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

A Mathematical Model of Pressure Ulcer Formation to Facilitate Prevention and Management

Pressure ulcers are a frequent issue involving localized damage to the skin and underlying tissues, commonly arising from prolonged hospitalization and immobilization. This paper introduces a mathematical model designed to elucidate the mechanics behind pressure ulcer formation, aiming to predict its occurrence and assist in its prevention. Utilizing differential geometry and elasticity theory, the model represents human skin and simulates its deformation under pressure. Additionally, a system of ordinary differential equations is employed to predict the outcomes of these deformations, estimating the cellular death rate in skin tissues and underlying layers. The model also incorporates changes in blood flow resulting from alterations in skin geometry. This comprehensive approach provides new insights into the optimal bed surfaces required to prevent pressure ulcers and offers a general predictive method to aid healthcare personnel in making informed decisions for at-risk patients. Compared to existing models in the literature, our model delivers a more thorough prediction method that aligns well with current data. It can forecast the time required for an immobilized individual to develop an ulcer in various body parts, considering different initial health conditions and treatment strategies.

Age-dependent ventilator-induced lung injury: Mathematical modeling, experimental data, and statistical analysis

A variety of pulmonary insults can prompt the need for life-saving mechanical ventilation; however, misuse, prolonged use, or an excessive inflammatory response, can result in ventilator-induced lung injury. Past research has observed an increased instance of respiratory distress in older patients and differences in the inflammatory response. To address this, we performed high pressure ventilation on young (2-3 months) and old (20-25 months) mice for 2 hours and collected data for macrophage phenotypes and lung tissue integrity. Large differences in macrophage activation at baseline and airspace enlargement after ventilation were observed in the old mice. The experimental data was used to determine plausible trajectories for a mathematical model of the inflammatory response to lung injury which includes variables for the innate inflammatory cells and mediators, epithelial cells in varying states, and repair mediators. Classification methods were used to identify influential parameters separating the parameter sets associated with the young or old data and separating the response to ventilation, which was measured by changes in the epithelial state variables. Classification methods ranked parameters involved in repair and damage to the epithelial cells and those associated with classically activated macrophages to be influential. Sensitivity results were used to determine candidate in-silico interventions and these interventions were most impact for transients associated with the old data, specifically those with poorer lung health prior to ventilation. Model results identified dynamics involved in M1 macrophages as a focus for further research, potentially driving the age-dependent differences in all macrophage phenotypes. The model also supported the pro-inflammatory response as a potential indicator of age-dependent differences in response to ventilation. This mathematical model can serve as a baseline model for incorporating other pulmonary injuries.

Artificial Intelligence Optical Biopsy for Evaluating the Functional State of Wounds

INTRODUCTION

The clinical characterization of the functional status of active wounds in terms of their driving cellular and molecular biology remains a considerable challenge that currently requires excision via a tissue biopsy. In this pilot study, we use convolutional Siamese neural network (SNN) architecture to predict the functional state of a wound using digital photographs of wounds in a canine model of volumetric muscle loss (VML).

METHODS

Digital images of VML injuries and tissue biopsies were obtained in a standardized fashion from an established canine model of VML. Gene expression profiles for each biopsy site were obtained using RNA sequencing. These profiles were converted to functional profiles by a manual review of validated gene ontology databases in which we determined a hierarchical representation of gene functions based on functional specificity. An SNN was trained to regress functional profile expression values, informed by an image segment showing the surface of a small tissue biopsy.

RESULTS

The SNN was able to predict the functional expression of a range of functions based with error ranging from ∼5% to ∼30%, with functions that are most closely associated with the early state of wound healing to be those best-predicted.

CONCLUSIONS

These initial results suggest promise for further research regarding this novel use of machine learning regression on medical images. The regression of functional profiles, as opposed to specific genes, both addresses the challenge of genetic redundancy and gives a deeper insight into the mechanistic configuration of a region of tissue in wounds.

