JSim, an open-source modeling system for data analysis

Adaptive remodeling of rat adrenomedullary stimulus-secretion coupling in a chronic hypertensive environment

Chronic elevated blood pressure impinges on the functioning of multiple organs and therefore harms body homeostasis. Elucidating the protective mechanisms whereby the organism copes with sustained or repetitive blood pressure rises is therefore a topical challenge. Here we address this issue in the adrenal medulla, the master neuroendocrine tissue involved in the secretion of catecholamines, influential hormones in blood pressure regulation. Combining electrophysiological techniques with catecholamine secretion assays on acute adrenal slices from spontaneously hypertensive rats, we show that chromaffin cell stimulus-secretion coupling is remodeled, resulting in a less efficient secretory function primarily upon sustained cholinergic challenges. The remodeling is supported by revamped both cellular and tissular mechanisms. This first includes a decrease in chromaffin cell excitability in response to sustained electrical stimulation. This hallmark was observed both experimentally and in a computational chromaffin cell model, and occurs with concomitant changes in voltage-gated ion channel expression. The cholinergic transmission at the splanchnic nerve-chromaffin cell synapses and the gap junctional communication between chromaffin cells are also weakened. As such, by disabling its competence to release catecholamines in response sustained stimulations, the hypertensive medulla has elaborated an adaptive shielding mechanism against damaging effects of redundant elevated catecholamine secretion and associated blood pressure.

A new approach to modeling transdermal ethanol kinetics

Measurement of ethanol above the skin surface (supradermal) is used to monitor blood alcohol concentrations (BAC) in both legal and consumer settings. Previously, the relationship between supradermal alcohol concentration (SAC) and BAC was described using partial and ordinary differential equations (PDE model: J. Appl. Physiol. 100: 649-55, 2006). Using a range of BAC profiles by varying absorption times and peak concentrations, the PDE model accurately predicted experimental measures of SAC. Recently, other mathematical models have relied on the PDE model. This paper proposes a new approach to modeling transdermal ethanol kinetics using a mass transfer coefficient and only ordinary differential equations (ODE model). Using a range of BAC profiles, the ODE model performed very similarly to the PDE model. The ODE model had slightly slower washout rates and slightly slower times to peak SAC and to zero SAC. Similar to the PDE model, a sensitivity analysis on the ODE model showed changes in solubility and diffusivity within the stratum corneum, stratum corneum thickness, and the volume of gas above the skin affected model performance. This new model will streamline integration into larger physiologic models, reduce computation time, and decrease the time to transform skin alcohol measurements to blood alcohol concentrations.

Simulation of coronary fractional flow reserve and whole-cycle flow based on optical coherence tomography in individual patients with coronary artery disease

Computer simulations of coronary fractional flow reserve (FFR) based on coronary imaging have emerged as an attractive alternative to invasive measurements. However, most methods are proprietary and employ non-physiological assumptions. Our aims were to develop and validate a physiologically realistic open-source simulation model for coronary flow, and to use this model to predict FFR based on intracoronary optical coherence tomography (OCT) data in individual patients. We included patients undergoing elective coronary angiography with angiographic borderline coronary stenosis. Invasive measurements of coronary hyperemic pressure and absolute flow and OCT imaging were performed. A computer model of coronary flow incorporating pulsatile flow and the effect of left ventricular contraction was developed and calibrated, and patient-specific flow simulation was performed. Forty-eight coronary arteries from 41 patients were included in the analysis. Average FFR was 0.79 ± 0.14, and 50% had FFR ≤ 0.80. Correlation between simulated and measured FFR was high (r = 0.83, p < 0.001). Average difference between simulated FFR and observed FFR in individual patients was - 0.009 ± 0.076. Overall diagnostic accuracy for simulated FFR ≤ 0.80 in predicting observed FFR ≤ 0.80 was 0.88 (0.75-0.95) with sensitivity 0.79 (0.58-0.93) and specificity 0.96 (0.79-1.00). The positive predictive value was 0.95 (0.75-1.00) and the negative predictive value was 0.82 (0.63-0.94). In conclusion, realistic simulations of whole-cycle coronary flow can be produced based on intracoronary OCT data with a new, computationally simple simulation model. Simulated FFR had moderate numerical agreement with observed FFR and a good diagnostic accuracy for predicting hemodynamic significance of coronary stenoses.

