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. Moreover, the heterogeneity within this particular group impairs the utility of statistical predictions for informing decision-making in very old individuals. In addition to these methodological problems, the diversity of cultural attitudes, available resources as well as variations of legal and professional norms limit the generalisability of prediction models, especially in patients with complex multi-morbidity and pre-existing functional impairments. Thus, current approaches to prognosticating outcomes in very old patients are imperfect and can generate substantial uncertainty about optimal trajectories of critical care in the individual. This article presents the state of the art and new approaches to predicting outcomes of intensive care for these patients. Special emphasis has been given to the integration of predictions into the decision-making for individual patients. This requires quantification of prognostic uncertainty and a careful alignment of decisions with the preferences of patients, who might prioritise functional outcomes over survival. Since the performance of outcome predictions for the individual patient may improve over time, time-limited trials in intensive care may be an appropriate way to increase the confidence in decisions about life-sustaining treatment.

Developing and validating a machine learning prognostic model for alerting to imminent deterioration of hospitalized patients with COVID-19.

Our study was aimed at developing and validating a new approach, embodied in a machine learning-based model, for sequentially monitoring hospitalized COVID-19 patients and directing professional attention to patients whose deterioration is imminent. Model development employed real-world patient data (598 prediction events for 210 patients), internal validation (315 prediction events for 97 patients), and external validation (1373 prediction events for 307 patients). Results show significant divergence in longitudinal values of eight routinely collected blood parameters appearing several days before deterioration. Our model uses these signals to predict the personal likelihood of transition from non-severe to severe status within well-specified short time windows. Internal validation of the model's prediction accuracy showed ROC AUC of 0.8 and 0.79 for prediction scopes of 48 or 96 h, respectively; external validation showed ROC AUC of 0.7 and 0.73 for the same prediction scopes. Results indicate the feasibility of predicting the forthcoming deterioration of non-severe COVID-19 patients by eight routinely collected blood parameters, including neutrophil, lymphocyte, monocyte, and platelets counts, neutrophil-to-lymphocyte ratio, CRP, LDH, and D-dimer. A prospective clinical study and an impact assessment will allow implementation of this model in the clinic to improve care, streamline resources and ease hospital burden by timely focusing the medical attention on potentially deteriorating patients.

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. To clarify whether such elevated drug concentrations could be reached by long-term drug accumulation, we mechanistically coupled the pharmacokinetics (MCPK) of dabrafenib and its metabolites. The MCPK model is qualitatively based on in vitro and quantitatively on clinical data to describe occupancy-dependent CYP3A4 enzyme induction, accumulation, and drug-drug interaction mechanisms. The prediction suggests an eight-fold increase in the steady-state concentration of potent desmethyl-dabrafenib and its inactive precursor carboxy-dabrafenib within four weeks upon 150 mg b.d. dabrafenib. While it is generally assumed that a higher dose is not critical, we found experimentally that a high physiological dabrafenib concentration fails to induce cell death in embedded 451LU melanoma spheroids.

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., genomic and proteomic), and a simple clinically motivated output (e.g., yes/no responder). Today, precision medicine technologies that have facilitated groundbreaking advances in oncology, notably in cancer immunotherapy, are approaching the limits of their potential, mainly due to the scarcity of methods for integrating genomic, proteomic and clinical patient information. A different approach to treatment personalization involves methodologies focusing on the dynamic interactions in the patient-disease-drug system, as portrayed in mathematical modeling. Achievements of this scientific approach, in the form of algorithms for predicting personal disease dynamics in individual patients under immunotherapeutic drugs, are reviewed as well. The contribution of the dynamic approaches to precision medicine is limited, at present, due to insufficient applicability and validation. Yet, the time is ripe for amalgamating together these two approaches, for maximizing their joint potential to personalize and improve cancer immunotherapy. We suggest the roadmap toward achieving this goal, technologically, and urge clinicians, pharmacologists, and computational biologists to join forces along the pharmaco-clinical track of this development.