Computational simulation of liver fibrosis dynamics

Liver fibrosis is a result of homeostasis breakdown caused by repetitive injury. The accumulation of collagens disrupts liver structure and function, which causes serious consequences such as cirrhosis. Various mathematical simulation models have been developed to understand these complex processes. We employed the agent-based modelling (ABM) approach and implemented inflammatory processes in central venous regions. Collagens were individually modelled and visualised depending on their origin: myofibroblast and portal fibroblast. Our simulation showed that the administration of toxic compounds induced accumulation of myofibroblast-derived collagens in central venous regions and portal fibroblast-derived collagens in portal areas. Subsequently, these collagens were bridged between central-central areas and spread all over areas. We confirmed the consistent dynamic behaviour of collagen formulation in our simulation and from histological sections obtained via in vivo experiments. Sensitivity analyses identified dead hepatocytes caused by inflammation and the ratio of residential liver cells functioned as a cornerstone for the initiation and progression of liver fibrosis. The validated mathematical model demonstrated here shows virtual experiments that are complementary to biological experiments, which contribute to understanding a new mechanism of liver fibrosis.

Optical Biopsy Using a Neural Network to Predict Gene Expression From Photos of Wounds

BACKGROUND

The clinical characterization of the biological status of complex wounds remains a considerable challenge. Digital photography provides a non-invasive means of obtaining wound information and is currently employed to assess wounds qualitatively. Advances in machine learning (ML) image processing provide a means of identifying "hidden" features in pictures. This pilot study trains a convolutional neural network (CNN) to predict gene expression based on digital photographs of wounds in a canine model of volumetric muscle loss (VML).

MATERIALS AND METHODS

Images of volumetric muscle loss injuries and tissue biopsies were obtained in a canine model of VML. A CNN was trained to regress gene expression values as a function of the extracted image segment (color and spatial distribution). Performance of the CNN was assessed in a held-back test set of images using Mean Absolute Percentage Error (MAPE).

RESULTS

The CNN was able to predict the gene expression of certain genes based on digital images, with a MAPE ranging from ∼10% to ∼30%, indicating the presence and identification of distinct, and identifiable patterns in gene expression throughout the wound.

CONCLUSIONS

These initial results suggest promise for further research regarding this novel use of ML regression on medical images. Specifically, the use of CNNs to determine the mechanistic biological state of a VML wound could aid both the design of future mechanistic interventions and the design of trials to test those therapies. Future work will expand the CNN training and/or test set, with potential expansion to predicting functional gene modules.

Exploring the first pressure injury and characteristics of subsequent pressure injury accrual following spinal cord injury

Context/Objective: Clinicians have guidance on prevention and treatment of pressure injuries, but little is known regarding characteristics of patients who develop additional pressure injuries. Thus, our objective was to explore the first pressure injury and characteristics of individuals who develop subsequent pressure injuries during acute care and inpatient rehabilitation following spinal cord injury.Design: Secondary analysis of longitudinal data from a cohort of adults following initial traumatic spinal cord injury.Setting: Urban acute care hospital and inpatient rehabilitation facilities.Participants: A convenience sample of adults (n = 38) who developed at least one pressure injury during acute care and inpatient rehabilitation.Interventions: Not applicable.Outcome Measures: The primary outcomes were number of additional pressure injuries and stage of care during which they occurred, prior to community discharge.Results: A covariate-adjusted model revealed that participants with ASIA D injury had a 67% decrease in the rate of additional pressure injury incidence compared to participants with ASIA A injury (Rate Ratio = .33, 95% CI [0.13, 0.88]). The severity of the first pressure injury had no significant association with subsequent pressure injury incidence (P = .10).Conclusion: These findings indicated that individuals with greater sensory and motor loss had an increased risk of developing additional pressure injuries compared to individuals with less impairment. These results are meaningful for stakeholders interested in understanding factors associated with developing subsequent pressure injuries during the index rehabilitation stay and provide a foundation for future research in this area.