Mathematical Models of HIV-1 Dynamics, Transcription, and Latency

HIV-1 latency is a major barrier to curing infections with antiretroviral therapy and, consequently, to eliminating the disease globally. The establishment, maintenance, and potential clearance of latent infection are complex dynamic processes and can be best described with the help of mathematical models followed by experimental validation. Here, we review the use of viral dynamics models for HIV-1, with a focus on applications to the latent reservoir. Such models have been used to explain the multi-phasic decay of viral load during antiretroviral therapy, the early seeding of the latent reservoir during acute infection and the limited inflow during treatment, the dynamics of viral blips, and the phenomenon of post-treatment control. Finally, we discuss that mathematical models have been used to predict the efficacy of potential HIV-1 cure strategies, such as latency-reversing agents, early treatment initiation, or gene therapies, and to provide guidance for designing trials of these novel interventions.

Open source code for the generation of digital reference objects for dynamic contrast-enhanced MRI analysis software validation

OBJECTIVES

Dynamic contrast-enhanced MR images can be analyzed through the application of a wide range of kinetic models. This process is prone to variability and a lack of standardization that can affect the measured metrics. There is a need for customized digital reference objects (DROs) for the validation of DCE-MRI software packages that undertake kinetic model analysis. DROs are currently available only for a small subset of the kinetic models commonly applied to DCE-MRI data. This work aimed to address this gap.

METHODS

Code was written in the MATLAB programming environment to generate customizable DROs. This modular code allows the insertion of a plug-in to describe the kinetic model to be tested. We input our generated DROs into three commercial and open-source analysis packages and assessed the agreement of kinetic model parameter values output with the 'ground-truth' values used in the DRO generation.

RESULTS

For the five kinetic models tested, the concordance correlation coefficient values were >98%, indicating excellent agreement of the results with 'ground-truth'.

CONCLUSIONS

Testing our DROs on three independent software packages produced concordant results, strongly suggesting our DRO generation code is correct. This implies that our DROs can be used to validate other third party software for the kinetic model analysis of DCE-MRI data.

ADVANCES IN KNOWLEDGE

This work extends published work of others to allow customized generation of test objects for any applied kinetic model and allows the incorporation of B1 mapping into the DRO for application at higher field strengths.

Systems analysis of the mechanisms governing the cardiovascular response to changes in posture and in peripheral demand during exercise

Blood flows and pressures throughout the human cardiovascular system are regulated in response to various dynamic perturbations, such as changes to peripheral demands in exercise, rapid changes in posture, or loss of blood from hemorrhage, via the coordinated action of the heart, the vasculature, and autonomic reflexes. To assess how the systemic and pulmonary arterial and venous circulation, the heart, and the baroreflex work together to effect the whole-body responses to these perturbations, we integrated an anatomically-based large-vessel arterial tree model with the TriSeg heart model, models capturing nonlinear characteristics of the large and small veins, and baroreflex-mediated regulation of vascular tone and cardiac chronotropy and inotropy. The model was identified by matching data from the Valsalva maneuver (VM), exercise, and head-up tilt (HUT). Thirty-one parameters were optimized using a custom parameter-fitting tool chain, resulting in an unique, high-fidelity whole-body human cardiovascular systems model. Because the model captures the effects of exercise and posture changes, it can be used to simulate numerous clinical assessments, such as HUT, the VM, and cardiopulmonary exercise stress testing. The model can also be applied as a framework for representing and simulating individual patients and pathologies. Moreover, it can serve as a framework for integrating multi-scale organ-level models, such as for the heart or the kidneys, into a whole-body model. Here, the model is used to analyze the relative importance of chronotropic, inotropic, and peripheral vascular contributions to the whole-body cardiovascular response to exercise. It is predicted that in normal physiological conditions chronotropy and inotropy make roughly equal contributions to increasing cardiac output and cardiac power output during exercise. Under upright exercise conditions, the nonlinear pressure-volume relationship of the large veins and sympathetic-mediated venous vasoconstriction are both required to maintain preload to achieve physiological exercise levels. The developed modeling framework is built using the open Modelica modeling language and is freely distributed.

