Relational grounding facilitates development of scientifically useful multiscale models

Utilizing virtual experiments to increase understanding of discrepancies involving in vitro-to-in vivo predictions of hepatic clearance

Predictions of xenobiotic hepatic clearance in humans using in vitro-to-in vivo extrapolation methods are frequently inaccurate and problematic. Multiple strategies are being pursued to disentangle responsible mechanisms. The objective of this work is to evaluate the feasibility of using insights gained from independent virtual experiments on two model systems to begin unraveling responsible mechanisms. The virtual culture is a software analog of hepatocytes in vitro, and the virtual human maps to hepatocytes within a liver within an idealized model human. Mobile objects (virtual compounds) map to amounts of xenobiotics. Earlier versions of the two systems achieved quantitative validation targets for intrinsic clearance (virtual culture) and hepatic clearance (virtual human). The major difference between the two systems is the spatial organization of the virtual hepatocytes. For each pair of experiments (virtual culture, virtual human), hepatocytes are configured the same. Probabilistic rules govern virtual compound movements and interactions with other objects. We focus on highly permeable virtual compounds and fix their extracellular unbound fraction at one of seven values (0.05–1.0). Hepatocytes contain objects that can bind and remove compounds, analogous to metabolism. We require that, for a subset of compound properties, per-hepatocyte compound exposure and removal rates during culture experiments directly predict corresponding measures made during virtual human experiments. That requirement serves as a cross-system validation target; we identify compound properties that enable achieving it. We then change compound properties, ceteris paribus, and provide model mechanism-based explanations for when and why measures made during culture experiments under- (or over-) predict corresponding measures made during virtual human experiments. The results show that, from the perspective of compound removal, the organization of hepatocytes within virtual livers is more efficient than within cultures, and the greater the efficiency difference, the larger the underprediction. That relationship is noteworthy because most in vitro-to-in vivo extrapolation methods abstract away the structural organization of hepatocytes within a liver. More work is needed on multiple fronts, including the study of an expanded variety of virtual compound properties. Nevertheless, the results support the feasibility of the approach and plan.

Coagulation and inflammation in cancer: Limitations and prospects for treatment

The development of so-called immune checkpoint inhibitors (ICIs), which target specific molecular processes of tumour growth, has had a transformative effect on cancer treatment. Widespread use of antibody-based medicines to inhibit tumour cell immune evasion by modulating T cell responses is becoming more common. Despite this, response rates are still low, and secondary resistance is an issue that arises often. In addition, a wide range of serious adverse effects is triggered by enhancing the immunological response. As a result of an increased mortality rate, a higher prevalence of thrombotic complications is connected with an increased incidence of immunological reactions, complement activation, and skin toxicity. This suggests that the tumour microenvironment's interaction between coagulation and inflammation is important at every stage of the tumour's life cycle. The coagulation system's function in tumour formation is the topic of this review. By better understanding the molecular mechanisms in which tumour cells circulate, plasmatic coagulation and immune system cells are engaged, new therapy options for cancer sufferers may be discovered.

Contrasting model mechanisms of alanine aminotransferase (ALT) release from damaged and necrotic hepatocytes as an example of general biomarker mechanisms

Interpretations of elevated blood levels of alanine aminotransferase (ALT) for drug-induced liver injury often assume that the biomarker is released passively from dying cells. However, the mechanisms driving that release have not been explored experimentally. The usefulness of ALT and related biomarkers will improve by developing mechanism-based explanations of elevated levels that can be expanded and elaborated incrementally. We provide the means to challenge the ability of closely related model mechanisms to generate patterns of simulated hepatic injury and ALT release that scale (or not) to be quantitatively similar to the wet-lab validation targets, which are elevated plasma ALT values following acetaminophen (APAP) exposure in mice. We build on a published model mechanism that helps explain the generation of characteristic spatiotemporal features of APAP hepatotoxicity within hepatic lobules. Discrete event and agent-oriented software methods are most prominent. We instantiate and leverage a small constellation of concrete model mechanisms. Their details during execution help bring into focus ways in which particular sources of uncertainty become entangled with cause-effect details within and across several levels. We scale ALT amounts in virtual mice directly to target plasma ALT values in individual mice. A virtual experiment comprises a set of Monte Carlo simulations. We challenge the sufficiency of four potentially explanatory theories for ALT release. The first of the tested model theories failed to achieve the initial validation target, but each of the three others succeeded. Results for one of the three model mechanisms matched all target ALT values quantitatively. It explains how ALT externalization is the combined consequence of lobular-location-dependent drug-induced cellular damage and hepatocyte death. Falsification of one (or more) of the model mechanisms provides new knowledge and incrementally shrinks the constellation of model mechanisms. The modularity and biomimicry of our explanatory models enable seamless transition from mice to humans.

