Mathematical Modeling Support for Lung Cancer Therapy-A Short Review

The paper presents a review of models that can be used to describe dynamics of lung cancer growth and its response to treatment at both cell population and intracellular processes levels. To address the latter, models of signaling pathways associated with cellular responses to treatment are overviewed. First, treatment options for lung cancer are discussed, and main signaling pathways and regulatory networks are briefly reviewed. Then, approaches used to model specific therapies are discussed. Following that, models of intracellular processes that are crucial in responses to therapies are presented. The paper is concluded with a discussion of the applicability of the presented approaches in the context of lung cancer.

Clinical implications of in silico mathematical modeling for glioblastoma: a critical review

Glioblastoma remains a clinical challenge in spite of years of extensive research. Novel approaches are needed in order to integrate the existing knowledge. This is the potential role of mathematical oncology. This paper reviews mathematical models on glioblastoma from the clinical doctor's point of view, with focus on 3D modeling approaches of radiation response of in vivo glioblastomas based on contemporary imaging techniques. As these models aim to provide a clinically useful tool in the era of personalized medicine, the integration of the latest advances in molecular and imaging science and in clinical practice by the in silico models is crucial for their clinical relevance. Our aim is to indicate areas of GBM research that have not yet been addressed by in silico models and to point out evidence that has come up from in silico experiments, which may be worth considering in the clinic. This review examines how close these models have come in predicting the outcome of treatment protocols and in shaping the future of radiotherapy treatments.

Modelling and Bayesian adaptive prediction of individual patients' tumour volume change during radiotherapy

The aim of this study is to develop a mathematical modelling method that can predict individual patients’ response to radiotherapy, in terms of tumour volume change during the treatment. The main concept is to start from a population-average model, which is subsequently updated from an individual’s tumour volume measurement. The model becomes increasingly personalized and so too does the prediction it produces. This idea of adaptive prediction was realised by using a Bayesian approach for updating the model parameters. The feasibility of the developed method was demonstrated on the data from 25 non-small cell lung cancer patients treated with helical tomotherapy, during which tumour volume was measured from daily imaging as part of the image-guided radiotherapy. The method could provide useful information for adaptive treatment planning and dose scheduling based on the patient’s personalised response.

Optimal treatment and stochastic modeling of heterogeneous tumors

In this work we review past articles that have mathematically studied cancer heterogeneity and the impact of this heterogeneity on the structure of optimal therapy. We look at past works on modeling how heterogeneous tumors respond to radiotherapy, and take a particularly close look at how the optimal radiotherapy schedule is modified by the presence of heterogeneity. In addition, we review past works on the study of optimal chemotherapy when dealing with heterogeneous tumors.

REVIEWERS

This article was reviewed by Thomas McDonald, David Axelrod, and Leonid Hanin.

Modular model of TNFalpha cytotoxicity

MOTIVATION

Tumour Necrosis Factor alpha (TNF) initiates a complex series of biochemical events in the cell upon binding to its type R1 receptor (TNF-R1). Recent experimental work has unravelled the molecular regulation of the signalling complexes that lead either to cell survival or death. Survival signals are activated by direct binding of TNF to TNF-R1 at the cell membrane whereas apoptotic signals by endocytosed TNF/TNF-R1 complexes. Here we describe a reduced, effective model with few free parameters, where we group some intricate mechanisms into effective modules, that successfully describes this complex set of actions. We study the parameter space to show that the model is structurally stable and robust over a broad range of parameter values.

RESULTS

We use state-of-the-art Bayesian methods (a Sequential Monte Carlo sampler) to perform inference of plausible values of the model parameters from experimental data. As a result, we obtain a robust model that can provide a solid basis for further modelling of TNF signalling. The model is also suitable for inclusion in multi-scale simulation programs that are presently under development to study the behaviour of large tumour cell populations.

AVAILABILITY

We provide supplementary material that includes all mathematical details and all algorithms (Matlab code) and models (SBML descriptions).

CONTACT

edoardo.milotti@ts.infn.it

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.

Radioimmunotherapy with radioactive nanoparticles: biological doses and treatment efficiency for vascularized tumors with or without a central hypoxic area

PURPOSE

Radioactive atoms attached to monoclonal antibodies are used in radioimmunotherapy to treat cancer while limiting radiation to healthy tissues. One limitation of this method is that only one radioactive atom is linked to each antibody and the deposited dose is often insufficient to eradicate solid and radioresistant tumors. In a previous study, simulations with the Monte Carlo N-Particle eXtended code showed that physical doses up to 50 Gy can be delivered inside tumors by replacing the single radionuclide by a radioactive nanoparticle of 5 nm diameter containing hundreds of radioactive atoms. However, tumoral and normal tissues are not equally sensitive to radiation, and previous works did not take account the biological effects such as cellular repair processes or the presence of less radiosensitive cells such as hypoxic cells.

METHODS

The idea is to adapt the linear-quadratic expression to the tumor model and to determine biological effective doses (BEDs) delivered through and around a tumor. This BED is then incorporated into a Poisson formula to determine the shell control probability (SCP) which predicts the cell cluster-killing efficiency at different distances "r" from the center of the tumor. BED and SCP models are used to analyze the advantages of injecting radioactive nanoparticles instead of a single radionuclide per vector in radioimmunotherapy.

RESULTS

Calculations of BED and SCP for different distances r from the center of a solid tumor, using the non-small-cell lung cancer as an example, were investigated for 90Y2O3 nanoparticles. With a total activity of about 3.5 and 20 MBq for tumor radii of 0.5 and 1.0 cm, respectively, results show that a very high BED is deposited in the well oxygenated part of the spherical carcinoma.

CONCLUSIONS

For either small or large solid tumors, BED and SCP calculations highlight the important benefit in replacing the single beta-emitter 90Y attached to each antibody by a 90Y2O3 nanoparticle.

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.