Myocardial adaptation and exercise performance in patients with pulmonary arterial hypertension assessed with patient-specific computer simulations

Myocardial function and exercise reserve are important determinants of outcome in pulmonary arterial hypertension (PAH) but are incompletely understood. For this study, we performed subject-specific computer simulations, based on invasive measurements and cardiac magnetic resonance imaging (CMR), to investigate whole circulation properties in PAH at rest and exercise and determinants of exercise reserve. CMR and right heart catheterization were performed in nine patients with idiopathic PAH, and CMR in 10 healthy controls. CMR during exercise was performed in seven patients with PAH. A full-circulation computer model was developed, and model parameters were optimized at the individual level. Patient-specific simulations were used to analyze the effect of right ventricular (RV) inotropic reserve on exercise performance. Simulations achieved a high consistency with observed data. RV contractile force was increased in patients with PAH (127.1 ± 28.7 kPa vs. 70.5 ± 14.5 kPa, P < 0.001), whereas left ventricular contractile force was reduced (107.5 ± 17.5 kPa vs. 133.9 ± 10.3 kPa, P = 0.002). During exercise, RV contractile force increased by 1.56 ± 0.17, P = 0.001. In silico experiments confirmed RV inotropic reserve as the important limiting factor for cardiac output. Subject-specific computer simulation of myocardial mechanics in PAH is feasible and can be used to evaluate myocardial performance. With this method, we demonstrate marked functional myocardial adaptation to PAH in the resting state, primarily composed of increased contractile force development by RV myofibers, and we show the negative impact of reduced RV inotropic reserve on cardiac output during exercise.NEW & NOTEWORTHY Computer simulations of the myocardial mechanics and hemodynamics of rest and exercise were performed in nine patients with pulmonary arterial hypertension and 10 control subjects, with the use of data from invasive catheterization and from cardiac magnetic resonance. This approach allowed a detailed analysis of myocardial adaptation to pulmonary arterial hypertension and showed how reduction in right ventricular inotropic reserve is the important limiting factor for an increase in cardiac output during exercise.

Sodium background currents in endocrine/neuroendocrine cells: Towards unraveling channel identity and contribution in hormone secretion

In endocrine/neuroendocrine tissues, excitability of secretory cells is patterned by the repertoire of ion channels and there is clear evidence that extracellular sodium (Na⁺) ions contribute to hormone secretion. While voltage-gated channels involved in action potential generation are well-described, the background 'leak' channels operating near the resting membrane potential are much less known, and in particular the channels supporting a background entry of Na⁺ ions. These background Na⁺ currents (called here 'I_Nab') have the ability to modulate the resting membrane potential and subsequently affect action potential firing. Here we compile and analyze the data collected from three endocrine/neuroendocrine tissues: the anterior pituitary gland, the adrenal medulla and the endocrine pancreas. We also model how I_Nab can be functionally involved in cellular excitability. Finally, towards deciphering the physiological role of I_Nab in endocrine/neuroendocrine cells, its implication in hormone release is also discussed.