In silico drug absorption tract: An agent-based biomimetic model for human oral drug absorption

Background

An agent-based modeling approach has been suggested as an alternative to traditional, equation-based modeling methods for describing oral drug absorption. It enables researchers to gain a better understanding of the pharmacokinetic (PK) mechanisms of a drug. This project demonstrates that a biomimetic agent-based model can adequately describe the absorption and disposition kinetics both of midazolam and clonazepam.

Methods

An agent-based biomimetic model, in silico drug absorption tract (ISDAT), was built to mimic oral drug absorption in humans. The model consisted of distinct spaces, membranes, and metabolic enzymes, and it was altogether representative of human physiology relating to oral drug absorption. Simulated experiments were run with the model, and the results were compared to the referent data from clinical equivalence trials. Acceptable similarity was verified by pre-specified criteria, which included 1) qualitative visual matching between the clinical and simulated concentration-time profiles, 2) quantitative similarity indices, namely, weighted root mean squared error (RMSE), and weighted mean absolute percentage error (MAPE) and 3) descriptive similarity which requires less than 25% difference between key PK parameters calculated by the clinical and the simulated concentration-time profiles. The model and its parameters were iteratively refined until all similarity criteria were met. Furthermore, simulated PK experiments were conducted to predict bioavailability (F). For better visualization, a graphical user interface for the model was developed and a video is available in Supporting Information.

Results

Simulation results satisfied all three levels of similarity criteria for both drugs. The weighted RMSE was 0.51 and 0.92, and the weighted MAPE was 5.99% and 8.43% for midazolam and clonazepam, respectively. Calculated PK parameter values, including area under the curve (AUC), peak plasma drug concentration (C_max), time to reach C_max (T_max), terminal elimination rate constant (Kel), terminal elimination half life (T_1/2), apparent oral clearance (CL/F), and apparent volume of distribution (V/F), were reasonable compared to the referent values. The predicted absolute oral bioavailability (F) was 44% for midazolam (literature reported value, 31–72%) and 93% (literature reported value, ≥ 90%) for clonazepam.

Conclusion

The ISDAT met all the pre-specified similarity criteria for both midazolam and clonazepam, and demonstrated its ability to describe absorption kinetics of both drugs. Therefore, the validated ISDAT can be a promising platform for further research into the use of similar in silico models for drug absorption kinetics.

A Model Mechanism-Based Explanation of an In Vitro-In Vivo Disconnect for Improving Extrapolation and Translation

An improved understanding of in vivo-to-in vitro hepatocyte changes is crucial to interpreting in vitro data correctly and further improving hepatocyte-based in vitro-to-in vivo extrapolations to human targets. We demonstrate using virtual experiments as a means of helping to untangle plausible causes of inaccurate extrapolations. We start with virtual mice that use biomimetic software livers. Previously, using these mice, we discovered model mechanisms that enabled achieving quantitative validation targets while also providing plausible causal explanations for temporal characteristics of acetaminophen hepatotoxicity. We isolated virtual hepatocytes, created a virtual culture, and then conducted dose-response experiments in both culture and mice. We expected to see differences between the two dose-response curves but were somewhat surprised that they crossed because it evidenced that simulated acetaminophen metabolism and toxicity are different for virtual culture and mouse contexts even though individual hepatocyte mechanisms were unchanged. Differences in dose-response curves provide a virtual example of an in vivo-to-in vitro disconnect. We use detailed results of experiments to explain this disconnect. Individual hepatocytes contribute differently to system-level phenomena. In liver, hepatocytes are exposed to acetaminophen sequentially. Relative production of the reactive acetaminophen metabolite is largest (smallest) in pericentral (periportal) hepatocytes. Because that sequential exposure is absent in culture, hepatocytes from different lobular locations do not respond the same. A virtual culture-to-mouse translation can stand as a scientifically challengeable hypothesis explaining an in vivo-to-in vitro disconnect. It provides a framework to develop more reliable interpretations of in vitro observations, which then may be used to improve extrapolations.

