Chemotherapy-induced cachexia and model-informed dosing to preserve lean mass in cancer treatment.

Although chemotherapy is a standard treatment for cancer, it comes with significant side effects. In particular, certain agents can induce severe muscle loss, known as cachexia, worsening patient quality of life and treatment outcomes. 5-fluorouracil, an anti-cancer agent used to treat several cancers, has been shown to cause muscle loss. Experimental data indicates a non-linear dose-dependence for muscle loss in mice treated with daily or week-day schedules. We present a mathematical model of chemotherapy-induced muscle wasting that captures this non-linear dose-dependence. Area-under-the-curve metrics are proposed to quantify the treatment's effects on lean mass and tumour control. Model simulations are used to explore alternate dosing schedules, aging effects, and morphine use in chemotherapy treatment with the aim of better protecting lean mass while actively targeting the tumour, ultimately leading to improved personalization of treatment planning and improved patient quality of life.

Modelling Radiation Cancer Treatment with a Death-Rate Term in Ordinary and Fractional Differential Equations.

Fractional calculus has recently been applied to the mathematical modelling of tumour growth, but its use introduces complexities that may not be warranted. Mathematical modelling with differential equations is a standard approach to study and predict treatment outcomes for population-level and patient-specific responses. Here, we use patient data of radiation-treated tumours to discuss the benefits and limitations of introducing fractional derivatives into three standard models of tumour growth. The fractional derivative introduces a history-dependence into the growth function, which requires a continuous death-rate term for radiation treatment. This newly proposed radiation-induced death-rate term improves computational efficiency in both ordinary and fractional derivative models. This computational speed-up will benefit common simulation tasks such as model parameterization and the construction and running of virtual clinical trials.

Modeling the Dichotomy of the Immune Response to Cancer: Cytotoxic Effects and Tumor-Promoting Inflammation.

Although the immune response is often regarded as acting to suppress tumor growth, it is now clear that it can be both stimulatory and inhibitory. The interplay between these competing influences has complex implications for tumor development, cancer dormancy, and immunotherapies. In fact, early immunotherapy failures were partly due to a lack in understanding of the nonlinear growth dynamics these competing immune actions may cause. To study this biological phenomenon theoretically, we construct a minimally parameterized framework that incorporates all aspects of the immune response. We combine the effects of all immune cell types, general principles of self-limited logistic growth, and the physical process of inflammation into one quantitative setting. Simulations suggest that while there are pro-tumor or antitumor immunogenic responses characterized by larger or smaller final tumor volumes, respectively, each response involves an initial period where tumor growth is stimulated beyond that of growth without an immune response. The mathematical description is non-identifiable which allows an ensemble of parameter sets to capture inherent biological variability in tumor growth that can significantly alter tumor-immune dynamics and thus treatment success rates. The ability of this model to predict non-intuitive yet clinically observed patterns of immunomodulated tumor growth suggests that it may provide a means to help classify patient response dynamics to aid identification of appropriate treatments exploiting immune response to improve tumor suppression, including the potential attainment of an immune-induced dormant state.

A review of mathematical models of cancer-immune interactions in the context of tumor dormancy.

The role of the immune system in tumor dormancy is now well established. In an immune-induced dormant state, potentially lethal cancer cells persist in a state where growth is restricted, to little or no increase, by the host's immune response. To describe this state in the context of cancer progression and immune response, basic temporal (spatially homogeneous) quantitative predator-prey constructs are discussed, along with some current and proposed augmentations that incorporate potentially significant biological phenomena such as the cancer cell transition to a quiescent state or the time delay in T-cell activation. Advances in cancer-immune modeling that describe complex interactions underlying the ability of the immune system to both promote and inhibit tumor growth are emphasized. Finally, the review concludes by discussing future mathematical challenges and their biological significance.

The effect of random virus failure following cell entry on infection outcome and the success of antiviral therapy.

A virus infection can be initiated with very few or even a single infectious virion, and as such can become extinct, i.e. stochastically fail to take hold or spread significantly. There are many ways that a fully competent infectious virion, having successfully entered a cell, can fail to cause a productive infection, i.e. one that yields infectious virus progeny. Though many stochastic models (SMs) have been developed and used to estimate a virus infection's establishment probability, these typically neglect infection failure post virus entry. The SM presented herein introduces parameter [Formula: see text] which corresponds to the probability that a virion's entry into a cell will result in a productive cell infection. We derive an expression for the likelihood of infection establishment in this new SM, and find that prophylactic therapy with an antiviral reducing [Formula: see text] is at least as good or better at decreasing the establishment probability, compared to antivirals reducing the rates of virus production or virus entry into cells, irrespective of the SM parameters. We investigate the difference in the fraction of cells consumed by so-called extinct versus established virus infections, and find that this distinction becomes biologically meaningless as the probability of establishment approaches zero. We explain why the release of virions continuously over an infectious cell's lifespan, rather than as a single burst at the end of the cell's lifespan, does not result in an increased risk of infection extinction. We show, instead, that the number of virus released, not the timing of the release, affects infection establishment and associated critical antiviral efficacy.