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. METHODS: We developed a simple mathematical model for the interactions of an advanced melanoma tumor with both the immune system and the immunotherapy drug, pembrolizumab. We implemented the model in an algorithm which, in conjunction with clinical pretreatment data, enables prediction of the personal patient response to the drug. To develop the algorithm, we retrospectively collected clinical data of 54 patients with advanced melanoma, who had been treated by pembrolizumab, and correlated personal pretreatment measurements to the mathematical model parameters. Using the algorithm together with the longitudinal tumor burden of each patient, we identified the personal mathematical models, and simulated them to predict the patient's time to progression. We validated the prediction capacity of the algorithm by the Leave-One-Out cross-validation methodology. RESULTS: Among the analyzed clinical parameters, the baseline tumor load, the Breslow tumor thickness, and the status of nodular melanoma were significantly correlated with the activation rate of CD8+ T cells and the net tumor growth rate. Using the measurements of these correlates to personalize the mathematical model, we predicted the time to progression of individual patients (Cohen's κ = 0.489). Comparison of the predicted and the clinical time to progression in patients progressing during the follow-up period showed moderate accuracy (R2 = 0.505). CONCLUSIONS: Our results show for the first time that a relatively simple mathematical mechanistic model, implemented in a personalization algorithm, can be personalized by clinical data, evaluated before immunotherapy onset. The algorithm, currently yielding moderately accurate predictions of individual patients' response to pembrolizumab, can be improved by training on a larger number of patients. Algorithm validation by an independent clinical dataset will enable its use as a tool for treatment personalization.

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. OBJECTIVE & METHODS: Here, we tested the hypothesis that extracellular inhibitors of the Wnt pathway, although acting upstream of the APC mutation, can restore normal levels of pathway activity in colon cancer cells. To this end, we developed and simulated a mathematical model for the Wnt pathway in different APC mutants, with or without the effects of the extracellular inhibitors, Secreted Frizzled-Related Protein1 (sFRP1) and Dickhopf1 (Dkk1). We compared our model predictions to experimental data in the literature. RESULTS: Our model accurately predicts T-cell factor (TCF) activity in mutant cells that vary in APC mutation. Model simulations suggest that both sFRP1 and DKK1 can reduce TCF activity in APC1638N/1572T and Apcmin/min mutants, but restoration of normal activity levels is possible only in the former. When applied in combination, synergism between the two inhibitors can reduce their effective doses to one-fourth of the doses required under single inhibitor application. Overall, re-establishment of normal Wnt pathway activity is predicted for every APC mutant in whom TCF activity is increased by up to 11 fold. CONCLUSIONS: Our work suggests that extracellular inhibitors can effectively restore normal Wnt pathway activity in APC-truncated cancer cells, even though these LoF mutations occur downstream of the inhibitory action. The insufficient activity of the truncated APC can be quantitatively balanced by the upstream intervention. This new concept of upstream intervention to control the effects of downstream mutations may be considered also for other partial LoF mutations in other signaling pathways.

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. The reviewed studies suggest that response to immunotherapy can be improved by patient-specific regimens, which can be worked out by personalized mathematical models. The studies further indicate that personalized models can be constructed and validated relatively early in treatment. EXPERT OPINION: The suggested methodology has the potential to raise the overall efficacy of the developed immunotherapy. If implemented already during drug development it may increase the prospects of the technology being approved for clinical use. However, schedule personalization, per se, does not comply with the current, 'one size fits all,' paradigm of clinical trials. It is worthwhile considering adjustment of the current paradigm to involve personally tailored immunotherapy regimens.

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. Our approach includes an iterative real-time in-treatment evaluation of patient-specific parameters from the accruing clinical data, construction of personalized models and their validation, model-based simulation of subsequent response to ongoing therapy, and suggestion of potentially more effective patient-specific modified treatment. Using a mathematical model of prostate cancer immunotherapy, we applied our model to data obtained in a clinical investigation of an allogeneic whole-cell therapeutic prostate cancer vaccine. Personalized models for the patients who responded to treatment were derived and validated by data collected before treatment and during its early phase. Simulations, based on personalized models, suggested that an increase in vaccine dose and administration frequency would stabilize the disease in most patients. Together, our findings suggest that application of our method could facilitate development of a new paradigm for studies of in-treatment personalization of the immune agent administration regimens (P-trials), with treatment modifications restricted to an approved range, resulting in more efficacious immunotherapies.