Simulation enabled search for explanatory mechanisms of the fracture healing process

A significant portion of bone fractures fail to heal properly, increasing healthcare costs. Advances in fracture management have slowed because translation barriers have limited generation of mechanism-based explanations for the healing process. When uncertainties are numerous, analogical modeling can be an effective strategy for developing plausible explanations of complex phenomena. We demonstrate the feasibility of engineering analogical models in software to facilitate discovery of biomimetic explanations for how fracture healing may progress. Concrete analogical models—Callus Analogs—were created using the MASON simulation toolkit. We designated a Target Region initial state within a characteristic tissue section of mouse tibia fracture at day-7 and posited a corresponding day-10 Target Region final state. The goal was to discover a coarse-grain analog mechanism that would enable the discretized initial state to transform itself into the corresponding Target Region final state, thereby providing an alternative way to study the healing process. One of nine quasi-autonomous Tissue Unit types is assigned to each grid space, which maps to an 80×80 μm region of the tissue section. All Tissue Units have an opportunity each time step to act based on individualized logic, probabilities, and information about adjacent neighbors. Action causes transition from one Tissue Unit type to another, and simulation through several thousand time steps generates a coarse-grain analog—a theory—of the healing process. We prespecified a minimum measure of success: simulated and actual Target Region states achieve ≥ 70% Similarity. We used an iterative refinement protocol to explore many combinations of Tissue Unit logic and action constraints. Workflows progressed through four stages of analog mechanisms. Similarities of 73–90% were achieved for Mechanisms 2–4. The range of Upper-Level similarities increased to 83–94% when we allowed for uncertainty about two Tissue Unit designations. We have demonstrated how Callus Analog experiments provide domain experts with a fresh medium and tools for thinking about and understanding the fracture healing process.

Translation barriers have limited the generation of mechanism-based explanations of fracture healing processes. Those barriers help explain why, to date, biological therapeutics have had only a minor impact on fracture management. Alternative approaches are needed, and we present one that is intended to help develop incrementally better mechanism-based explanations of fracture healing phenomena. We created virtual Callus Analogs to simulate how the histologic appearance of a mouse fracture callus may transition from day-7 to day-10. Callus Analogs use software-based model mechanisms, and simulation experiments enable challenging and improving those model mechanisms. During execution, model mechanism operation provides a coarse-grain explanation (a theory) of a four-day portion of the healing process. Simulated day-10 callus histologic images achieved 73–94% Similarity to a corresponding day-10 fracture callus image, thus demonstrating feasibility. Simulated healing provides an alternative perspective on the actual healing process and an alternative way of thinking about plausible fracture healing mechanisms. Our working hypothesis is that the approach can be extended to cover more of the healing process while making features of simulated and actual fracture healing increasingly analogous. The methods presented are intended to be extensible to other research areas that use histologic analysis to investigate and explain tissue level phenomena.

Competing Mechanistic Hypotheses of Acetaminophen-Induced Hepatotoxicity Challenged by Virtual Experiments

Acetaminophen-induced liver injury in mice is a model for drug-induced liver injury in humans. A precondition for improved strategies to disrupt and/or reverse the damage is a credible explanatory mechanism for how toxicity phenomena emerge and converge to cause hepatic necrosis. The Target Phenomenon in mice is that necrosis begins adjacent to the lobule's central vein (CV) and progresses outward. An explanatory mechanism remains elusive. Evidence supports that location dependent differences in NAPQI (the reactive metabolite) formation within hepatic lobules (NAPQI zonation) are necessary and sufficient prerequisites to account for that phenomenon. We call that the NZ-mechanism hypothesis. Challenging that hypothesis in mice is infeasible because 1) influential variables cannot be controlled, and 2) it would require sequential intracellular measurements at different lobular locations within the same mouse. Virtual hepatocytes use independently configured periportal-to-CV gradients to exhibit lobule-location dependent behaviors. Employing NZ-mechanism achieved quantitative validation targets for acetaminophen clearance and metabolism but failed to achieve the Target Phenomenon. We posited that, in order to do so, at least one additional feature must exhibit zonation by decreasing in the CV direction. We instantiated and explored two alternatives: 1) a glutathione depletion threshold diminishes in the CV direction; and 2) ability to repair mitochondrial damage diminishes in the CV direction. Inclusion of one or the other feature into NZ-mechanism failed to achieve the Target Phenomenon. However, inclusion of both features enabled successfully achieving the Target Phenomenon. The merged mechanism provides a multilevel, multiscale causal explanation of key temporal features of acetaminophen hepatotoxicity in mice. We discovered that variants of the merged mechanism provide plausible quantitative explanations for the considerable variation in 24-hour necrosis scores among 37 genetically diverse mouse strains following a single toxic acetaminophen dose.