Characteristics of mathematical modeling languages that facilitate model reuse in systems biology: a software engineering perspective

Reuse of mathematical models becomes increasingly important in systems biology as research moves toward large, multi-scale models composed of heterogeneous subcomponents. Currently, many models are not easily reusable due to inflexible or confusing code, inappropriate languages, or insufficient documentation. Best practice suggestions rarely cover such low-level design aspects. This gap could be filled by software engineering, which addresses those same issues for software reuse. We show that languages can facilitate reusability by being modular, human-readable, hybrid (i.e., supporting multiple formalisms), open, declarative, and by supporting the graphical representation of models. Modelers should not only use such a language, but be aware of the features that make it desirable and know how to apply them effectively. For this reason, we compare existing suitable languages in detail and demonstrate their benefits for a modular model of the human cardiac conduction system written in Modelica.

Hierarchical semantic composition of biosimulation models using bond graphs

Simulating complex biological and physiological systems and predicting their behaviours under different conditions remains challenging. Breaking systems into smaller and more manageable modules can address this challenge, assisting both model development and simulation. Nevertheless, existing computational models in biology and physiology are often not modular and therefore difficult to assemble into larger models. Even when this is possible, the resulting model may not be useful due to inconsistencies either with the laws of physics or the physiological behaviour of the system. Here, we propose a general methodology for composing models, combining the energy-based bond graph approach with semantics-based annotations. This approach improves model composition and ensures that a composite model is physically plausible. As an example, we demonstrate this approach to automated model composition using a model of human arterial circulation. The major benefit is that modellers can spend more time on understanding the behaviour of complex biological and physiological systems and less time wrangling with model composition.

Evolution of mathematical models of cardiomyocyte electrophysiology

Advanced computational techniques and mathematical modeling have become more and more important to the study of cardiac electrophysiology. In this review, we provide a brief history of the evolution of cardiomyocyte electrophysiology models and highlight some of the most important ones that had a major impact on our understanding of the electrical activity of the myocardium and associated transmembrane ion fluxes in normal and pathological states. We also present the use of these models in the study of various arrhythmogenesis mechanisms, particularly the integration of experimental pharmacology data into advanced humanized models for in silico proarrhythmogenic risk prediction as an essential component of the Comprehensive in vitro Proarrhythmia Assay (CiPA) drug safety paradigm.

Location and function of transient receptor potential canonical channel 1 in ventricular myocytes

Transient receptor potential canonical 1 (TRPC1) protein is abundantly expressed in cardiomyocytes. While TRPC1 is supposed to be critically involved in cardiac hypertrophy, its physiological role in cardiomyocytes is poorly understood. We investigated the subcellular location of TRPC1 and its contribution to Ca²⁺ signaling in mammalian ventricular myocytes. Immunolabeling, three-dimensional scanning confocal microscopy and quantitative colocalization analysis revealed an abundant intracellular location of TRPC1 in neonatal rat ventricular myocytes (NRVMs) and adult rabbit ventricular myocytes. TRPC1 was colocalized with intracellular proteins including sarco/endoplasmic reticulum Ca²⁺ ATPase 2 in the sarcoplasmic reticulum (SR). Colocalization with wheat germ agglutinin, which labels the glycocalyx and thus marks the sarcolemma including the transverse tubular system, was low. Super-resolution and immunoelectron microscopy supported the intracellular location of TRPC1. We investigated Ca²⁺ signaling in NRVMs after adenoviral TRPC1 overexpression or silencing. In NRVMs bathed in Na⁺ and Ca²⁺ free solution, TRPC1 overexpression and silencing was associated with a decreased and increased SR Ca²⁺ content, respectively. In isolated rabbit cardiomyocytes bathed in Na⁺ and Ca²⁺ free solution, we found an increased decay of the cytosolic Ca²⁺ concentration [Ca²⁺]_i and increased SR Ca²⁺ content in the presence of the TRPC channel blocker SKF-96365. In a computational model of rabbit ventricular myocytes at physiological pacing rates, Ca²⁺ leak through SR TRPC channels increased the systolic and diastolic [Ca²⁺]_i with only minor effects on the action potential and SR Ca²⁺ content. Our studies suggest that TRPC1 channels are localized in the SR, and not present in the sarcolemma of ventricular myocytes. The studies provide evidence for a role of TRPC1 as a contributor to SR Ca²⁺ leak in cardiomyocytes, which was previously explained by ryanodine receptors only. We propose that the findings will guide us to an understanding of TRPC1 channels as modulators of [Ca²⁺]_i and contractility in cardiomyocytes.