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 ß-catenin accumulation, and the effects of inhibitors, such as sFRPs (secreted Frizzled-related proteins) and Dkk (Dickkopf). Model parameters were retrieved from experimental data reported previously. The model was retrospectively validated by accurately predicting the effects of Wnt3a and sFRP1 on ß-catenin levels in two independent published experiments (R(2) between 0.63 and 0.91). Prospective validation was obtained by testing the model's accuracy in predicting the effect of Dkk1 on Wnt-induced ß-catenin accumulation (R(2)≈0.94). Model simulations under different combinations of sFRP1 and Dkk1 predicted a clear synergistic effect of these two inhibitors on ß-catenin accumulation, which may point towards a new treatment avenue. Our model allows precise calculation of the effect of inhibitors applied alone or in combination, and provides a flexible framework for identifying potential targets for intervention in the Wnt signalling pathway.

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. Mathematical oncology can simulate tumor characteristics in silico and predict the tumor response to novel therapeutics. Using similar methods to classical pharmacokinetics/pharmacodynamics-type models, mathematical oncology translates the findings into a multiparameter model system and simulates T-cell therapy for malignant diseases. The tumor and immune system dynamics model can provide minimal requirements (in terms of T-cell dose and T-cell functionality) depending on the tumor characteristics (growth rate, residual tumor size) for a clinical study, and help select the best treatment schedule (repetitive doses, minimally required duration, etc.). Here, we present a new mathematical model developed for modeling cellular immunotherapy for melanoma. Computer simulations based on the new model offer an explanation for the observed finding from clinical trials that the patients with the smallest tumor load respond better. We simulate different parameters critical for improvement of cellular therapy for patients with high tumor load of fast-growing tumors. We show that tumor growth rate and tumor load are crucial in predicting the outcome of T-cell therapy. Rather than intuitively extrapolating from experimental data, we demonstrate how mathematical oncology can assist in rational planning of clinical trials.

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. Further analysis of the same model has indicated that excessive stem cell proliferation leading to malignant transformation mainly results from altered sensitivity to such micro-environmental signals. Our aim in this work is to expand the analysis to the dynamics of established populations of cancer cells and to examine possible therapeutic avenues for eliminating CSCs. The proposed model considers two populations of cells: CSCs, which can divide indefinitely, and differentiated cancer cells, which do not divide and have a limited lifespan. We assume that total cell density has negative feedback on CSC proliferation and that high CSC density activates CSC differentiation. We show that neither stimulation of CSC differentiation nor inhibition of CSC proliferation alone is sufficient for complete CSC elimination and cancer cure, since each of these two therapies affects a different subpopulation of CSCs. However, a combination of these two strategies can substantially reduce the population sizes and densities of all types of cancer cells. Therefore, we propose that in clinical trials, CSC differentiation therapy should only be examined in combination with chemotherapy. Our conclusions are corroborated by clinical experience with differentiating agents in acute promyelocytic leukemia and neuroblastoma.

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. Preliminary model analysis of the single cell dynamics indicated that Dickkopf1 (Dkk1), a protein known to negatively regulate the Wnt pathway, can serve as anti-proliferation and pro-maturation signal to the cell. Simulations of the multi-scale tissue model suggested that Dkk1 may be a QS factor, regulating SC density on the level of the whole tissue: relatively low levels of exogenously applied Dkk1 have little effect on SC numbers, whereas high levels drive SCs into differentiation. To verify these model predictions, we treated the MCF-7 cell line and primary breast cancer (BC) cells from 3 patient samples with different concentrations and dosing regimens of Dkk1, and evaluated subsequent formation of mammospheres (MS) and the mammary SC marker CD44(+)CD24(lo). As predicted by the model, low concentrations of Dkk1 had no effect on primary BC cells, or even increased MS formation among MCF-7 cells, whereas high Dkk1 concentrations decreased MS formation among both primary BC cells and MCF-7 cells. CONCLUSIONS/SIGNIFICANCE: Our study suggests that Dkk1 treatment may be more robust than other methods for eliminating CSCs, as it challenges a general cellular homeostasis mechanism, namely, fate decision by QS. The study also suggests that low dose Dkk1 administration may be counterproductive; we showed experimentally that in some cases it can stimulate CSC proliferation, although this needs validating in vivo.

