Ensembles of uncertain mathematical models can identify network response to therapeutic interventions

Digital twin mathematical models suggest individualized hemorrhagic shock resuscitation strategies

BACKGROUND

Optimizing resuscitation to reduce inflammation and organ dysfunction following human trauma-associated hemorrhagic shock is a major clinical hurdle. This is limited by the short duration of pre-clinical studies and the sparsity of early data in the clinical setting.

METHODS

We sought to bridge this gap by linking preclinical data in a porcine model with clinical data from patients from the Prospective, Observational, Multicenter, Major Trauma Transfusion (PROMMTT) study via a three-compartment ordinary differential equation model of inflammation and coagulation.

RESULTS

The mathematical model accurately predicts physiologic, inflammatory, and laboratory measures in both the porcine model and patients, as well as the outcome and time of death in the PROMMTT cohort. Model simulation suggests that resuscitation with plasma and red blood cells outperformed resuscitation with crystalloid or plasma alone, and that earlier plasma resuscitation reduced injury severity and increased survival time.

CONCLUSIONS

This workflow may serve as a translational bridge from pre-clinical to clinical studies in trauma-associated hemorrhagic shock and other complex disease settings.

A Review of Quantitative Systems Pharmacology Models of the Coagulation Cascade: Opportunities for Improved Usability

Despite the numerous therapeutic options to treat bleeding or thrombosis, a comprehensive quantitative mechanistic understanding of the effects of these and potential novel therapies is lacking. Recently, the quality of quantitative systems pharmacology (QSP) models of the coagulation cascade has improved, simulating the interactions between proteases, cofactors, regulators, fibrin, and therapeutic responses under different clinical scenarios. We aim to review the literature on QSP models to assess the unique capabilities and reusability of these models. We systematically searched the literature and BioModels database reviewing systems biology (SB) and QSP models. The purpose and scope of most of these models are redundant with only two SB models serving as the basis for QSP models. Primarily three QSP models have a comprehensive scope and are systematically linked between SB and more recent QSP models. The biological scope of recent QSP models has expanded to enable simulations of previously unexplainable clotting events and the drug effects for treating bleeding or thrombosis. Overall, the field of coagulation appears to suffer from unclear connections between models and irreproducible code as previously reported. The reusability of future QSP models can improve by adopting model equations from validated QSP models, clearly documenting the purpose and modifications, and sharing reproducible code. The capabilities of future QSP models can improve from more rigorous validation by capturing a broader range of responses to therapies from individual patient measurements and integrating blood flow and platelet dynamics to closely represent in vivo bleeding or thrombosis risk.

Personalized modulation of coagulation factors using a thrombin dynamics model to treat trauma-induced coagulopathy

Current trauma-induced coagulopathy resuscitation protocols use slow laboratory measurements, rules-of-thumb, and clinician gestalt to administer large volumes of uncharacterized, non-tailored blood products. These one-size-fits-all treatment approaches have high mortality. Here, we provide significant evidence that trauma patient survival 24 h after hospital admission occurs if and only if blood protein coagulation factor concentrations equilibrate at a normal value, either from inadvertent plasma-based modulation or from innate compensation. This result motivates quantitatively guiding trauma patient coagulation factor levels while accounting for protein interactions. Toward such treatment, we develop a Goal-oriented Coagulation Management (GCM) algorithm, a personalized and automated ordered sequence of operations to compute and specify coagulation factor concentrations that rectify clotting. This novel GCM algorithm also integrates new control-oriented advancements that we make in this work: an improvement of a prior thrombin dynamics model that captures the coagulation process to control, a use of rapidly-measurable concentrations to help predict patient state, and an accounting of patient-specific effects and limitations when adding coagulation factors to remedy coagulopathy. Validation of the GCM algorithm's guidance shows superior performance over clinical practice in attaining normal coagulation factor concentrations and normal clotting profiles simultaneously.