An Agent-Based Approach to Dynamically Represent the Pharmacokinetic Properties of Baicalein

Baicalein, a typical flavonoid presented in Scutellariae radix, exhibits a unique metabolic profile during first-pass metabolism: parallel glucuronidation and sulfation pathways, with possible substrate inhibition in both pathways. In this project, we aimed to construct an agent-based model to dynamically represent baicalein pharmacokinetics and to verify the substrate inhibition hypothesis. The model consisted of three 3D spaces and two membranes: apical space (S1), intracellular space (S2), basolateral space (S3), apical membrane (M1), and basolateral membrane (M2). In silico enzymes (UDP-glucuronosyltransferases (UGTs) and sulfotransferases (SULTs)) and binder components were placed in S2. The model was then executed to simulate one-pass metabolism experiments of baicalein. With the implementation of a two-site enzyme design, the simulated results captured the preset qualitative and quantitative features of the wet-lab observations. The feasible parameter set showed that substrate inhibition happened in both conjugation pathways of baicalein. The simulation results suggested that the sulfation pathway was dominant at low concentrations and that SULT was more inclined to substrate inhibition than UGT. Cross-model validation was satisfactory. Our findings were consistent with a previously reported catenary model. We conclude that the mechanisms represented by our model are plausible. Our novel modeling approach could dynamically represent the metabolic pathways of baicalein in a Caco-2 system.

Augmenting Surgery via Multi-scale Modeling and Translational Systems Biology in the Era of Precision Medicine: A Multidisciplinary Perspective

In this era of tremendous technological capabilities and increased focus on improving clinical outcomes, decreasing costs, and increasing precision, there is a need for a more quantitative approach to the field of surgery. Multiscale computational modeling has the potential to bridge the gap to the emerging paradigms of Precision Medicine and Translational Systems Biology, in which quantitative metrics and data guide patient care through improved stratification, diagnosis, and therapy. Achievements by multiple groups have demonstrated the potential for (1) multiscale computational modeling, at a biological level, of diseases treated with surgery and the surgical procedure process at the level of the individual and the population; along with (2) patient-specific, computationally-enabled surgical planning, delivery, and guidance and robotically-augmented manipulation. In this perspective article, we discuss these concepts, and cite emerging examples from the fields of trauma, wound healing, and cardiac surgery.

A Computational, Tissue-Realistic Model of Pressure Ulcer Formation in Individuals with Spinal Cord Injury

People with spinal cord injury (SCI) are predisposed to pressure ulcers (PU). PU remain a significant burden in cost of care and quality of life despite improved mechanistic understanding and advanced interventions. An agent-based model (ABM) of ischemia/reperfusion-induced inflammation and PU (the PUABM) was created, calibrated to serial images of post-SCI PU, and used to investigate potential treatments in silico. Tissue-level features of the PUABM recapitulated visual patterns of ulcer formation in individuals with SCI. These morphological features, along with simulated cell counts and mediator concentrations, suggested that the influence of inflammatory dynamics caused simulations to be committed to "better" vs. "worse" outcomes by 4 days of simulated time and prior to ulcer formation. Sensitivity analysis of model parameters suggested that increasing oxygen availability would reduce PU incidence. Using the PUABM, in silico trials of anti-inflammatory treatments such as corticosteroids and a neutralizing antibody targeted at Damage-Associated Molecular Pattern molecules (DAMPs) suggested that, at best, early application at a sufficiently high dose could attenuate local inflammation and reduce pressure-associated tissue damage, but could not reduce PU incidence. The PUABM thus shows promise as an adjunct for mechanistic understanding, diagnosis, and design of therapies in the setting of PU.

