clinical Trial Data Drastically Narrows the Window of Possible Solutions to the Problem of Clinical Adaptation of a Multiscale Cancer Model

The development of computational models for simulating tumor growth and response to treatment has gained significant momentum during the last few decades. At the dawn of the era of personalized medicine, providing insight into complex mechanisms involved in cancer and contributing to patient-specific therapy optimization constitute particularly inspiring pursuits. The in silico oncology community is facing the great challenge of effectively translating simulation models into clinical practice, which presupposes a thorough sensitivity analysis, adaptation and validation process based on real clinical data. In this paper, the behavior of a clinically-oriented, multiscale model of solid tumor response to chemotherapy is investigated, using the paradigm of nephroblastoma response to preoperative chemotherapy in the context of the SIOP/GPOH clinical trial. A sorting of the model's parameters according to the magnitude of their effect on the output has unveiled the relative importance of the corresponding biological mechanisms; major impact on the result of therapy is credited to the oxygenation and nutrient availability status of the tumor and the balance between the symmetric and asymmetric modes of stem cell division. The effect of a number of parameter combinations on the extent of chemotherapy-induced tumor shrinkage and on the tumor's growth rate are discussed. A real clinical case of nephroblastoma has served as a proof of principle study case, demonstrating the basics of an ongoing clinical adaptation and validation process. By using clinical data in conjunction with plausible values of model parameters, an excellent fit of the model to the available medical data of the selected nephroblastoma case has been achieved, in terms of both volume reduction and histological constitution of the tumor. In this context, the exploitation of multiscale clinical data drastically narrows the window of possible solutions to the clinical adaptation problem

A Numerical Handling of the Boundary Conditions Imposed by the Skull on an Inhomogeneous Diffusion-Reaction Model of Glioblastoma Invasion Into the Brain: Clinical Validation Aspects

A novel explicit triscale reaction-diffusion numerical model of glioblastoma multiforme tumor growth is presented. The model incorporates the handling of Neumann boundary conditions imposed by the cranium and takes into account both the inhomogeneous nature of human brain and the complexity of the skull geometry. The finite-difference time-domain method is adopted. To demonstrate the workflow of a possible clinical validation procedure, a clinical case/scenario is addressed. A good agreement of the in silico calculated value of the doubling time (ie, the time for tumor volume to double) with the value of the same quantity based on tomographic imaging data has been observed. A theoretical exploration suggests that a rough but still quite informative value of the doubling time may be calculated based on a homogeneous brain model. The model could serve as the main component of a continuous mathematics-based glioblastoma oncosimulator aiming at supporting the clinician in the optimal patient-individualized design of treatment using the patient’s multiscale data and experimenting in silico (ie, on the computer)

Differentiation resistance through altered retinoblastoma protein function in acute lymphoblastic leukemia: in silico modeling of the deregulations in the G1/S restriction point pathway

Background: As in many cancer types, the G1/S restriction point (RP) is deregulated in Acute Lymphoblastic Leukemia (ALL). Hyper-phosphorylated retinoblastoma protein (hyper-pRb) is found in high levels in ALL cells. Nevertheless, the ALL lymphocyte proliferation rate for the average patient is surprisingly low compared to its normal counterpart of the same maturation level. Additionally, as stated in literature, ALL cells possibly reside at or beyond the RP which is located in the late-G1 phase. This state may favor their differentiation resistant phenotype. A major phenomenon contributing to this fact is thought to be the observed limited redundancy in the phosphorylation of retinoblastoma protein (pRb) by the various Cyclin Dependent Kinases (Cdks). The latter may result in partial loss of pRb functions despite hyper-phosphorylation.Results: To test this hypothesis, an in silico model aiming at simulating the biochemical regulation of the RP in ALL is introduced. By exploiting experimental findings derived from leukemic cells and following a semi-quantitative calibration procedure, the model has been shown to satisfactorily reproduce such a behavior for the RP pathway. At the same time, the calibrated model has been proved to be in agreement with the observed variation in the ALL cell cycle duration.Conclusions: The proposed model aims to contribute to a better understanding of the complex phenomena governing the leukemic cell cycle. At the same time it constitutes a significant first step in the creation of a personalized proliferation rate predictor that can be used in the context of multiscale cancer modeling. Such an approach is expected to play an important role in the refinement and the advancement of mechanistic modeling of ALL in the context of the emergent and promising scientific domains of In Silico Oncology and more generally In Silico Medicine

Coupling biomechanics to a cellular level model: An approach to patient-specific image driven multi-scale and multi-physics tumor simulation

Modeling of tumor growth has been performed according to various approaches addressing different biocomplexity levels and spatiotemporal scales. Mathematical treatments range from partial differential equation based diffusion models to rule-based cellular level simulators, aiming at both improving our quantitative understanding of the underlying biological processes and, in the mid- and long term, constructing reliable multi-scale predictive platforms to support patient-individualized treatment planning and optimization. The aim of this paper is to establish a multi-scale and multi-physics approach to tumor modeling taking into account both the cellular and the macroscopic mechanical level. Therefore, an already developed biomodel of clinical tumor growth and response to treatment is self-consistently coupled with a biomechanical model. Results are presented for the free growth case of the imageable component of an initially point-like glioblastoma multiforme tumor. The composite model leads to significant tumor shape corrections that are achieved through the utilization of environmental pressure information and the application of biomechanical principles. Using the ratio of smallest to largest moment of inertia of the tumor material to quantify the effect of our coupled approach, we have found a tumor shape correction of 20\% by coupling biomechanics to the cellular simulator as compared to a cellular simulation without preferred growth directions. We conclude that the integration of the two models provides additional morphological insight into realistic tumor growth behavior. Therefore, it might be used for the development of an advanced oncosimulator focusing on tumor types for which morphology plays an important role in surgical and/or radio-therapeutic treatment planning