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. For model validation in the absence of any other pertinent marker, we used the clinically measured changes in prostate-specific antigen (PSA) levels as a correlate of tumor burden. Up to 26 PSA levels measured per patient were divided into each patient's training set and his validation set. The training set, used for model personalization, contained the patient's initial sequence of PSA levels; the validation set contained his subsequent PSA data points. Personalized models were simulated to predict changes in tumor burden and PSA levels and predictions were compared to the validation set. The model accurately predicted PSA levels over the entire measured period in 12 of the 15 vaccination-responsive patients (the coefficient of determination between the predicted and observed PSA values was R(2) = 0.972). The model could not account for the inconsistent changes in PSA levels in 3 of the 15 responsive patients at the end of treatment. Each validated personalized model was simulated under many hypothetical immunotherapy protocols to suggest alternative vaccination regimens. Personalized regimens predicted to enhance the effects of therapy differed among the patients. CONCLUSIONS/SIGNIFICANCE: Using a few initial measurements, we constructed robust patient-specific models of PCa immunotherapy, which were retrospectively validated by clinical trial results. Our results emphasize the potential value and feasibility of individualized model-suggested immunotherapy protocols.

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. This dichotomy is mainly driven by intercellular communication, low intensity of which causes perpetual proliferation. Another driving force is the cells' kinetic parameters. Reduced tissue life span of differentiated cells results in uncontrolled proliferation. Model's analysis, showing that under the Quorum Sensing control, stem cell fraction within a steady state population is fixed, is corroborated by experiments in breast carcinoma cells. Experimental results show that the plating densities of CD44+ cells and of CD44+/24lo/ESA+ cells do not affect stem cell fraction near confluence. CONCLUSIONS: This study suggests that stem cell immortalization may be triggered by reduced intercellular communication, rather than exclusively result from somatic evolution, and implies that stem cell proliferation can be attenuated by signal manipulation, or enhanced by cytotoxics targeted to differentiated cells. In vivo verification and identification of the Quorum Sensing mediating molecules will pave the way to a higher level control of stem cell proliferation in cancer and in tissue engineering.

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). Our model encompasses considerations of the interactive dynamics of aCTL, tumor cells, major histocompatibility complex (MHC) class I and MHC class II molecules, as well as cytokines, such as TGF-beta and IFN-gamma, which dampen or increase the pro-inflammatory environment, respectively. Computer simulations were used for model verification and for retrieving putative treatment scenarios. The mathematical model successfully retrieved clinical trial results of efficacious aCTL immunotherapy for recurrent anaplastic oligodendroglioma and anaplastic astrocytoma (WHO grade III). It predicted that cellular adoptive immunotherapy failed in GBM because the administered dose was 20-fold lower than required for therapeutic efficacy. Model analysis suggests that GBM may be eradicated by new dose-intensive strategies, e.g., 3 x 10(8) aCTL every 4 days for small tumor burden, or 2 x 10(9) aCTL, infused every 5 days for larger tumor burden. Further analysis pinpoints crucial bio-markers relating to tumor growth rate, tumor size, and tumor sensitivity to the immune system, whose estimation enables regimen personalization. We propose that adoptive cellular immunotherapy was prematurely abandoned. It may prove efficacious for GBM, if dose intensity is augmented, as prescribed by the mathematical model. Re-initiation of clinical trials, using calculated individualized regimens for grade III-IV malignant glioma, is suggested.

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. In both models, the only nontrivial critical point is always unstable, while one of the trivial critical points is always stable. The models predict unlimited growth, if the initial condition is close enough to the nontrivial critical point, and this growth may be characterized by oscillations in tumor and vascular mass. We suggest that angiogenesis per se does not suffice for explaining the observed stabilization of vascular tumor size.