Serum proteins on nanoparticles: early stages of the "protein corona".

Nanoparticles in biological systems such as the bloodstream are exposed to a complex solution of biomolecules. A "corona" monolayer of proteins has historically been thought to form on nanoparticles upon introduction into such environments. To examine the first steps of protein binding, Fluorescence Correlation/Cross Correlation Spectroscopy and Fluorescence Resonance Energy Transfer were used to directly analyze four different nanoparticle systems. CdSe/ZnS core/shell quantum dots, 100 nm diameter polystyrene fluospheres, 200 nm diameter polystyrene fluospheres, and 200 nm diameter PEG-grafted DOTAP liposomes were studied with respect to serum protein binding, using bovine serum albumin as a model. Surface heterogeneity is found to be a key factor in protein binding to these nanoparticles, and as such we present a novel conceptualization of the early hard corona as low-ratio, non-uniform binding rather than a uniform monolayer.

Mathematically modelling inflammation as a promoter of tumour growth.

Inflammation is now known to play a significant role in tumour growth and progression. It is also difficult to adequately quantify systemic inflammation and the resulting localized effects in cancer. Here, we use experimental data to infer the possible contributions of inflammation in a mouse model of cancer. The model is validated by predicting tumour growth under anti-inflammatory treatments, and combination cancer therapies are explored. We then extend the model to consider simultaneous tumour implants at two distinct sites, which experimentally was shown to result in one large and one small tumour. We use this model to examine the role inflammation may play in the growth rate separation. Finally, we use this predictive two-tumour model to explore implications of inflammation on metastases, surgical removal of the primary and adjuvant anti-inflammatory treatments. This work suggests that improved tumour control can be obtained by targeting both the cancer and host, through anti-inflammatory treatments, including reduced metastatic burden post-surgical removal of primary tumours.

Mathematical Model of Muscle Wasting in Cancer Cachexia.

Cancer cachexia is a debilitating condition characterized by an extreme loss of skeletal muscle mass, which negatively impacts patients' quality of life, reduces their ability to sustain anti-cancer therapies, and increases the risk of mortality. Recent discoveries have identified the myostatin/activin A/ActRIIB pathway as critical to muscle wasting by inducing satellite cell quiescence and increasing muscle-specific ubiquitin ligases responsible for atrophy. Remarkably, pharmacological blockade of the ActRIIB pathway has been shown to reverse muscle wasting and prolong the survival time of tumor-bearing animals. To explore the implications of this signaling pathway and potential therapeutic targets in cachexia, we construct a novel mathematical model of muscle tissue subjected to tumor-derived cachectic factors. The model formulation tracks the intercellular interactions between cancer cell, satellite cell, and muscle cell populations. The model is parameterized by fitting to colon-26 mouse model data, and the analysis provides insight into tissue growth in healthy, cancerous, and post-cachexia treatment conditions. Model predictions suggest that cachexia fundamentally alters muscle tissue health, as measured by the stem cell ratio, and this is only partially recovered by anti-cachexia treatment. Our mathematical findings suggest that after blocking the myostatin/activin A pathway, partial recovery of cancer-induced muscle loss requires the activation and proliferation of the satellite cell compartment with a functional differentiation program.

Tumor-immune dynamics regulated in the microenvironment inform the transient nature of immune-induced tumor dormancy.

Cancer in a host induces responses that increase the ability of the microenvironment to sustain the growing mass, for example, angiogenesis, but cancer cells can have varying sensitivities to these sustainability signals. Here, we show that these sensitivities are significant determinants of ultimate tumor fate, especially in response to treatments and immune interactions. We present a mathematical model of cancer-immune interactions that modifies generalized logistic growth with both immune-predation and immune-recruitment. The role of a growing environmental carrying capacity is discussed as a possible regulatory mechanism for tumor growth, and this regulation is shown to modify cancer-immune interactions and the possibility of achieving immune-induced tumor dormancy. This mathematical model qualitatively matches experimental observations of immune-induced tumor dormancy as it predicts dormancy as a transient period of growth that necessarily ends in either tumor elimination or tumor escape. As dormant tumors may exist asymptomatically and may be easier to treat with conventional therapy, an understanding of the mechanisms behind tumor dormancy may lead to new treatments aimed at prolonging the dormant state or converting an aggressive cancer to the dormant state.

Mathematical models of immune-induced cancer dormancy and the emergence of immune evasion.