Modeling Thrombin Generation in Plasma under Diffusion and Flow

We investigate the capacity of published numerical models of thrombin generation to reproduce experimentally observed threshold behavior under conditions in which diffusion and/or flow are important. Computational fluid dynamics simulations incorporating species diffusion, fluid flow, and biochemical reactions are compared with published data for thrombin generation in vitro in 1) quiescent plasma exposed to patches of tissue factor and 2) plasma perfused through a capillary coated with tissue factor. Clot time is correctly predicted in individual cases, and some models qualitatively replicate thrombin generation thresholds across a series of tissue factor patch sizes or wall shear rates. Numerical results suggest that there is not a genuine patch size threshold in quiescent plasma-clotting always occurs given enough time-whereas the shear rate threshold observed under flow is a genuine physical limit imposed by flow-mediated washout of active coagulation factors. Despite the encouraging qualitative results obtained with some models, no single model robustly reproduces all experiments, demonstrating that greater understanding of the underlying reaction network, and particularly of surface reactions, is required. In this direction, additional simulations provide evidence that 1) a surface-localized enzyme, speculatively identified as meizothrombin, is significantly active toward the fluorescent thrombin substrate used in the experiments or, less likely, 2) thrombin is irreversibly inhibited at a faster-than-expected rate, possibly explained by a stimulatory effect of plasma heparin on antithrombin. These results highlight the power of simulation to provide novel mechanistic insights that augment experimental studies and build our understanding of complex biophysicochemical processes. Further validation work is critical to unleashing the full potential of coagulation models as tools for drug development and personalized medicine.

Understanding biochemical design principles with ensembles of canonical non-linear models

Systems biology applies concepts from engineering in order to understand biological networks. If such an understanding was complete, biologists would be able to design ad hoc biochemical components tailored for different purposes, which is the goal of synthetic biology. Needless to say that we are far away from creating biological subsystems as intricate and precise as those found in nature, but mathematical models and high throughput techniques have brought us a long way in this direction. One of the difficulties that still needs to be overcome is finding the right values for model parameters and dealing with uncertainty, which is proving to be an extremely difficult task. In this work, we take advantage of ensemble modeling techniques, where a large number of models with different parameter values are formulated and then tested according to some performance criteria. By finding features shared by successful models, the role of different components and the synergies between them can be better understood. We will address some of the difficulties often faced by ensemble modeling approaches, such as the need to sample a space whose size grows exponentially with the number of parameters, and establishing useful selection criteria. Some methods will be shown to reduce the predictions from many models into a set of understandable “design principles” that can guide us to improve or manufacture a biochemical network. Our proposed framework formulates models within standard formalisms in order to integrate information from different sources and minimize the dimension of the parameter space. Additionally, the mathematical properties of the formalism enable a partition of the parameter space into independent subspaces. Each of these subspaces can be paired with a set of criteria that depend exclusively on it, thus allowing a separate sampling/screening in spaces of lower dimension. By applying tests in a strict order where computationally cheaper tests are applied first to each subspace and applying computationally expensive tests to the remaining subset thereafter, the use of resources is optimized and a larger number of models can be examined. This can be compared to a complex database query where the order of the requests can make a huge difference in the processing time. The method will be illustrated by analyzing a classical model of a metabolic pathway with end-product inhibition. Even for such a simple model, the method provides novel insight.

Virtual endovascular treatment of intracranial aneurysms: models and uncertainty

Virtual endovascular treatment models (VETMs) have been developed with the view to aid interventional neuroradiologists and neurosurgeons to pre-operatively analyze the comparative efficacy and safety of endovascular treatments for intracranial aneurysms. Based on the current state of VETMs in aneurysm rupture risk stratification and in patient-specific prediction of treatment outcomes, we argue there is a need to go beyond personalized biomechanical flow modeling assuming deterministic parameters and error-free measurements. The mechanobiological effects associated with blood clot formation are important factors in therapeutic decision making and models of post-treatment intra-aneurysmal biology and biochemistry should be linked to the purely hemodynamic models to improve the predictive power of current VETMs. The influence of model and parameter uncertainties associated to each component of a VETM is, where feasible, quantified via a random-effects meta-analysis of the literature. This allows estimating the pooled effect size of these uncertainties on aneurysmal wall shear stress. From such meta-analyses, two main sources of uncertainty emerge where research efforts have so far been limited: (1) vascular wall distensibility, and (2) intra/intersubject systemic flow variations. In the future, we suggest that current deterministic computational simulations need to be extended with strategies for uncertainty mitigation, uncertainty exploration, and sensitivity reduction techniques. WIREs Syst Biol Med 2017, 9:e1385. doi: 10.1002/wsbm.1385 For further resources related to this article, please visit the WIREs website.