Accuracy of Myocardial Blood Flow Estimation From Dynamic Contrast-Enhanced Cardiac CT Compared With PET

Background The accuracy of absolute myocardial blood flow (MBF) from dynamic contrast-enhanced cardiac computed tomography acquisitions has not been fully characterized. We evaluate computed tomography (CT) compared with rubidium-82 positron emission tomography (PET) MBF estimates in a high-risk population. Methods In a prospective trial, patients receiving clinically indicated rubidium-82 PET exams were recruited to receive a dynamic contrast-enhanced cardiac computed tomography exam. The CT protocol included a rest and stress dynamic portion each acquiring 12 to 18 cardiac-gated frames. The global MBF was estimated from the PET and CT exam. Results Thirty-four patients referred for cardiac rest-stress PET were recruited. Of the 68 dynamic contrast-enhanced cardiac computed tomography scans, 5 were excluded because of injection errors or mismatched hemodynamics. The CT-derived global MBF was highly correlated with the PET MBF (r=0.92; P<0.001) with a mean difference of 0.7±26.4%. The CT MBF estimates were within 20% of PET estimates ( P<0.02) with a mean of (1) MBF for resting flow of PET versus CT of 0.9±0.3 versus 1.0±0.2 mL/min per gram and (2) MBF for stress flow of 2.1±0.7 versus 2.0±0.8 mL/min per gram. Myocardial flow reserve was -14±28% underestimated with CT (PET versus CT myocardial flow reserve, 2.5±0.6 versus 2.2±0.6). The proposed rest+stress+computed tomography angiography protocol had a dose length product of 598±76 mGy×cm resulting in an approximate effective dose of 8.4±1.1 mSv. Conclusions In a high-risk clinical population, a clinically practical dynamic contrast-enhanced cardiac computed tomography provided unbiased MBF estimates within 20% of rubidium-82 PET. Although unbiased, the CT estimates contain substantial variance with an standard error of the estimate of 0.44 mL/min per gram. Myocardial flow reserve estimation was not as accurate as individual MBF estimates.

Transcriptional Circuit Fragility Influences HIV Proviral Fate

Transcriptional circuit architectures in several organisms have been evolutionarily selected to dictate precise given responses. Unlike these cellular systems, HIV is regulated through a complex circuit composed of two successive phases (host and viral), which create a positive feedback loop facilitating viral replication. However, it has long remained unclear whether both phases operate identically and to what extent the host phase influences the entire circuit. Here, we report that, although the host phase is regulated by a checkpoint whereby KAP1 mediates transcription activation, the virus evolved a minimalist system bypassing KAP1. Given the complex circuit's architecture, cell-to-cell KAP1 fluctuations impart heterogeneity in the host transcriptional responses, thus affecting the feedback loop. Mathematical modeling of a complete circuit reveals how these oscillations ultimately influence homogeneous reactivation potential of a latent virus. Thus, although HIV drives molecular innovation to fuel robust gene activation, it experiences transcriptional fragility, thereby influencing viral fate and cure efforts.

MITK-ModelFit: A generic open-source framework for model fits and their exploration in medical imaging - design, implementation and application on the example of DCE-MRI

Background

Many medical imaging techniques utilize fitting approaches for quantitative parameter estimation and analysis. Common examples are pharmacokinetic modeling in dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI)/computed tomography (CT), apparent diffusion coefficient calculations and intravoxel incoherent motion modeling in diffusion-weighted MRI and Z-spectra analysis in chemical exchange saturation transfer MRI. Most available software tools are limited to a special purpose and do not allow for own developments and extensions. Furthermore, they are mostly designed as stand-alone solutions using external frameworks and thus cannot be easily incorporated natively in the analysis workflow.

