74,230 research outputs found
Programmable models of growth and mutation of cancer-cell populations
In this paper we propose a systematic approach to construct mathematical
models describing populations of cancer-cells at different stages of disease
development. The methodology we propose is based on stochastic Concurrent
Constraint Programming, a flexible stochastic modelling language. The
methodology is tested on (and partially motivated by) the study of prostate
cancer. In particular, we prove how our method is suitable to systematically
reconstruct different mathematical models of prostate cancer growth - together
with interactions with different kinds of hormone therapy - at different levels
of refinement.Comment: In Proceedings CompMod 2011, arXiv:1109.104
Mathematical modeling of the metastatic process
Mathematical modeling in cancer has been growing in popularity and impact
since its inception in 1932. The first theoretical mathematical modeling in
cancer research was focused on understanding tumor growth laws and has grown to
include the competition between healthy and normal tissue, carcinogenesis,
therapy and metastasis. It is the latter topic, metastasis, on which we will
focus this short review, specifically discussing various computational and
mathematical models of different portions of the metastatic process, including:
the emergence of the metastatic phenotype, the timing and size distribution of
metastases, the factors that influence the dormancy of micrometastases and
patterns of spread from a given primary tumor.Comment: 24 pages, 6 figures, Revie
Addressing current challenges in cancer immunotherapy with mathematical and computational modeling
The goal of cancer immunotherapy is to boost a patient's immune response to a
tumor. Yet, the design of an effective immunotherapy is complicated by various
factors, including a potentially immunosuppressive tumor microenvironment,
immune-modulating effects of conventional treatments, and therapy-related
toxicities. These complexities can be incorporated into mathematical and
computational models of cancer immunotherapy that can then be used to aid in
rational therapy design. In this review, we survey modeling approaches under
the umbrella of the major challenges facing immunotherapy development, which
encompass tumor classification, optimal treatment scheduling, and combination
therapy design. Although overlapping, each challenge has presented unique
opportunities for modelers to make contributions using analytical and numerical
analysis of model outcomes, as well as optimization algorithms. We discuss
several examples of models that have grown in complexity as more biological
information has become available, showcasing how model development is a dynamic
process interlinked with the rapid advances in tumor-immune biology. We
conclude the review with recommendations for modelers both with respect to
methodology and biological direction that might help keep modelers at the
forefront of cancer immunotherapy development.Comment: Accepted for publication in the Journal of the Royal Society
Interfac
Patient-specific, mechanistic models of tumor growth incorporating artificial intelligence and big data
Despite the remarkable advances in cancer diagnosis, treatment, and
management that have occurred over the past decade, malignant tumors remain a
major public health problem. Further progress in combating cancer may be
enabled by personalizing the delivery of therapies according to the predicted
response for each individual patient. The design of personalized therapies
requires patient-specific information integrated into an appropriate
mathematical model of tumor response. A fundamental barrier to realizing this
paradigm is the current lack of a rigorous, yet practical, mathematical theory
of tumor initiation, development, invasion, and response to therapy. In this
review, we begin by providing an overview of different approaches to modeling
tumor growth and treatment, including mechanistic as well as data-driven models
based on ``big data" and artificial intelligence. Next, we present illustrative
examples of mathematical models manifesting their utility and discussing the
limitations of stand-alone mechanistic and data-driven models. We further
discuss the potential of mechanistic models for not only predicting, but also
optimizing response to therapy on a patient-specific basis. We then discuss
current efforts and future possibilities to integrate mechanistic and
data-driven models. We conclude by proposing five fundamental challenges that
must be addressed to fully realize personalized care for cancer patients driven
by computational models
Mathematical modeling of tumor therapy with oncolytic viruses: Effects of parametric heterogeneity on cell dynamics
One of the mechanisms that ensure cancer robustness is tumor heterogeneity,
and its effects on tumor cells dynamics have to be taken into account when
studying cancer progression. There is no unifying theoretical framework in
mathematical modeling of carcinogenesis that would account for parametric
heterogeneity. Here we formulate a modeling approach that naturally takes stock
of inherent cancer cell heterogeneity and illustrate it with a model of
interaction between a tumor and an oncolytic virus. We show that several
phenomena that are absent in homogeneous models, such as cancer recurrence,
tumor dormancy, an others, appear in heterogeneous setting. We also demonstrate
that, within the applied modeling framework, to overcome the adverse effect of
tumor cell heterogeneity on cancer progression, a heterogeneous population of
an oncolytic virus must be used. Heterogeneity in parameters of the model, such
as tumor cell susceptibility to virus infection and virus replication rate, can
lead to complex, time-dependent behaviors of the tumor. Thus, irregular,
quasi-chaotic behavior of the tumor-virus system can be caused not only by
random perturbations but also by the heterogeneity of the tumor and the virus.
The modeling approach described here reveals the importance of tumor cell and
virus heterogeneity for the outcome of cancer therapy. It should be
straightforward to apply these techniques to mathematical modeling of other
types of anticancer therapy.Comment: 45 pages, 6 figures; submitted to Biology Direc
Molecular biology of breast cancer metastasis: The use of mathematical models to determine relapse and to predict response to chemotherapy in breast cancer
Breast cancer mortality rates have shown only modest improvemen despite the advent of effective chemotherapeutic agents which have been administered to a large percentage of women with breast cancer. In an effort to improve breast cancer treatment strategies, a variety of mathematical models have been developed that describe the natural history of breast cancer and the effects of treatment on the cancer. These models help researchers to develop, quantify, and test various treatment hypotheses quickly and efficiently. The present review discusses several of these models, with a focus on how they have been used to predict the initiation time of metastatic growth, the effect of operative therapy on the growth of metastases, and the optimal administration strategy for chemotherapy
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Mathematical modelling of nanoparticle delivery to vascular tumours
This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.The goal of any cancer therapy is to achieve efficient, tissue-specific targeting of drugs to cancer cells. However, most anticancer agents act on healthy and malignant tissue alike, potentially resulting in side effects to healthy tissue. This has motivated the development of treatment strategies that are cancer-cell
specific; one approach uses biomimetic polymer vesicles (BPV) to deliver chemotherapeutic drugs into cells before releasing them. BPVs are synthetic membrane enclosed, nanometre-sized structures, and provide ideal drug delivery vectors because specific targeting to cancer cells can be achieved by coating with tumourspecific
molecules. We present several mathematical models covering a wide range of length-scales pertinent to BPV-mediated delivery protocols and focus on capturing the in vivo environment by evaluating the impact of the underlying vascular structure upon the governing transport mechanisms. Firstly, we present models of specific binding of BPVs to cancer cells. Subsequently we examine the implications of these model outputs in the contexts of both discrete capillary architectures and higher level homogenized-models that track blood and BPV transport at the tissue scale (both intra- and extra-tumorally). Numerical solutions are discussed, and recommendations are presented on that optimal integration of the models to generate quantitative predictions associated with BPV treatment efficacy
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