Quantitative systems pharmacology model of erythropoiesis to simulate therapies targeting anemia due to chronic kidney disease.

Anemia induced by chronic kidney disease (CKD) has multiple underlying mechanistic causes and generally worsens as CKD progresses. Erythropoietin (EPO) is a key endogenous protein which increases the number of erythrocyte progenitors that mature into red blood cells that carry hemoglobin (Hb). Recombinant human erythropoietin (rHuEPO) in its native and re-engineered forms is used as a therapeutic to alleviate CKD-induced anemia by stimulating erythropoiesis. However, due to safety risks associated with erythropoiesis-stimulating agents (ESAs), a new class of drugs, prolyl hydroxylase inhibitors (PHIs), has been developed. Instead of administering exogenous EPO, PHIs facilitate the accumulation of HIF-α, which results in the increased production of endogenous EPO. Clinical trials for ESAs and PHIs generally involve balancing decisions related to safety and efficacy by carefully evaluating the criteria for patient selection and adaptive trial design. To enable such decisions, we developed a quantitative systems pharmacology (QSP) model of erythropoiesis which captures key aspects of physiology and its disruption in CKD. Furthermore, CKD virtual populations of varying severities were developed, calibrated, and validated against public data. Such a model can be used to simulate alternative trial protocols while designing phase 3 clinical trials, as well as an asset for reverse translation in understanding emerging clinical data.

Can a propensity score matching method be applied to assessing efficacy from single-arm proof-of-concept trials in oncology?

As a result of the escalating number of new cancer treatments being developed and competition among pharmaceutical companies, decisions regarding how to proceed with phase III trials are frequently based on findings from either single-arm phase I expansion cohorts or phase II studies that compare the efficacy of the study drug to a standard-of-care benchmark derived from historical data. However, even when eligibility criteria are matched, differences in the distribution of baseline patient features may influence the outcome of single-arm trials in real-world scenarios. Therefore, novel methods are needed to enhance the accuracy of efficacy prediction from current cohorts relative to historical data. In this study, we demonstrated the feasibility of using the propensity score matching (PSM) method to improve decision making by matching relevant baseline features between current and historical cohorts. According to our findings, utilizing the PSM method may provide a less biased means of comparing outcomes between current and historical cohorts relative to a naïve approach, which relies solely on differences in average outcomes between the cohorts.

Incorporating lesion-to-lesion heterogeneity into early oncology decision making.

RECISTv1.1 (Response Evaluation Criteria In Solid Tumors) is the most commonly used response grading criteria in early oncology trials. In this perspective, we argue that RECISTv1.1 is ambiguous regarding lesion-to-lesion variation that can introduce bias in decision making. We show theoretical examples of how lesion-to-lesion variability causes bias in RECISTv1.1, leading to misclassification of patient response. Next, we review immune checkpoint inhibitor (ICI) clinical trial data and find that lesion-to-lesion heterogeneity is widespread in ICI-treated patients. We illustrate the implications of ignoring lesion-to-lesion heterogeneity in interpreting biomarker data, selecting treatments for patients with progressive disease, and go/no-go decisions in drug development. Further, we propose that Quantitative Systems Pharmacology (QSP) models can aid in developing better metrics of patient response and treatment efficacy by capturing patient responses robustly by considering lesion-to-lesion heterogeneity. Overall, we believe patient response evaluation with an appreciation of lesion-to-lesion heterogeneity can potentially improve decision-making at the early stage of oncology drug development and benefit patient care.

Beyond the single average tumor: Understanding IO combinations using a clinical QSP model that incorporates heterogeneity in patient response.