JuPOETs: a constrained multiobjective optimization approach to estimate biochemical model ensembles in the Julia programming language

Background

Ensemble modeling is a promising approach for obtaining robust predictions and coarse grained population behavior in deterministic mathematical models. Ensemble approaches address model uncertainty by using parameter or model families instead of single best-fit parameters or fixed model structures. Parameter ensembles can be selected based upon simulation error, along with other criteria such as diversity or steady-state performance. Simulations using parameter ensembles can estimate confidence intervals on model variables, and robustly constrain model predictions, despite having many poorly constrained parameters.

Results

In this software note, we present a multiobjective based technique to estimate parameter or models ensembles, the Pareto Optimal Ensemble Technique in the Julia programming language (JuPOETs). JuPOETs integrates simulated annealing with Pareto optimality to estimate ensembles on or near the optimal tradeoff surface between competing training objectives. We demonstrate JuPOETs on a suite of multiobjective problems, including test functions with parameter bounds and system constraints as well as for the identification of a proof-of-concept biochemical model with four conflicting training objectives. JuPOETs identified optimal or near optimal solutions approximately six-fold faster than a corresponding implementation in Octave for the suite of test functions. For the proof-of-concept biochemical model, JuPOETs produced an ensemble of parameters that gave both the mean of the training data for conflicting data sets, while simultaneously estimating parameter sets that performed well on each of the individual objective functions.

Conclusions

JuPOETs is a promising approach for the estimation of parameter and model ensembles using multiobjective optimization. JuPOETs can be adapted to solve many problem types, including mixed binary and continuous variable types, bilevel optimization problems and constrained problems without altering the base algorithm. JuPOETs is open source, available under an MIT license, and can be installed using the Julia package manager from the JuPOETs GitHub repository

Targeted clinical control of trauma patient coagulation through a thrombin dynamics model

We present a methodology for personalizing the clinical treatment of severely injured patients with acute traumatic coagulopathy (ATC), an endogenous biological response of impaired coagulation that occurs early after trauma and shock and that is associated with increased bleeding, morbidity, and mortality. Despite biological characterization of ATC, it is not easily or rapidly diagnosed, not always captured by slow laboratory testing, and not accurately represented by coagulation models. This lack of knowledge, combined with the inherent time pressures of trauma treatment, forces surgeons to treat ATC patients according to empirical resuscitation protocols. These entail transfusing large volumes of poorly characterized, nontargeted blood products that are not tailored to an individual, the injury, or coagulation dynamics. Massive transfusion mortality remains at 40 to 70% in the best of trauma centers. As an alternative to blunt treatments, time-consuming tests, and mechanistic models, we used dynamical systems theory to create a simple, biologically meaningful, and highly accurate model that (i) quickly forecasts a driver of downstream coagulation, thrombin concentration after tissue factor stimulation, using rapidly measurable concentrations of blood protein factors and (ii) determines the amounts of additional coagulation factors needed to rectify the predicted thrombin dynamics and potentially remedy ATC. We successfully demonstrate in vitro thrombin control consistent with the model. Compared to another model, we decreased the mean errors in two key trauma patient parameters: peak thrombin concentration after tissue factor stimulation and the time until this peak occurs. Our methodology helps to advance individualized resuscitation of trauma-induced coagulation deficits.

Population Heterogeneity in the Epithelial to Mesenchymal Transition Is Controlled by NFAT and Phosphorylated Sp1

Epithelial to mesenchymal transition (EMT) is an essential differentiation program during tissue morphogenesis and remodeling. EMT is induced by soluble transforming growth factor β (TGF-β) family members, and restricted by vascular endothelial growth factor family members. While many downstream molecular regulators of EMT have been identified, these have been largely evaluated individually without considering potential crosstalk. In this study, we created an ensemble of dynamic mathematical models describing TGF-β induced EMT to better understand the operational hierarchy of this complex molecular program. We used ordinary differential equations (ODEs) to describe the transcriptional and post-translational regulatory events driving EMT. Model parameters were estimated from multiple data sets using multiobjective optimization, in combination with cross-validation. TGF-β exposure drove the model population toward a mesenchymal phenotype, while an epithelial phenotype was enhanced following vascular endothelial growth factor A (VEGF-A) exposure. Simulations predicted that the transcription factors phosphorylated SP1 and NFAT were master regulators promoting or inhibiting EMT, respectively. Surprisingly, simulations also predicted that a cellular population could exhibit phenotypic heterogeneity (characterized by a significant fraction of the population with both high epithelial and mesenchymal marker expression) if treated simultaneously with TGF-β and VEGF-A. We tested this prediction experimentally in both MCF10A and DLD1 cells and found that upwards of 45% of the cellular population acquired this hybrid state in the presence of both TGF-β and VEGF-A. We experimentally validated the predicted NFAT/Sp1 signaling axis for each phenotype response. Lastly, we found that cells in the hybrid state had significantly different functional behavior when compared to VEGF-A or TGF-β treatment alone. Together, these results establish a predictive mechanistic model of EMT susceptibility, and potentially reveal a novel signaling axis which regulates carcinoma progression through an EMT versus tubulogenesis response.

