Prognosticating the outcome of intensive care in older patients-a narrative review.

Prognosis determines major decisions regarding treatment for critically ill patients. Statistical models have been developed to predict the probability of survival and other outcomes of intensive care. Although they were trained on the characteristics of large patient cohorts, they often do not represent very old patients (age ≥ 80 years) appropriately.

Mechanistically Coupled PK (MCPK) Model to Describe Enzyme Induction and Occupancy Dependent DDI of Dabrafenib Metabolism.

Dabrafenib inhibits the cell proliferation of metastatic melanoma with the oncogenic BRAF(V600)-mutation. However, dabrafenib monotherapy is associated with pERK reactivation, drug resistance, and consequential relapse. A clinical drug-dose determination study shows increased pERK levels upon daily administration of more than 300 mg dabrafenib.

Accelerating the Development of Personalized Cancer Immunotherapy by Integrating Molecular Patients' Profiles with Dynamic Mathematical Models.

We review the evolution, achievements, and limitations of the current paradigm shift in medicine, from the "one-size-fits-all" model to "Precision Medicine." Precision, or personalized, medicine-tailoring the medical treatment to the personal characteristics of each patient-engages advanced statistical methods to evaluate the relationships between static patient profiling (e.g.

Predicting response to pembrolizumab in metastatic melanoma by a new personalization algorithm.

Background: At present, immune checkpoint inhibitors, such as pembrolizumab, are widely used in the therapy of advanced non-resectable melanoma, as they induce more durable responses than other available treatments. However, the overall response rate does not exceed 50% and, considering the high costs and low life expectancy of nonresponding patients, there is a need to select potential responders before therapy. Our aim was to develop a new personalization algorithm which could be beneficial in the clinical setting for predicting time to disease progression under pembrolizumab treatment.

Extracellular inhibitors can attenuate tumorigenic Wnt pathway activity in adenomatous polyposis coli mutants: Predictions of a validated mathematical model.

Background: Despite considerable investigational efforts, no method to overcome the pathogenesis caused by loss of function (LoF) mutations in tumor suppressor genes has been successfully translated to the clinic. The most frequent LoF mutation in human cancers is Adenomatous polyposis coli (APC), causing aberrant activation of the Wnt pathway. In nearly all colon cancer tumors, the APC protein is truncated, but still retains partial binding abilities.

Employing dynamical computational models for personalizing cancer immunotherapy.

Introduction: Recently, cancer immunotherapy has shown considerable success, but due to the complexity of the immune-cancer interactions, clinical outcomes vary largely between patients. A possible approach to overcome this difficulty may be to develop new methodologies for personal predictions of therapy outcomes, by the integration of patient data with dynamical mathematical models of the drug-affected pathophysiological processes.

Areas Covered: This review unfolds the story of mathematical modeling in cancer immunotherapy, and examines the feasibility of using these models for immunotherapy personalization.

Reconsidering the paradigm of cancer immunotherapy by computationally aided real-time personalization.

Although therapeutic vaccination often induces markers of tumor-specific immunity, therapeutic responses remain rare. An improved understanding of patient-specific dynamic interactions of immunity and tumor progression, combined with personalized application of immune therapeutics would increase the efficacy of immunotherapy. Here, we developed a method to predict and enhance the individual response to immunotherapy by using personalized mathematical models, constructed in the early phase of treatment.

A new validated mathematical model of the Wnt signalling pathway predicts effective combinational therapy by sFRP and Dkk.

The Wnt signalling pathway controls cell proliferation and differentiation, and its deregulation is implicated in different diseases including cancer. Learning how to manipulate this pathway could substantially contribute to the development of therapies. We developed a mathematical model describing the initial sequence of events in the Wnt pathway, from ligand binding to β-catenin accumulation, and the effects of inhibitors, such as sFRPs (secreted Frizzled-related proteins) and Dkk (Dickkopf).

Improving T-cell immunotherapy for melanoma through a mathematically motivated strategy: efficacy in numbers?

T-cell mediated immunotherapy for malignant diseases has become an effective treatment option, especially in malignant melanoma. Recent advances have enabled the transfer of high T-cell numbers with high functionality. However, with more T cells becoming technically available for transfer, questions about dose, treatment schedule, and safety become most relevant.

Strategies for cancer stem cell elimination: insights from mathematical modeling.

The cancer stem cell (CSC) hypothesis states that only a small fraction of a malignant cell population is responsible for tumor growth and relapse. Understanding the relationships between CSC dynamics and cancer progression may contribute to improvements in cancer treatment. Analysis of a simple discrete mathematical model has suggested that homeostasis in developing tissues is governed by a "quorum sensing" control mechanism, in which stem cells differentiate or proliferate according to feedback they receive from neighboring cell populations.

Dickkopf1 regulates fate decision and drives breast cancer stem cells to differentiation: an experimentally supported mathematical model.

Background: Modulation of cellular signaling pathways can change the replication/differentiation balance in cancer stem cells (CSCs), thus affecting tumor growth and recurrence. Analysis of a simple, experimentally verified, mathematical model suggests that this balance is maintained by quorum sensing (QS).

Methodology/principal Findings: To explore the mechanism by which putative QS cellular signals in mammary stem cells (SCs) may regulate SC fate decisions, we developed a multi-scale mathematical model, integrating extra-cellular and intra-cellular signal transduction within the mammary tissue dynamics.

Predicting outcomes of prostate cancer immunotherapy by personalized mathematical models.

Background: Therapeutic vaccination against disseminated prostate cancer (PCa) is partially effective in some PCa patients. We hypothesized that the efficacy of treatment will be enhanced by individualized vaccination regimens tailored by simple mathematical models.

Methodology/principal Findings: We developed a general mathematical model encompassing the basic interactions of a vaccine, immune system and PCa cells, and validated it by the results of a clinical trial testing an allogeneic PCa whole-cell vaccine.

Disruption of a Quorum Sensing mechanism triggers tumorigenesis: a simple discrete model corroborated by experiments in mammary cancer stem cells.

Background: The balance between self-renewal and differentiation of stem cells is expected to be tightly controlled in order to maintain tissue homeostasis throughout life, also in the face of environmental hazards. Theory, predicting that homeostasis is maintained by a negative feedback on stem cell proliferation, implies a Quorum Sensing mechanism in higher vertebrates.

Results: Application of this theory to a cellular automata model of stem cell development in disrupted environments shows a sharply dichotomous growth dynamics: maturation within 50-400 cell cycles, or immortalization.

Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics.

Glioblastoma (GBM), a highly aggressive (WHO grade IV) primary brain tumor, is refractory to traditional treatments, such as surgery, radiation or chemotherapy. This study aims at aiding in the design of more efficacious GBM therapies. We constructed a mathematical model for glioma and the immune system interactions, that may ensue upon direct intra-tumoral administration of ex vivo activated alloreactive cytotoxic-T-lymphocytes (aCTL).

Critical-point analysis for three-variable cancer angiogenesis models.

We perform critical-point analysis for three-variable systems that represent essential processes of the growth of the angiogenic tumor, namely, tumor growth, vascularization, and generation of angiogenic factor (protein) as a function of effective vessel density. Two models that describe tumor growth depending on vascular mass and regulation of new vessel formation through a key angiogenic factor are explored. The first model is formulated in terms of ODEs, while the second assumes delays in this regulation, thus leading to a system of DDEs.