Mathematical Model Predicts that Acceleration of Diabetic Wound Healing is Dependent on Spatial Distribution of VEGF-A mRNA (AZD8601)

Introduction

Pharmacologic approaches for promoting angiogenesis have been utilized to accelerate healing of chronic wounds in diabetic patients with varying degrees of success. We hypothesize that the distribution of proangiogenic drugs in the wound area critically impacts the rate of closure of diabetic wounds. To evaluate this hypothesis, we developed a mathematical model that predicts how spatial distribution of VEGF-A produced by delivery of a modified mRNA (AZD8601) accelerates diabetic wound healing.

Methods

We modified a previously published model of cutaneous wound healing based on coupled partial differential equations that describe the density of sprouting capillary tips, chemoattractant concentration, and density of blood vessels in a circular wound. Key model parameters identified by a sensitivity analysis were fit to data obtained from an in vivo wound healing study performed in the dorsum of diabetic mice, and a pharmacokinetic model was used to simulate mRNA and VEGF-A distribution following injections with AZD8601. Due to the limited availability of data regarding the spatial distribution of AZD8601 in the wound bed, we performed simulations with perturbations to the location of injections and diffusion coefficient of mRNA to understand the impact of these spatial parameters on wound healing.

Results

When simulating injections delivered at the wound border, the model predicted that injections delivered on day 0 were more effective in accelerating wound healing than injections delivered at later time points. When the location of the injection was varied throughout the wound space, the model predicted that healing could be accelerated by delivering injections a distance of 1–2 mm inside the wound bed when compared to injections delivered on the same day at the wound border. Perturbations to the diffusivity of mRNA predicted that restricting diffusion of mRNA delayed wound healing by creating an accumulation of VEGF-A at the wound border. Alternatively, a high mRNA diffusivity had no effect on wound healing compared to a simulation with vehicle injection due to the rapid loss of mRNA at the wound border to surrounding tissue.

Conclusions

These findings highlight the critical need to consider the location of drug delivery and diffusivity of the drug, parameters not typically explored in pre-clinical experiments, when designing and testing drugs for treating diabetic wounds.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-021-00678-9.

Agent-based models of inflammation in translational systems biology: A decade later

Agent-based modeling is a rule-based, discrete-event, and spatially explicit computational modeling method that employs computational objects that instantiate the rules and interactions among the individual components ("agents") of system. Agent-based modeling is well suited to translating into a computational model the knowledge generated from basic science research, particularly with respect to translating across scales the mechanisms of cellular behavior into aggregated cell population dynamics manifesting at the tissue and organ level. This capacity has made agent-based modeling an integral method in translational systems biology (TSB), an approach that uses multiscale dynamic computational modeling to explicitly represent disease processes in a clinically relevant fashion. The initial work in the early 2000s using agent-based models (ABMs) in TSB focused on examining acute inflammation and its intersection with wound healing; the decade since has seen vast growth in both the application of agent-based modeling to a wide array of disease processes as well as methodological advancements in the use and analysis of ABM. This report presents an update on an earlier review of ABMs in TSB and presents examples of exciting progress in the modeling of various organs and diseases that involve inflammation. This review also describes developments that integrate the use of ABMs with cutting-edge technologies such as high-performance computing, machine learning, and artificial intelligence, with a view toward the future integration of these methodologies. This article is categorized under: Translational, Genomic, and Systems Medicine > Translational Medicine Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models Models of Systems Properties and Processes > Organismal Models.