Results

We present a framework for medical image fitting tasks that is included in the Medical Imaging Interaction Toolkit MITK, following a rigorous open-source, well-integrated and operating system independent policy. Software engineering-wise, the local models, the fitting infrastructure and the results representation are abstracted and thus can be easily adapted to any model fitting task on image data, independent of image modality or model. Several ready-to-use libraries for model fitting and use-cases, including fit evaluation and visualization, were implemented. Their embedding into MITK allows for easy data loading, pre- and post-processing and thus a natural inclusion of model fitting into an overarching workflow. As an example, we present a comprehensive set of plug-ins for the analysis of DCE MRI data, which we validated on existing and novel digital phantoms, yielding competitive deviations between fit and ground truth.

Conclusions

Providing a very flexible environment, our software mainly addresses developers of medical imaging software that includes model fitting algorithms and tools. Additionally, the framework is of high interest to users in the domain of perfusion MRI, as it offers feature-rich, freely available, validated tools to perform pharmacokinetic analysis on DCE MRI data, with both interactive and automatized batch processing workflows.

Efficient Modeling and Simulation of Space-Dependent Biological Systems

We recently demonstrated the possibility to model and to simulate biological functions using hardware description languages (HDLs) and associated simulators traditionally used for microelectronics. Nevertheless, those languages are not suitable to model and simulate space-dependent systems described by partial differential equations. However, in more and more applications space- and time-dependent models are unavoidable. For this purpose, we investigated a new modeling approach to simulate molecular diffusion on a mesoscopic scale still based on HDL. Our work relies on previous investigations on an electrothermal simulation tool for integrated circuits, and analogies that can be drawn between electronics, thermodynamics, and biology. The tool is composed of four main parts: a simple but efficient mesher that divides space into parallelepipeds (or rectangles in 2D) of adaptable size, a set of interconnected biological models, a SPICE simulator that handles the model and Python scripts that interface the different tools. Simulation results obtained with our tool have been validated on simple cases for which an analytical solution exists and compared with experimental data gathered from literature. Compared with existing approaches, our simulator has three main advantages: a very simple algorithm providing a direct interface between the diffusion model and biological model of each cell, the use of a powerful and widely proven simulation core (SPICE) and the ability to interface biological models with other domains of physics, enabling the study of transdisciplinary systems.

A Multi-Institutional Comparison of Dynamic Contrast-Enhanced Magnetic Resonance Imaging Parameter Calculations

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) provides quantitative metrics (e.g. K^trans, v_e) via pharmacokinetic models. We tested inter-algorithm variability in these quantitative metrics with 11 published DCE-MRI algorithms, all implementing Tofts-Kermode or extended Tofts pharmacokinetic models. Digital reference objects (DROs) with known K^trans and v_e values were used to assess performance at varying noise levels. Additionally, DCE-MRI data from 15 head and neck squamous cell carcinoma patients over 3 time-points during chemoradiotherapy were used to ascertain K^trans and v_e kinetic trends across algorithms. Algorithms performed well (less than 3% average error) when no noise was present in the DRO. With noise, 87% of K^trans and 84% of v_e algorithm-DRO combinations were generally in the correct order. Low Krippendorff’s alpha values showed that algorithms could not consistently classify patients as above or below the median for a given algorithm at each time point or for differences in values between time points. A majority of the algorithms produced a significant Spearman correlation in v_e of the primary gross tumor volume with time. Algorithmic differences in K^trans and v_e values over time indicate limitations in combining/comparing data from distinct DCE-MRI model implementations. Careful cross-algorithm quality-assurance must be utilized as DCE-MRI results may not be interpretable using differing software.

