A Poroelasticity Theory Approach to Study the Mechanisms Leading to Elevated Interstitial Fluid Pressure in Solid Tumours.

Although the mechanisms responsible for elevated interstitial fluid pressure (IFP) in tumours remain obscure, it seems clear that high IFP represents a barrier to drug delivery (since the resulting adverse pressure gradient implies a reduction in the driving force for transvascular exchange of both fluid and macromolecules). R. Jain and co-workers studied this problem, and although the conclusions drawn from their idealized mathematical models offered useful insights into the causes of elevated IFP, they by no means gave a definitive explanation for this phenomenon. In this paper, we use poroelasticity theory to also develop a macroscopic mathematical model to describe the time evolution of a solid tumour, but focus our attention on the mechanisms responsible for the rise of the IFP, from that for a healthy interstitium to that measured in malignant tumours. In particular, we discuss a number of possible time scales suggested by our mathematical model and propose a tumour-dependent time scale that leads to results in agreement with experimental observations. We apply our mathematical model to simulate the effect of "vascular normalization" (as proposed by Jain in Nat Med 7:987-989, 2001) on the IFP profile and discuss and contrast our conclusions with those of previous work in the literature.

Replicator dynamics of cancer stem cell: Selection in the presence of differentiation and plasticity.

The cancer stem cell hypothesis has evolved into one of the most important paradigms in cancer research. According to cancer stem cell hypothesis, somatic mutations in a subpopulation of cells can transform them into cancer stem cells with the unique potential of tumour initiation. Stem cells have the potential to produce lineages of non-stem cell populations (differentiated cells) via a ubiquitous hierarchal division scheme. Differentiation of a stem cell into (partially) differentiated cells can happen either symmetrically or asymmetrically. The selection dynamics of a mutant cancer stem cell should be investigated in the light of a stem cell proliferation hierarchy and presence of a non-stem cell population. By constructing a three-compartment Moran-type model composed of normal stem cells, mutant (cancer) stem cells and differentiated cells, we derive the replicator dynamics of stem cell frequencies where asymmetric differentiation and differentiated cell death rates are included in the model. We determine how these new factors change the conditions for a successful mutant invasion and discuss the variation on the steady state fraction of the population as different model parameters are changed. By including the phenotypic plasticity/dedifferentiation, in which a progenitor/differentiated cell can transform back into a cancer stem cell, we show that the effective fitness of mutant stem cells is not only determined by their proliferation and death rates but also according to their dedifferentiation potential. By numerically solving the model we derive the phase diagram of the advantageous and disadvantageous phases of cancer stem cells in the space of proliferation and dedifferentiation potentials. The result shows that at high enough dedifferentiation rates even a previously disadvantageous mutant can take over the population of normal stem cells. This observation has implications in different areas of cancer research including experimental observations that imply metastatic cancer stem cell types might have lower proliferation potential than other stem cell phenotypes while showing much more phenotypic plasticity and can undergo clonal expansion.

The effect of radiation quality on the risks of second malignancies.

UNLABELLED: Abstract Purpose: Numerous studies have implicated elevated second cancer risks as a result of radiation therapy. Our aim in this paper was to contribute to an understanding of the effects of radiation quality on second cancer risks. In particular, we developed a biologically motivated model to study the effects of linear energy transfer (LET) of charged particles (including protons, alpha particles and heavy ions Carbon and Neon) on the risk of second cancer. MATERIALS AND METHODS: A widely used approach to estimate the risk uses the so-called initiation-inactivation-repopulation model. Based on the available experimental data for the LET dependence of radiobiological parameters and mutation rate, we generalized this formulation to include the effects of radiation quality. We evaluated the secondary cancer risks for protons in the clinical range of LET, i.e., around 4-10 (KeV/µm), which lies in the plateau region of the Bragg peak. RESULTS: For protons, at a fixed radiation dose, we showed that the increase in second cancer risks correlated directly with increasing values of LET to a certain point, and then decreased. Interestingly, we obtained a higher risk for proton LET of 10 KeV/µm compared to the lower LET of 4 KeV/µm in the low dose region. In the case of heavy ions, the risk was higher for Carbon ions than Neon ions (even though they have almost the same LET). We also compared protons and alpha particles with the same LET, and it was interesting to note that the second cancer risks were higher for protons compared to alpha particles in the low-dose region. CONCLUSION: Overall, this study demonstrated the importance of including LET dependence in the estimation of second cancer risk. Our theoretical risk predictions were noticeably high; however, the biological end points should be tested experimentally for multiple treatment fields and to improve theoretical predictions.

Modeling age-dependent radiation-induced second cancer risks and estimation of mutation rate: an evolutionary approach.