In silico, experimental, mechanistic model for extended-release felodipine disposition exhibiting complex absorption and a highly variable food interaction

The objective of this study was to develop and explore new, in silico experimental methods for deciphering complex, highly variable absorption and food interaction pharmacokinetics observed for a modified-release drug product. Toward that aim, we constructed an executable software analog of study participants to whom product was administered orally. The analog is an object- and agent-oriented, discrete event system, which consists of grid spaces and event mechanisms that map abstractly to different physiological features and processes. Analog mechanisms were made sufficiently complicated to achieve prespecified similarity criteria. An equation-based gastrointestinal transit model with nonlinear mixed effects analysis provided a standard for comparison. Subject-specific parameterizations enabled each executed analog’s plasma profile to mimic features of the corresponding six individual pairs of subject plasma profiles. All achieved prespecified, quantitative similarity criteria, and outperformed the gastrointestinal transit model estimations. We observed important subject-specific interactions within the simulation and mechanistic differences between the two models. We hypothesize that mechanisms, events, and their causes occurring during simulations had counterparts within the food interaction study: they are working, evolvable, concrete theories of dynamic interactions occurring within individual subjects. The approach presented provides new, experimental strategies for unraveling the mechanistic basis of complex pharmacological interactions and observed variability.

Toward modular biological models: defining analog modules based on referent physiological mechanisms

Background

Currently, most biomedical models exist in isolation. It is often difficult to reuse or integrate models or their components, in part because they are not modular. Modular components allow the modeler to think more deeply about the role of the model and to more completely address a modeling project’s requirements. In particular, modularity facilitates component reuse and model integration for models with different use cases, including the ability to exchange modules during or between simulations. The heterogeneous nature of biology and vast range of wet-lab experimental platforms call for modular models designed to satisfy a variety of use cases. We argue that software analogs of biological mechanisms are reasonable candidates for modularization. Biomimetic software mechanisms comprised of physiomimetic mechanism modules offer benefits that are unique or especially important to multi-scale, biomedical modeling and simulation.

Results

We present a general, scientific method of modularizing mechanisms into reusable software components that we call physiomimetic mechanism modules (PMMs). PMMs utilize parametric containers that partition and expose state information into physiologically meaningful groupings. To demonstrate, we modularize four pharmacodynamic response mechanisms adapted from an in silico liver (ISL). We verified the modularization process by showing that drug clearance results from in silico experiments are identical before and after modularization. The modularized ISL achieves validation targets drawn from propranolol outflow profile data. In addition, an in silico hepatocyte culture (ISHC) is created. The ISHC uses the same PMMs and required no refactoring. The ISHC achieves validation targets drawn from propranolol intrinsic clearance data exhibiting considerable between-lab variability. The data used as validation targets for PMMs originate from both in vitro to in vivo experiments exhibiting large fold differences in time scale.

Conclusions

This report demonstrates the feasibility of PMMs and their usefulness across multiple model use cases. The pharmacodynamic response module developed here is robust to changes in model context and flexible in its ability to achieve validation targets in the face of considerable experimental uncertainty. Adopting the modularization methods presented here is expected to facilitate model reuse and integration, thereby accelerating the pace of biomedical research.

Tuneable resolution as a systems biology approach for multi-scale, multi-compartment computational models

The use of multi-scale mathematical and computational models to study complex biological processes is becoming increasingly productive. Multi-scale models span a range of spatial and/or temporal scales and can encompass multi-compartment (e.g., multi-organ) models. Modeling advances are enabling virtual experiments to explore and answer questions that are problematic to address in the wet-lab. Wet-lab experimental technologies now allow scientists to observe, measure, record, and analyze experiments focusing on different system aspects at a variety of biological scales. We need the technical ability to mirror that same flexibility in virtual experiments using multi-scale models. Here we present a new approach, tuneable resolution, which can begin providing that flexibility. Tuneable resolution involves fine- or coarse-graining existing multi-scale models at the user's discretion, allowing adjustment of the level of resolution specific to a question, an experiment, or a scale of interest. Tuneable resolution expands options for revising and validating mechanistic multi-scale models, can extend the longevity of multi-scale models, and may increase computational efficiency. The tuneable resolution approach can be applied to many model types, including differential equation, agent-based, and hybrid models. We demonstrate our tuneable resolution ideas with examples relevant to infectious disease modeling, illustrating key principles at work. WIREs Syst Biol Med 2014, 6:225–245. doi:10.1002/wsbm.1270

How to cite this article:WIREs Syst Biol Med 2014, 6:289–309. doi:10.1002/wsbm.1270

Investigation of inflammation and tissue patterning in the gut using a Spatially Explicit General-purpose Model of Enteric Tissue (SEGMEnT)