Using a Systems Pharmacology Model of the Blood Coagulation Network to Predict the Effects of Various Therapies on Biomarkers

A number of therapeutics have been developed or are under development aiming to modulate the coagulation network to treat various diseases. We used a systems model to better understand the effect of modulating various components on blood coagulation. A computational model of the coagulation network was built to match in-house in vitro thrombin generation and activated Partial Thromboplastin Time (aPTT) data with various concentrations of recombinant factor VIIa (FVIIa) or factor Xa added to normal human plasma or factor VIII-deficient plasma. Sensitivity analysis applied to the model revealed that lag time, peak thrombin concentration, area under the curve (AUC) of the thrombin generation profile, and aPTT show different sensitivity to changes in coagulation factors' concentrations and type of plasma used (normal or factor VIII-deficient). We also used the model to explore how variability in concentrations of the proteins in coagulation network can impact the response to FVIIa treatment.

Kinetic model facilitates analysis of fibrin generation and its modulation by clotting factors: implications for hemostasis-enhancing therapies

Current mechanistic knowledge of protein interactions driving blood coagulation has come largely from experiments with simple synthetic systems, which only partially represent the molecular composition of human blood plasma. Here, we investigate the ability of the suggested molecular mechanisms to account for fibrin generation and degradation kinetics in diverse, physiologically relevant in vitro systems. We represented the protein interaction network responsible for thrombin generation, fibrin formation, and fibrinolysis as a computational kinetic model and benchmarked it against published and newly generated data reflecting diverse experimental conditions. We then applied the model to investigate the ability of fibrinogen and a recently proposed prothrombin complex concentrate composition, PCC-AT (a combination of the clotting factors II, IX, X, and antithrombin), to restore normal thrombin and fibrin generation in diluted plasma. The kinetic model captured essential features of empirically detected effects of prothrombin, fibrinogen, and thrombin-activatable fibrinolysis inhibitor titrations on fibrin formation and degradation kinetics. Moreover, the model qualitatively predicted the impact of tissue factor and tPA/tenecteplase level variations on the fibrin output. In the majority of considered cases, PCC-AT combined with fibrinogen accurately approximated both normal thrombin and fibrin generation in diluted plasma, which could not be accomplished by fibrinogen or PCC-AT acting alone. We conclude that a common network of protein interactions can account for key kinetic features characterizing fibrin accumulation and degradation in human blood plasma under diverse experimental conditions. Combined PCC-AT/fibrinogen supplementation is a promising strategy to reverse the deleterious effects of dilution-induced coagulopathy associated with traumatic bleeding.

Augmentation of thrombin generation in neonates undergoing cardiopulmonary bypass

INTRODUCTION

Factor concentrates are currently available and becoming increasingly used off-label for treatment of bleeding. We compared recombinant activated factor VII (rFVIIa) with three-factor prothrombin complex concentrate (3F-PCC) for the ability to augment thrombin generation (TG) in neonatal plasma after cardiopulmonary bypass (CPB). First, we used a computer-simulated coagulation model to assess the impact of rFVIIa and 3F-PCC, and then performed similar measurements ex vivo using plasma from neonates undergoing CPB.

METHODS

Simulated TG was computed according to the coagulation factor levels from umbilical cord plasma and the therapeutic levels of rFVIIa, 3F-PCC, or both. Subsequently, 11 neonates undergoing cardiac surgery were enrolled. Two blood samples were obtained from each neonate: pre-CPB and post-CPB after platelet and cryoprecipitate transfusion. The post-CPB products sample was divided into control (no treatment), control plus rFVIIa (60 nM), and control plus 3F-PCC (0.3 IU ml(-1)) aliquots. Three parameters of TG were measured ex vivo.

RESULTS

The computer-simulated post-CPB model demonstrated that rFVIIa failed to substantially improve lag time, TG rate and peak thrombin without supplementing prothrombin. Ex vivo data showed that addition of rFVIIa post-CPB significantly shortened lag time; however, rate and peak were not statistically significantly improved. Conversely, 3F-PCC improved all TG parameters in parallel with increased prothrombin levels in both simulated and ex vivo post-CPB samples.

