Benjamin Ribba

A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies

BackgroundRadiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation.MethodsIn this paper, we propose a multiscale model of cancer growth based on the genetic and molecular features of the evolution of colorectal cancer. The model includes key genes, cellular kinetics, tissue dynamics, macroscopic tumor evolution and radiosensitivity dependence on the cell cycle phase. We investigate the role of gene-dependent cell cycle regulation in the response of tumors to therapeutic irradiation protocols.ResultsSimulation results emphasize the importance of tumor tissue features and the need to consider regulating factors such as hypoxia, as well as tumor geometry and tissue dynamics, in predicting and improving radiotherapeutic efficacy.ConclusionThis model provides insight into the coupling of complex biological processes, which leads to a better understanding of oncogenesis. This will hopefully lead to improved irradiation therapy.

A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy

Tumor angiogenesis is the process by which new blood vessels are formed and enhance the oxygenation and growth of tumors. As angiogenesis is recognized as being a critical event in cancer development, considerable efforts have been made to identify inhibitors of this process. Cytostatic treatments that target the molecular events of the angiogenesis process have been developed, and have met with some success. However, it is usually difficult to preclinically assess the effectiveness of targeted therapies, and apparently promising compounds sometimes fail in clinical trials. We have developed a multiscale mathematical model of angiogenesis and tumor growth. At the molecular level, the model focuses on molecular competition between pro- and anti-angiogenic substances modeled on the basis of pharmacological laws. At the tissue scale, the model uses partial differential equations to describe the spatio-temporal changes in cancer cells during three stages of the cell cycle, as well as those of the endothelial cells that constitute the blood vessel walls. This model is used to qualitatively assess how efficient endostatin gene therapy is. Endostatin is an anti-angiogenic endogenous substance. The gene therapy entails overexpressing endostatin in the tumor and in the surrounding tissue. Simulations show that there is a critical treatment dose below which increasing the duration of treatment leads to a loss of efficacy. This theoretical model may be useful to evaluate the efficacy of therapies targeting angiogenesis, and could therefore contribute to designing prospective clinical trials.

A Tumor Growth Inhibition Model For Low-Grade Glioma Treated With Chemotherapy or Radiotherapy

Purpose: To develop a tumor growth inhibition model for adult diffuse low-grade gliomas (LGG) able to describe tumor size evolution in patients treated with chemotherapy or radiotherapy. Experimental Design: Using longitudinal mean tumor diameter (MTD) data from 21 patients treated with first-line procarbazine, 1-(2-chloroethyl)-3-cyclohexyl-l-nitrosourea, and vincristine (PCV) chemotherapy, we formulated a model consisting of a system of differential equations, incorporating tumor-specific and treatment-related parameters that reflect the response of proliferative and quiescent tumor tissue to treatment. The model was then applied to the analysis of longitudinal tumor size data in 24 patients treated with first-line temozolomide (TMZ) chemotherapy and in 25 patients treated with first-line radiotherapy. Results: The model successfully described the MTD dynamics of LGG before, during, and after PCV chemotherapy. Using the same model structure, we were also able to successfully describe the MTD dynamics in LGG patients treated with TMZ chemotherapy or radiotherapy. Tumor-specific parameters were found to be consistent across the three treatment modalities. The model is robust to sensitivity analysis, and preliminary results suggest that it can predict treatment response on the basis of pretreatment tumor size data. Conclusions: Using MTD data, we propose a tumor growth inhibition model able to describe LGG tumor size evolution in patients treated with chemotherapy or radiotherapy. In the future, this model might be used to predict treatment efficacy in LGG patients and could constitute a rational tool to conceive more effective chemotherapy schedules. Clin Cancer Res; 18(18); 5071–80. ©2012 AACR.

The Use of Hybrid Cellular Automaton Models for Improving Cancer Therapy

The Hybrid Cellular Automata (HCA) modelling framework can be an efficient approach to a number of biological problems, particularly those which involve the integration of multiple spatial and temporal scales. As such, HCA may become a key modelling tool in the development of the so-called integrative biology. In this paper, we first discuss HCA on a general level and then present results obtained when this approach was implemented in cancer research.

Computational Modeling of Solid Tumor Growth: The Avascular Stage

In this paper, we present a mathematical model for avascular tumor growth and its numerical study in two and three dimensions. For this purpose, we use a multiscale model using PDEs to describe the evolution of the tumor cell densities. In our model, cell cycle regulation depends mainly on microenvironment. The cancer growth of volume induces cell motion and tumor expansion. According to biology, cells grow against a basal membrane which interacts mechanically with the tumor. We use a level set method to describe this membrane, and we compute its influence on cell movement, thanks to a Stokes equation. The evolution of oxygen, diffusing from blood vessels to cancer cells and used to estimate hypoxia, is given by a stationary diffusion equation solved with a penalty method. The model has been applied to investigate the therapeutic benefit of anti-invasive agents and constitutes now the basis of a numerical platform for tumor growth simulations.

Enabling multiscale modeling in systems medicine.

CITATION: Wolkenhauer, O. et al. 2014. Enabling multiscale modeling in systems medicine. Genome Medicine, 6:21, doi:10.1186/gm538.