A quantitative systems pharmacology model for metastatic melanoma was developed for immuno-oncology with the goal of predicting efficacy of combination checkpoint therapy with pembrolizumab and ipilimumab. This literature-based model is developed at multiple scales: (i) tumor and immune cell interactions at a lesion level; (ii) multiple heterogeneous target lesions, nontarget lesion growth, and appearance of new metastatic lesion at a patient level; and (iii) interpatient differences at a population level. The model was calibrated to pembrolizumab and ipilimumab monotherapy in patients with melanoma from Robert et al., specifically, waterfall plot showing target lesion response and overall response rate (Response Evaluation Criteria in Solid Tumors [RECIST] version 1.1), which additionally considers nontarget lesion growth and appearance of new metastatic lesions. We then used the model to predict waterfall and RECIST version 1.1 for combination treatment reported in Long et al. A key insight from this work was that nontarget lesions growth and appearance of new metastatic lesion contributed significantly to disease progression, despite reduction in target lesions. Further, the lesion level simulations of combination therapy show substantial efficacy in warm lesions (intermediary immunogenicity) but limited advantage of combination in both cold and hot lesions (low and high immunogenicity). Because many patients with metastatic disease are expected to have a mixture of these lesions, disease progression in such patients may be driven by a subset of cold lesions that are unresponsive to checkpoint inhibitors. These patients may benefit more from the combinations which include therapies to target cold lesions than double checkpoint inhibitors.

In vitro to in vivo extrapolation and species response comparisons for drug-induced liver injury (DILI) using DILIsym™: a mechanistic, mathematical model of DILI.

Drug-induced liver injury (DILI) is not only a major concern for all patients requiring drug therapy, but also for the pharmaceutical industry. Many new in vitro assays and pre-clinical animal models are being developed to help screen compounds for the potential to cause DILI. This study demonstrates that mechanistic, mathematical modeling offers a method for interpreting and extrapolating results. The DILIsym™ model (version 1A), a mathematical representation of DILI, was combined with in vitro data for the model hepatotoxicant methapyrilene (MP) to carry out an in vitro to in vivo extrapolation. In addition, simulations comparing DILI responses across species illustrated how modeling can aid in selecting the most appropriate pre-clinical species for safety testing results relevant to humans. The parameter inputs used to predict DILI for MP were restricted to in vitro inputs solely related to ADME (absorption, distribution, metabolism, elimination) processes. MP toxicity was correctly predicted to occur in rats, but was not apparent in the simulations for humans and mice (consistent with literature). When the hepatotoxicity of MP and acetaminophen (APAP) was compared across rats, mice, and humans at an equivalent dose, the species most susceptible to APAP was not susceptible to MP, and vice versa. Furthermore, consideration of variability in simulated population samples (SimPops™) provided confidence in the predictions and allowed examination of the biological parameters most predictive of outcome. Differences in model sensitivity to the parameters were related to species differences, but the severity of DILI for each drug/species combination was also an important factor.

A mathematical simulation of the inflammatory response to anthrax infection.

Bacillus anthracis (anthrax) can trigger an acute inflammatory response that results in multisystem organ failure and death. Previously, we developed a mathematical model of acute inflammation after gram-negative infection that had been matched qualitatively to literature data. We modified the properties of the invading bacteria in that model to those specific to B. anthracis and simulated the host response to anthrax infection. We simulated treatment strategies against anthrax in a genetically diverse population including the following: (1) antibiotic treatment initiated at various time points, (2) antiprotective antigen vaccine, and (3) a combination of antibiotics and vaccine. In agreement with studies in mice, our simulations showed that antibiotics only improve survival if administered early in the course of anthrax infection. Vaccination that leads to the formation of antibodies to protective antigen is anti-inflammatory and beneficial in averting shock and improving survival. However, antibodies to protective antigen alone are predicted not to be universally protective against anthrax infection. Rather, our simulations suggest that an optimal strategy would require both vaccination and antibiotic administration.

In silico models of acute inflammation in animals.

Trauma and hemorrhagic shock elicit an acute inflammatory response, predisposing patients to sepsis, organ dysfunction, and death. Few approved therapies exist for these acute inflammatory states, mainly due to the complex interplay of interacting inflammatory and physiological elements working at multiple levels. Various animal models have been used to simulate these phenomena, but these models often do not replicate the clinical setting of multiple overlapping insults. Mathematical modeling of complex systems is an approach for understanding the interplay among biological interactions. We constructed a mathematical model using ordinary differential equations that encompass the dynamics of cells and cytokines of the acute inflammatory response, as well as global tissue dysfunction. The model was calibrated in C57Bl/6 mice subjected to (1) various doses of lipopolysaccharide (LPS) alone, (2) surgical trauma, and (3) surgery + hemorrhagic shock. We tested the model's predictive ability in scenarios on which it had not been trained, namely, (1) surgery +/- hemorrhagic shock + LPS given at times after the beginning of surgical instrumentation, and (2) surgery + hemorrhagic shock + bilateral femoral fracture. Software was created that facilitated fitting of the mathematical model to experimental data, as well as for simulation of experiments with various inflammatory challenges and associated variations (gene knockouts, inhibition of specific cytokines, etc.). Using this software, the C57Bl/6-specific model was recalibrated for inflammatory analyte data in CD14-/- mice and was used to elucidate altered features of inflammation in these animals. In other experiments, rats were subjected to surgical trauma +/- LPS or to bacterial infection via fibrin clots impregnated with various inocula of Escherichia coli. Mathematical modeling may provide insights into the complex dynamics of acute inflammation in a manner that can be tested in vivo using many fewer animals than has been possible previously.