Agent-Based Modeling in Molecular Systems Biology

Molecular systems orchestrating the biology of the cell typically involve a complex web of interactions among various components and span a vast range of spatial and temporal scales. Computational methods have advanced our understanding of the behavior of molecular systems by enabling us to test assumptions and hypotheses, explore the effect of different parameters on the outcome, and eventually guide experiments. While several different mathematical and computational methods are developed to study molecular systems at different spatiotemporal scales, there is still a need for methods that bridge the gap between spatially-detailed and computationally-efficient approaches. In this review, we summarize the capabilities of agent-based modeling (ABM) as an emerging molecular systems biology technique that provides researchers with a new tool in exploring the dynamics of molecular systems/pathways in health and disease.

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.

Predictors of pressure ulcer incidence following traumatic spinal cord injury: a secondary analysis of a prospective longitudinal study

STUDY DESIGN

Secondary analysis of data from a prospective cohort study.

OBJECTIVES

The objective of this study was to identify the medical and demographic factors associated with the development of pressure ulcers during acute-care hospitalization and inpatient rehabilitation following acute spinal cord injury.

SETTING

The study was carried out at acute hospitalization, inpatient rehabilitation and outpatient rehabilitation sites at a university medical center in the United States.

METHODS

Adults with acute traumatic spinal cord injury (n=104) were recruited within 24-72 h of admission to the hospital. Pressure ulcer incidence was recorded.

RESULTS

Thirty-nine participants out of 104 (37.5%) developed at least one pressure ulcer during acute-care hospitalization and inpatient rehabilitation. Univariate logistic regression analyses revealed significant association of pressure ulcer incidence for those with pneumonia and mechanical ventilation (P=0.01) and higher injury severity (ASIA A) (P=0.01). Multiple logistic regression showed that the odds of formation of a first pressure ulcer in participants with ASIA A was 4.5 times greater than that for participants with ASIA B, CI (1-20.65), P=0.05, and 4.6 times greater than that for participants with ASIA C, CI (1.3-16.63), P=0.01.

CONCLUSION

Among individuals with acute traumatic SCI, those with high-injury severity were at an increased risk to develop pressure ulcers. Pneumonia was noted to be associated with the formation of pressure ulcers.

A Clinicoepidemiological Profile of Chronic Wounds in Wound Healing Department in Shanghai

The aim of the study was to update the clinical database of chronic wounds in order to derive an evidence based understanding of the condition and hence to guide future clinical management in China. A total of 241 patients from January 1, 2011 to April 30, 2016 with chronic wounds of more than 2 weeks’ duration were studied in wound healing department in Shanghai. Results revealed that among all the patients the mean age was 52.5 ± 20.2 years (range 2-92 years). The mean initial area of wounds was 30.3 ± 63.0 cm2 (range 0.25-468 cm2). The mean duration of wounds was 68.5 ± 175.2 months (range 0.5-840 months). The previously reported causes of chronic wounds were traumatic or surgical wounds (n = 82, 34.0%), followed by pressure ulcers (n = 59, 24.5%). To study the effects of age, patients were divided into 2 groups: less than 60 years (<60), and 60 years or older (≥60). The proportion of wounds etiology between the 2 age groups was analyzed, and there was significant statistical difference ( P < .05, 95% confidence interval [CI] = 0.076-0.987). To study the associations between outcome and clinical characteristics in chronic wounds, chi-square test was used. There were significant differences in the factor of wound infection. ( P = .035, 95% CI = 0.031-0.038) Regarding therapies, 72.6% (n = 175) of the patients were treated with negative pressure wound therapy. Among all the patients, 29.9% (n = 72) of them were completely healed when discharged while 62.7% (n = 150) of them improved. The mean treatment cost was 12055.4 ± 9206.3 Chinese Yuan (range 891-63626 Chinese Yuan). In conclusion, traumatic or surgical wounds have recently become the leading cause of chronic wounds in Shanghai, China. Etiology of the 2 age groups was different. Infection could significantly influence the wound outcome.

Solving Immunology?