The mucosa of the intestinal tract represents a finely tuned system where tissue structure strongly influences, and is turn influenced by, its function as both an absorptive surface and a defensive barrier. Mucosal architecture and histology plays a key role in the diagnosis, characterization and pathophysiology of a host of gastrointestinal diseases. Inflammation is a significant factor in the pathogenesis in many gastrointestinal diseases, and is perhaps the most clinically significant control factor governing the maintenance of the mucosal architecture by morphogenic pathways. We propose that appropriate characterization of the role of inflammation as a controller of enteric mucosal tissue patterning requires understanding the underlying cellular and molecular dynamics that determine the epithelial crypt-villus architecture across a range of conditions from health to disease. Towards this end we have developed the Spatially Explicit General-purpose Model of Enteric Tissue (SEGMEnT) to dynamically represent existing knowledge of the behavior of enteric epithelial tissue as influenced by inflammation with the ability to generate a variety of pathophysiological processes within a common platform and from a common knowledge base. In addition to reproducing healthy ileal mucosal dynamics as well as a series of morphogen knock-out/inhibition experiments, SEGMEnT provides insight into a range of clinically relevant cellular-molecular mechanisms, such as a putative role for Phosphotase and tensin homolog/phosphoinositide 3-kinase (PTEN/PI3K) as a key point of crosstalk between inflammation and morphogenesis, the protective role of enterocyte sloughing in enteric ischemia-reperfusion and chronic low level inflammation as a driver for colonic metaplasia. These results suggest that SEGMEnT can serve as an integrating platform for the study of inflammation in gastrointestinal disease.

Agent-based modeling: a systematic assessment of use cases and requirements for enhancing pharmaceutical research and development productivity

A crisis continues to brew within the pharmaceutical research and development (R&D) enterprise: productivity continues declining as costs rise, despite ongoing, often dramatic scientific and technical advances. To reverse this trend, we offer various suggestions for both the expansion and broader adoption of modeling and simulation (M&S) methods. We suggest strategies and scenarios intended to enable new M&S use cases that directly engage R&D knowledge generation and build actionable mechanistic insight, thereby opening the door to enhanced productivity. What M&S requirements must be satisfied to access and open the door, and begin reversing the productivity decline? Can current methods and tools fulfill the requirements, or are new methods necessary? We draw on the relevant, recent literature to provide and explore answers. In so doing, we identify essential, key roles for agent-based and other methods. We assemble a list of requirements necessary for M&S to meet the diverse needs distilled from a collection of research, review, and opinion articles. We argue that to realize its full potential, M&S should be actualized within a larger information technology framework—a dynamic knowledge repository—wherein models of various types execute, evolve, and increase in accuracy over time. We offer some details of the issues that must be addressed for such a repository to accrue the capabilities needed to reverse the productivity decline. © 2013 Wiley Periodicals, Inc.

Individualized, discrete event, simulations provide insight into inter- and intra-subject variability of extended-release, drug products

OBJECTIVE

Develop and validate particular, concrete, and abstract yet plausible in silico mechanistic explanations for large intra- and interindividual variability observed for eleven bioequivalence study participants. Do so in the face of considerable uncertainty about mechanisms.

METHODS

We constructed an object-oriented, discrete event model called subject (we use small caps to distinguish computational objects from their biological counterparts). It maps abstractly to a dissolution test system and study subject to whom product was administered orally. A subject comprises four interconnected grid spaces and event mechanisms that map to different physiological features and processes. Drugs move within and between spaces. We followed an established, Iterative Refinement Protocol. Individualized mechanisms were made sufficiently complicated to achieve prespecified Similarity Criteria, but no more so. Within subjects, the dissolution space is linked to both a product-subject Interaction Space and the GI tract. The GI tract and Interaction Space connect to plasma, from which drug is eliminated.

RESULTS

We discovered parameterizations that enabled the eleven subject simulation results to achieve the most stringent Similarity Criteria. Simulated profiles closely resembled those with normal, odd, and double peaks. We observed important subject-by-formulation interactions within subjects.

CONCLUSION

We hypothesize that there were interactions within bioequivalence study participants corresponding to the subject-by-formulation interactions within subjects. Further progress requires methods to transition currently abstract subject mechanisms iteratively and parsimoniously to be more physiologically realistic. As that objective is achieved, the approach presented is expected to become beneficial to drug development (e.g., controlled release) and to a reduction in the number of subjects needed per study plus faster regulatory review.