CONCLUSIONS

Our data highlight the importance of prothrombin replacement in restoring TG. Despite a low content of FVII, 3F-PCC exerts potent procoagulant activity compared with rFVIIa ex vivo. Further clinical evaluation regarding the efficacy and safety of 3F-PCC is warranted.

Models for thrombin generation and risk of disease

Computational models can offer an integrated view of blood clotting dynamics and may ultimately be instructive regarding an individual's risk of bleeding or clotting. Appropriately, developed and validated models could allow clinicians to simulate the outcomes of therapeutics and estimate risk of disease. Computational models that describe the dynamics of thrombin generation have been developed and have been used in combination with empirical studies to understand thrombin dynamics on a mechanistic basis. The translation of an individual's specific coagulation factor composition data using these models into an integrated assessment of hemostatic status may provide a route for advancing the long-term goal of individualized medicine. This review details the integrated approaches to understanding: (i) What is normal thrombin generation in individuals? (ii) What is the effect of normal range plasma composition variation on thrombin generation in pathologic states? (iii) Can disease progression or anticoagulation be followed by understanding the boundaries of normal thrombin generation defined by plasma composition? (iv) What are the controversies and limitations of current computational approaches? Progress in these areas can bring us closer to developing models that can be used to aid in identifying hemostatic risk.

A review of macroscopic thrombus modeling methods

Hemodynamics applied to mechanobiology offers powerful means to predict thrombosis, and to understand the kinetics of thrombus formation on areas of vascular damage in blood flowing through the human circulatory system. Specifically, the advances in computational processing and the progress in modeling complex biological processes with spatio-temporal multi-scale methods have the potential to shift the way in which cardiovascular diseases are diagnosed and treated. This article systematically surveys the state of the art of macroscopic computational fluid dynamics (CFD) Computational fluid dynamics techniques for modeling thrombus formation, highlighting their strengths and weaknesses. In particular, a comprehensive and systematic revision of the hemodynamics models and methods is given, and the strengths and weaknesses of those employed for studying thrombus formation are highlighted.

Multiscale models of breast cancer progression

Breast cancer initiation, invasion and metastasis span multiple length and time scales. Molecular events at short length scales lead to an initial tumorigenic population, which left unchecked by immune action, acts at increasingly longer length scales until eventually the cancer cells escape from the primary tumor site. This series of events is highly complex, involving multiple cell types interacting with (and shaping) the microenvironment. Multiscale mathematical models have emerged as a powerful tool to quantitatively integrate the convective-diffusion-reaction processes occurring on the systemic scale, with the molecular signaling processes occurring on the cellular and subcellular scales. In this study, we reviewed the current state of the art in cancer modeling across multiple length scales, with an emphasis on the integration of intracellular signal transduction models with pro-tumorigenic chemical and mechanical microenvironmental cues. First, we reviewed the underlying biomolecular origin of breast cancer, with a special emphasis on angiogenesis. Then, we summarized the development of tissue engineering platforms which could provide high-fidelity ex vivo experimental models to identify and validate multiscale simulations. Lastly, we reviewed top-down and bottom-up multiscale strategies that integrate subcellular networks with the microenvironment. We present models of a variety of cancers, in addition to breast cancer specific models. Taken together, we expect as the sophistication of the simulations increase, that multiscale modeling and bottom-up agent-based models in particular will become an increasingly important platform technology for basic scientific discovery, as well as the identification and validation of potentially novel therapeutic targets.

Metabolic ensemble modeling for strain engineers

Previous mathematical modeling efforts have made significant contributions to the development of systems biology for predicting biological behavior quantitatively. However, dynamic metabolic model construction remains challenging due to uncertainties in mechanistic structures and parameters. In addition, parameter estimation and model validation often require designated experiments conducted only for purpose of modeling. Such difficulties have hampered the progress of modeling in biology and biotechnology. To circumvent these problems, ensemble approaches have been used to account for uncertainties in model structure and parameters. Specifically, this review focuses on approaches that utilize readily available fermentation data for parameter screening and model validation. Time course data for metabolite measurements, if available, can further calibrate the model. The basis for this approach is explained in non-mathematical terms accessible to experimentalists. Information gained from such an approach has been shown to be useful in designing Escherichia coli strains for metabolic engineering and synthetic biology.