Emergent responses of the immune system result from the integration of molecular and cellular networks over time and across multiple organs. High-content and high-throughput analysis technologies, concomitantly with data-driven and mechanistic modeling, hold promise for the systematic interrogation of these complex pathways. However, connecting genetic variation and molecular mechanisms to individual phenotypes and health outcomes has proven elusive. Gaps remain in data, and disagreements persist about the value of mechanistic modeling for immunology. Here, we present the perspectives that emerged from the National Institute of Allergy and Infectious Disease (NIAID) workshop 'Complex Systems Science, Modeling and Immunity' and subsequent discussions regarding the potential synergy of high-throughput data acquisition, data-driven modeling, and mechanistic modeling to define new mechanisms of immunological disease and to accelerate the translation of these insights into therapies.

Optimization and Control of Agent-Based Models in Biology: A Perspective

Agent-based models (ABMs) have become an increasingly important mode of inquiry for the life sciences. They are particularly valuable for systems that are not understood well enough to build an equation-based model. These advantages, however, are counterbalanced by the difficulty of analyzing and using ABMs, due to the lack of the type of mathematical tools available for more traditional models, which leaves simulation as the primary approach. As models become large, simulation becomes challenging. This paper proposes a novel approach to two mathematical aspects of ABMs, optimization and control, and it presents a few first steps outlining how one might carry out this approach. Rather than viewing the ABM as a model, it is to be viewed as a surrogate for the actual system. For a given optimization or control problem (which may change over time), the surrogate system is modeled instead, using data from the ABM and a modeling framework for which ready-made mathematical tools exist, such as differential equations, or for which control strategies can explored more easily. Once the optimization problem is solved for the model of the surrogate, it is then lifted to the surrogate and tested. The final step is to lift the optimization solution from the surrogate system to the actual system. This program is illustrated with published work, using two relatively simple ABMs as a demonstration, Sugarscape and a consumer-resource ABM. Specific techniques discussed include dimension reduction and approximation of an ABM by difference equations as well systems of PDEs, related to certain specific control objectives. This demonstration illustrates the very challenging mathematical problems that need to be solved before this approach can be realistically applied to complex and large ABMs, current and future. The paper outlines a research program to address them.

Multiscale Modeling in the Clinic: Drug Design and Development

A wide range of length and time scales are relevant to pharmacology, especially in drug development, drug design and drug delivery. Therefore, multiscale computational modeling and simulation methods and paradigms that advance the linkage of phenomena occurring at these multiple scales have become increasingly important. Multiscale approaches present in silico opportunities to advance laboratory research to bedside clinical applications in pharmaceuticals research. This is achievable through the capability of modeling to reveal phenomena occurring across multiple spatial and temporal scales, which are not otherwise readily accessible to experimentation. The resultant models, when validated, are capable of making testable predictions to guide drug design and delivery. In this review we describe the goals, methods, and opportunities of multiscale modeling in drug design and development. We demonstrate the impact of multiple scales of modeling in this field. We indicate the common mathematical and computational techniques employed for multiscale modeling approaches used in pharmacometric and systems pharmacology models in drug development and present several examples illustrating the current state-of-the-art models for (1) excitable systems and applications in cardiac disease; (2) stem cell driven complex biosystems; (3) nanoparticle delivery, with applications to angiogenesis and cancer therapy; (4) host-pathogen interactions and their use in metabolic disorders, inflammation and sepsis; and (5) computer-aided design of nanomedical systems. We conclude with a focus on barriers to successful clinical translation of drug development, drug design and drug delivery multiscale models.