Etoposide pharmacokinetics and survival in patients with small cell lung cancer: A multicentre study

PURPOSE To investigate the prognostic value of systemic exposure to etoposide (Area Under the concentration Curve (AUC(VP16))) on overall survival (OS) in patients with small cell lung cancer (SCLC). PATIENTS AND METHODS Data from 52 patients with limited stage (n=17) or metastatic (n=35) SCLC were analysed. They received at least two courses of etoposide (120mg/(m(2)day) on 3 days) combined with either doxorubicin-ifosfamide (AVI, n=29) or platinum compounds (carboplatin: n=16; cisplatin: n=7). Population pharmacokinetic-pharmacodynamic (PK-PD) study was performed using NON-linear Mixed Effect Model (NONMEM) and Splus software with univariate and multivariate analyses. RESULTS Etoposide plasma concentration vs. time was described by a two compartment model. Etoposide clearance (CL) was significantly dependant on serum creatinine (Scr). Ifosfamide (IFO) coadministration increased etoposide clearance by 28% (median CL(VP16): 2.42L/h vs. 1.89L/h, p<0.0005) leading to a reduced systemic exposure (median AUC(VP16): 260mgh/L vs. 339mgh/L). No influence of body surface area (BSA) on CL(VP16) was observed. Median percent decrease of absolute neutrophil count (ANC) after the first chemotherapy course was greater when etoposide 24h concentration was above 0.33mg/L (88% vs. 0%, p=0.028). Median OS was significantly longer in patients treated without ifosfamide (11.0 months vs. 7.0 months, p=0.049) and in patients with CL(VP16)<2.22L/h (14 months vs. 7 months, p=0.013) and AUC(VP16)>254.8mgh/L (11 months vs. 7 months, p=0.048). The independent prognostic factors regarding OS were LDH, CL(VP16) and AUC(VP16). CONCLUSION In this study it was found that CL(VP16) is reduced in patients with elevated serum creatinine, whilst ifosfamide coadministration increases CL(VP16) and reduces AUC(VP16), demonstrating the interaction between VP16 and ifosfamide. CL(VP16) and AUC(VP16) correlate significantly with overall survival of patients with SCLC patients receiving etoposide regimens.

Pharmacometrics Markup Language (PharmML): Opening New Perspectives for Model Exchange in Drug Development

The lack of a common exchange format for mathematical models in pharmacometrics has been a long‐standing problem. Such a format has the potential to increase productivity and analysis quality, simplify the handling of complex workflows, ensure reproducibility of research, and facilitate the reuse of existing model resources. Pharmacometrics Markup Language (PharmML), currently under development by the Drug Disease Model Resources (DDMoRe) consortium, is intended to become an exchange standard in pharmacometrics by providing means to encode models, trial designs, and modeling steps.

Predictive values of hCG clearance for risk of methotrexate resistance in low-risk gestational trophoblastic neoplasias

BACKGROUND Early identification of patients at high risk for chemoresistance among those treated with methotrexate (MTX) for low-risk gestational trophoblastic neoplasia (GTN) is needed. We modeled human chorionic gonadotropin (hCG) decline during MTX therapy using a kinetic population approach to calculate individual hCG clearance (CL(hCG)) and assessed the predictive value of CL(hCG) for MTX resistance. PATIENTS AND METHODS A total of 154 patients with low-risk GTN treated with 8-day MTX regimen were retrospectively studied. NONMEM was used to model hCG decrease equations between day 0 and day 40 of chemotherapy. Receiver operating characteristic curve analysis defined the best CL(hCG) threshold. Univariate/multivariate survival analyses determined the predictive value of CL(hCG) and compared it with published predictive factors. RESULTS A monoexponential equation best modeled hCG decrease: hCG(t) = 3900 x e(-0.149 x t). Median CL(hCG) was 0.57 l/day (quartiles: 0.37-0.74). Only choriocarcinoma pathology [yes versus no: hazard ratio (HR) = 6.01; 95% confidence interval (CI) 2.2-16.6; P < 0.001] and unfavorable CL(hCG) quartile (< or =0.37 versus >0.37 l/day: HR = 6.75; 95% CI 2.7-16.8; P < 0.001) were significant independent predictive factors of MTX resistance risk. CONCLUSION In the second largest cohort of low-risk GTN patients reported to date, choriocarcinoma pathology and CL(hCG) < or =0.37 l/day were major independent predictive factors for MTX resistance risk.

Computational analysis of the influence of the microenvironment on carcinogenesis

The tumour microenvironment is known to play an important role in determining the sequence of acquired phenotypic traits that characterise cancer evolution. A more precise understanding of this role could have a major influence in the understanding of cancer growth and development, and potentially in the optimisation of innovative anti-cancer treatments delivery. However, to lead such an analysis in the basis of traditional biological experiments and observations is almost utopian given the complexity of the underlying biological processes and the typical time scales involved. In this context, computer models constitute a complementary exploratory tool. In this paper we introduce a two-dimensional cellular automaton that models key cancer cell capabilities. The model has been especially designed to mimic the behaviour of a cancer colony growing in vitro and to analyse the effect of different environmental conditions on the sequence of acquisition of phenotypic traits. Our results indicate that microenvironmental factors such as the local concentration of oxygen or nutrients and cell overcrowding may determine the expansion of the tumour colony. The results also show that tumour cells evolve and that their phenotypes adapt to the microenvironment so that environmental stress determines the dominance of particular phenotypical traits.