Cancer dormancy, a state in which cancer cells persist in a host without significant growth, is a natural forestallment of progression to manifest disease and is thus of great clinical interest. Experimental work in mice suggests that in immune-induced dormancy, the longer a cancer remains dormant in a host, the more resistant the cancer cells become to cytotoxic T-cell-mediated killing. In this work, mathematical models are used to analyse the possible causative mechanisms of cancer escape from immune-induced dormancy. Using a data-driven approach, both decaying efficacy in immune predation and immune recruitment are analysed with results suggesting that decline in recruitment is a stronger determinant of escape than increased resistance to predation. Using a mechanistic approach, the existence of an immune-resistant cancer cell subpopulation is considered, and the effects on cancer dormancy and potential immunoediting mechanisms of cancer escape are analysed and discussed. The immunoediting mechanism assumes that the immune system selectively prunes the cancer of immune-sensitive cells, which is shown to cause an initially heterogeneous population to become a more homogeneous, and more resistant, population. The fact that this selection may result in the appearance of decreasing efficacy in T-cell cytotoxic effect with time in dormancy is also demonstrated. This work suggests that through actions that temporarily delay cancer growth through the targeted removal of immune-sensitive subpopulations, the immune response may actually progress the cancer to a more aggressive state.

Transcriptional changes induced by the tumor dormancy-associated microRNA-190.

Tumor dormancy is a highly prevalent stage in cancer progression. We have previously generated and characterized in vivo experimental models of human tumor dormancy in which micro-tumors remain occult until they spontaneously shift into rapid tumor growth. We showed that the dormant micro-tumors undergo a stable microRNA (miRNA) switch during their transition from dormancy to a fast-growing phenotype and reported the identification of a consensus signature of human tumor dormancy-associated miRNAs (DmiRs). miRNA-190 (miR-190) is among the most upregulated DmiRs in all dormant tumors analyzed. Upregulation of miR-190 led to prolonged tumor dormancy in otherwise fast-growing glioblastomas and osteosarcomas. Here we investigate the transcriptional changes induced by miR-190 expression in cancer cells and show similar patterns of miR-190 mediated transcriptional reprogramming in both glioblastoma and osteosarcoma cells. The data suggests that miR-190 mediated effects rely on an extensive network of molecular changes in tumor cells and that miR-190 affects several transcriptional factors, tumor suppressor genes and interferon response pathways. The molecular mechanisms governing tumor dormancy described in this work may provide promising targets for early prevention of cancer and may lead to novel treatments to convert the malignant tumor phenotype into an asymptomatic dormant state.

A MATHEMATICAL ANALYSIS OF PHYSIOLOGICAL AND MOLECULAR MECHANISMS THAT MODULATE PRESSURE GRADIENTS AND FACILITATE VENTRICULAR EXPANSION IN HYDROCEPHALUS.

Perhaps the greatest paradox in the hydrocephalus field is the failure of researchers to consistently measure transmantle pressure gradients (ventricle to subarachnoid space) in either human or animal models of the communicating form of the disorder. Without such a gradient, conceptualization of how ventricular distention occurs is difficult. Based on evidence from both a mathematical model [35] and experiments in skin [51], we observed that the intraventricular injection of anti-ß1 integrin antibodies in rat brains results in a reduction of periventricular pressures to values below those monitored in the ventricles. In addition, many of these animals developed hydrocephalus [30]. We conclude that the dissociation of ß1 integrins from the surrounding matrix fibers generates pressure gradients favouring ventricular expansion suggesting a novel mechanism for hydrocephalus development. Several issues, however, need further clarification. If hydrostatic pressure declines in the periventricular tissues then fluid absorption must occur. Aquaporin-4 (AQP4) is a likely candidate for this absorption as it is the predominant water channel in the brain. Indeed, when capillary function is negated, periventricular interstitial fluid pressures increase after anti-ß1 integrin antibody administration. This suggests that capillary absorption of parenchymal water may play a pivotal role in the generation of pressure gradients in our hydrocephalus model. Focusing on these issues, we present two poroelastic models to investigate the role of intramantle pressure gradients in ventriculomegaly and to determine if integrin-matrix disassociation represents a complete causative mechanism for hydrocephalus development.

A MATHEMATICAL INVESTIGATION OF THE ROLE OF INTRACRANIAL PRESSURE PULSATIONS AND SMALL GRADIENTS IN THE PATHOGENESIS OF HYDROCEPHALUS.

Cerebrospinal fluid (CSF) pulsations have been proposed as a possible causative mechanism for the ventricular enlargement that characterizes the neurological condition known as hydrocephalus. This paper summarizes recent work by the authors to anaylze the effect of CSF pulsations on brain tissue to determine if they are mechanically capable of enlarging the cerebral ventricles. First a poroelastic model is presented to analyze the interactions that occur between the fluid and porous solid constituents of brain tissue due to CSF pulsations. A viscoelastic model is then presented to analyze the effects of the fluid pulsations on the solid brain tissue. The combined results indicate that CSF pulsations in a healthy brain are incapable of causing tissue damage and thus the ventricular enlargement observed in hydrocephalus. Therefore they cannot be the primary cause of this condition. Finally, a hyper-viscoelastic model is presented and used to demonstrate that small long-term transmantle pressure gradients may be a possible cause of communicating hydrocephalus in infants.