Modeling keratinocyte wound healing dynamics: Cell-cell adhesion promotes sustained collective migration

The in vitro migration of keratinocyte cell sheets displays behavioral and biochemical similarities to the in vivo wound healing response of keratinocytes in animal model systems. In both cases, ligand-dependent Epidermal Growth Factor Receptor (EGFR) activation is sufficient to elicit collective cell migration into the wound. Previous mathematical modeling studies of in vitro wound healing assays assume that physical connections between cells have a hindering effect on cell migration, but biological literature suggests a more complicated story. By combining mathematical modeling and experimental observations of collectively migrating sheets of keratinocytes, we investigate the role of cell-cell adhesion during in vitro keratinocyte wound healing assays. We develop and compare two nonlinear diffusion models of the wound healing process in which cell-cell adhesion either hinders or promotes migration. Both models can accurately fit the leading edge propagation of cell sheets during wound healing when using a time-dependent rate of cell-cell adhesion strength. The model that assumes a positive role of cell-cell adhesion on migration, however, is robust to changes in the leading edge definition and yields a qualitatively accurate density profile. Using RNAi for the critical adherens junction protein, α-catenin, we demonstrate that cell sheets with wild type cell-cell adhesion expression maintain migration into the wound longer than cell sheets with decreased cell-cell adhesion expression, which fails to exhibit collective migration. Our modeling and experimental data thus suggest that cell-cell adhesion promotes sustained migration as cells pull neighboring cells into the wound during wound healing.

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.

Reverse Engineering the Inflammatory "Clock": From Computational Modeling to Rational Resetting

Properly-regulated inflammation is central to homeostasis. Traumatic injury, hemorrhagic shock, septic shock, and other injury-related processes such as wound healing are associated with dysregulated inflammation. Like many biological processes, inflammation is a dynamic, complex system whose function, like that of an analog clock, cannot be discerned simply from a laundry list of its parts (data). The advent of multiplexed platforms for gathering biological data, while providing an unprecedented level of detailed information about the inflammatory response, has paradoxically also proven to be overwhelming. This problem is especially acute when the datasets involve time courses, since typical statistical analyses and data-driven modeling are geared towards single time points. Various groups have addressed this problem using dynamic approaches to data-driven and mechanistic computational modeling. These modeling tools can be thought of as the "gears" and "hands" of the "clock," and have led to insights regarding principal drivers, dynamic networks, feedbacks, and regulatory switches that characterize and perhaps regulate the inflammatory response. In parallel, mechanistic computational models have given an abstracted sense of how the inflammatory "clock" works, leading to in silico models of critically ill individuals and populations. Integrating data-driven and mechanistic modeling may point the way to a rational "resetting" of inflammation via model-driven precision medicine.

Automated parameter estimation for biological models using Bayesian statistical model checking

Background

Probabilistic models have gained widespread acceptance in the systems biology community as a useful way to represent complex biological systems. Such models are developed using existing knowledge of the structure and dynamics of the system, experimental observations, and inferences drawn from statistical analysis of empirical data. A key bottleneck in building such models is that some system variables cannot be measured experimentally. These variables are incorporated into the model as numerical parameters. Determining values of these parameters that justify existing experiments and provide reliable predictions when model simulations are performed is a key research problem.

Domain experts usually estimate the values of these parameters by fitting the model to experimental data. Model fitting is usually expressed as an optimization problem that requires minimizing a cost-function which measures some notion of distance between the model and the data. This optimization problem is often solved by combining local and global search methods that tend to perform well for the specific application domain. When some prior information about parameters is available, methods such as Bayesian inference are commonly used for parameter learning. Choosing the appropriate parameter search technique requires detailed domain knowledge and insight into the underlying system.

Results

Using an agent-based model of the dynamics of acute inflammation, we demonstrate a novel parameter estimation algorithm by discovering the amount and schedule of doses of bacterial lipopolysaccharide that guarantee a set of observed clinical outcomes with high probability. We synthesized values of twenty-eight unknown parameters such that the parameterized model instantiated with these parameter values satisfies four specifications describing the dynamic behavior of the model.

Conclusions

We have developed a new algorithmic technique for discovering parameters in complex stochastic models of biological systems given behavioral specifications written in a formal mathematical logic. Our algorithm uses Bayesian model checking, sequential hypothesis testing, and stochastic optimization to automatically synthesize parameters of probabilistic biological models.