Although the survival rate of cancer patients has significantly increased due to advances in anti-cancer therapeutics, one of the major side effects of these therapies, particularly radiotherapy, is the potential manifestation of radiation-induced secondary malignancies. In this work, a novel evolutionary stochastic model is introduced that couples short-term formalism (during radiotherapy) and long-term formalism (post-treatment). This framework is used to estimate the risks of second cancer as a function of spontaneous background and radiation-induced mutation rates of normal and pre-malignant cells. By fitting the model to available clinical data for spontaneous background risk together with data of Hodgkin's lymphoma survivors (for various organs), the second cancer mutation rate is estimated. The model predicts a significant increase in mutation rate for some cancer types, which may be a sign of genomic instability. Finally, it is shown that the model results are in agreement with the measured results for excess relative risk (ERR) as a function of exposure age and that the model predicts a negative correlation of ERR with increase in attained age. This novel approach can be used to analyze several radiotherapy protocols in current clinical practice and to forecast the second cancer risks over time for individual patients.

Modeling the spatial distribution of chronic tumor hypoxia: implications for experimental and clinical studies.

Tumor oxygenation status is considered one of the important prognostic markers in cancer since it strongly influences the response of cancer cells to various treatments; in particular, to radiation therapy. Thus, a proper and accurate assessment of tumor oxygen distribution before the treatment may highly affect the outcome of the treatment. The heterogeneous nature of tumor hypoxia, mainly influenced by the complex tumor microenvironment, often makes its quantification very difficult. The usual methods used to measure tumor hypoxia are biomarkers and the polarographic needle electrode. Although these techniques may provide an acceptable assessment of hypoxia, they are invasive and may not always give a spatial distribution of hypoxia, which is very useful for treatment planning. An alternative method to quantify the tumor hypoxia is to use theoretical simulations with the knowledge of tumor vasculature. The purpose of this paper is to model tumor hypoxia using a known spatial distribution of tumor vasculature obtained from image data, to analyze the accuracy of polarographic needle electrode measurements in quantifying hypoxia, to quantify the optimum number of measurements required to satisfactorily evaluate the tumor oxygenation status, and to study the effects of hypoxia on radiation response. Our results indicate that the model successfully generated an accurate oxygenation map for tumor cross-sections with known vascular distribution. The method developed here provides a way to estimate tumor hypoxia and provides guidance in planning accurate and effective therapeutic strategies and invasive estimation techniques. Our results agree with the previous findings that the needle electrode technique gives a good estimate of tumor hypoxia if the sampling is done in a uniform way with 5-6 tracks of 20-30 measurements each. Moreover, the analysis indicates that the accurate measurement of oxygen profile can be very useful in determining right radiation doses to the patients.

Drug delivery through the skin: molecular simulations of barrier lipids to design more effective noninvasive dermal and transdermal delivery systems for small molecules, biologics, and cosmetics.

The delivery of drugs through the skin provides a convenient route of administration that is often preferable to injection because it is noninvasive and can typically be self-administered. These two factors alone result in a significant reduction of medical complications and improvement in patient compliance. Unfortunately, a significant obstacle to dermal and transdermal drug delivery alike is the resilient barrier that the epidermal layers of the skin, primarily the stratum corneum, presents for the diffusion of exogenous chemical agents. Further advancement of transdermal drug delivery requires the development of novel delivery systems that are suitable for modern, macromolecular protein and nucleotide therapeutic agents. Significant effort has already been devoted to obtain a functional understanding of the physical barrier properties imparted by the epidermis, specifically the membrane structures of the stratum corneum. However, structural observations of membrane systems are often hindered by low resolutions, making it difficult to resolve the molecular mechanisms related to interactions between lipids found within the stratum corneum. Several models describing the molecular diffusion of drug molecules through the stratum corneum have now been postulated, where chemical permeation enhancers are thought to disrupt the underlying lipid structure, resulting in enhanced permeability. Recent investigations using biphasic vesicles also suggested a possibility for novel mechanisms involving the formation of complex polymorphic lipid phases. In this review, we discuss the advantages and limitations of permeation-enhancing strategies and how computational simulations, at the atomic scale, coupled with physical observations can provide insight into the mechanisms of diffusion through the stratum corneum.

Mathematical modeling of the brain: principles and challenges.

OBJECTIVE: The use of mathematics in the study of phenomena and systems of interest to medicine has become quite popular in recent years, but not much progress has been made as a result of these efforts. The aim of this article is to identify the reasons for this failure and to suggest procedures for more successful outcomes. METHODS: We review and assess a variety of mathematical modeling procedures, from microscopic (at the level of molecular behavior) to macroscopic standpoints, from lumped-parameters to distributed-parameters approaches. Using examples that are as simple as possible, we elucidate the difference between the predictive and the explanatory powers of mathematical models, as well as the uses (and abuses) of analogy in their construction. RESULTS: Mathematical medicine is a truly interdisciplinary area that brings together medical researchers, engineers, and applied mathematicians whose vast differences in expertise and background make collaboration difficult. CONCLUSION: The lack of a common language and a common way of understanding what a mathematical model is, and what it can do, is identified as the main source of the slow progress to date, and constructive suggestions are made to improve the situation.