The acute inflammatory response in diverse shock states.

A poorly controlled acute inflammatory response can lead to organ dysfunction and death. Severe systemic inflammation can be induced and perpetuated by diverse insults such as the administration of toxic bacterial products (e.g., endotoxin), traumatic injury, and hemorrhage. Here, we probe whether these varied shock states can be explained by a universal inflammatory system that is initiated through different means and, once initiated, follows a course specified by the cellular and molecular mechanisms of the immune and endocrine systems. To examine this question, we developed a mathematical model incorporating major elements of the acute inflammatory response in C57Bl/6 mice, using input from experimental data. We found that a single model with different initiators including the autonomic system could describe the response to various insults. This model was able to predict a dose range of endotoxin at which mice would die despite having been calibrated only in nonlethal inflammatory paradigms. These results show that the complex biology of inflammation can be modeled and supports the hypothesis that shock states induced by a range of physiologic challenges could arise from a universal response that is differently initiated and modulated.

In silico design of clinical trials: a method coming of age.

OBJECTIVE: To determine the feasibility and potential usefulness of mathematical models in evaluating immunomodulatory strategies in clinical trials of severe sepsis. DESIGN: Mathematical modeling of immunomodulation in simulated patients. SETTING: Computer laboratory. MEASUREMENTS AND MAIN RESULTS: We introduce and evaluate the concept of conducting a randomized clinical trial in silico based on simulated patients generated from a mechanistic mathematical model of bacterial infection, the acute inflammatory response, global tissue dysfunction, and a therapeutic intervention. Trial populations are constructed to reflect heterogeneity in bacterial load and virulence as well as propensity to mount and modulate an inflammatory response. We constructed a cohort of 1,000 trial patients submitted to therapy with one of three different doses of a neutralizing antibody directed against tumor necrosis factor (anti-TNF) for 6, 24, or 48 hrs. We present cytokine profiles over time and expected outcome for each cohort. We identify subgroups with high propensity for being helped or harmed by the proposed intervention and identify early serum markers for each of those subgroups. The mathematical simulation confirms the inability of simple markers to predict outcome of sepsis. The simulation clearly separates cases with favorable and unfavorable outcome on the basis of global tissue dysfunction. Control survival was 62.9% at 1 wk. Depending on dose and duration of treatment, survival ranged from 57.1% to 80.8%. Higher doses of anti-TNF, although effective, also result in considerable harm to patients. A statistical analysis based on a simulated cohort identified markers of favorable or adverse response to anti-TNF treatment. CONCLUSIONS: A mathematical simulation of anti-TNF therapy identified clear windows of opportunity for this intervention as well as populations that can be harmed by anti-TNF therapy. The construction of an in silico clinical trial could provide profound insight into the design of clinical trials of immunomodulatory therapies, ranging from optimal patient selection to individualized dosage and duration of proposed therapeutic interventions.

The dynamics of acute inflammation.

When the body is infected, it mounts an acute inflammatory response to rid itself of the pathogens and restore health. Uncontrolled acute inflammation due to infection is defined clinically as sepsis and can culminate in organ failure and death. We consider a three-dimensional ordinary differential equation model of inflammation consisting of a pathogen, and two inflammatory mediators. The model reproduces the healthy outcome and diverse negative outcomes, depending on initial conditions and parameters. We analyze the various bifurcations between the different outcomes when key parameters are changed and suggest various therapeutic strategies. We suggest that the clinical condition of sepsis can arise from several distinct physiological states, each of which requires a different treatment approach.