Crops In Silico: Generating Virtual Crops Using an Integrative and Multi-scale Modeling Platform

Multi-scale models can facilitate whole plant simulations by linking gene networks, protein synthesis, metabolic pathways, physiology, and growth. Whole plant models can be further integrated with ecosystem, weather, and climate models to predict how various interactions respond to environmental perturbations. These models have the potential to fill in missing mechanistic details and generate new hypotheses to prioritize directed engineering efforts. Outcomes will potentially accelerate improvement of crop yield, sustainability, and increase future food security. It is time for a paradigm shift in plant modeling, from largely isolated efforts to a connected community that takes advantage of advances in high performance computing and mechanistic understanding of plant processes. Tools for guiding future crop breeding and engineering, understanding the implications of discoveries at the molecular level for whole plant behavior, and improved prediction of plant and ecosystem responses to the environment are urgently needed. The purpose of this perspective is to introduce Crops in silico (cropsinsilico.org), an integrative and multi-scale modeling platform, as one solution that combines isolated modeling efforts toward the generation of virtual crops, which is open and accessible to the entire plant biology community. The major challenges involved both in the development and deployment of a shared, multi-scale modeling platform, which are summarized in this prospectus, were recently identified during the first Crops in silico Symposium and Workshop.

Equations for O2 and CO2 solubilities in saline and plasma: combining temperature and density dependences

Solubilities of respiratory gasses in water, saline, and plasma decrease with rising temperatures and solute concentrations. Henry's Law, C = α·P, states that the equilibrium concentration of a dissolved gas is solubility times partial pressure. Solubilities in the water of a solution depend on temperature and the content of other solutes. Blood temperatures may differ more than 20°C between skin and heart, and an erythrocyte will undergo that range as blood circulates. The concentrations of O₂ and CO₂ are the driving forces for diffusion, exchanges, and for reactions. We provide an equation for O₂ and CO₂ solubilities, α, that allows for continuous changes in temperature, T, and solution density, ρ, in dynamically changing states:[Formula: see text]This two-exponential expression with a density scalar γ, and a density exponent β, accounts for solubility changes due to density changes of an aqueous solution. It fits experimental data on solubilities in water, saline, and plasma over temperatures from 20 to 40°C, and for plasma densities, ρ_sol up to 1.020 g/ml with ~0.3% error. The amounts of additional bound O₂ (to Hb) and CO₂ (bicarbonate and carbamino) depend on the concentrations in the local water space and the reaction parameters. During exercise, solubility changes are large; both ρ_sol and T change rapidly with spatial position and with time. In exercise hemoconcentration plasma, ρ_sol exceeds 1.02, whereas T may range over 20°C. The six parameters for O₂ and the six for CO₂ are constants, so solubilities are calculable continuously as T and ρ_sol change.NEW & NOTEWORTHY Solubilities for oxygen and carbon dioxide are dependent on the density of the solution, on temperature, and on the partial pressure. We provide a brief equation suitable for hand calculators or mathematical modeling, accounting for these factors over a wide range of temperatures and solution densities for use in rapidly changing conditions, such as extreme exercise or osmotic transients, with better than 0.5% accuracy.

Modeling the differentiation of A- and C-type baroreceptor firing patterns

The baroreceptor neurons serve as the primary transducers of blood pressure for the autonomic nervous system and are thus critical in enabling the body to respond effectively to changes in blood pressure. These neurons can be separated into two types (A and C) based on the myelination of their axons and their distinct firing patterns elicited in response to specific pressure stimuli. This study has developed a comprehensive model of the afferent baroreceptor discharge built on physiological knowledge of arterial wall mechanics, firing rate responses to controlled pressure stimuli, and ion channel dynamics within the baroreceptor neurons. With this model, we were able to predict firing rates observed in previously published experiments in both A- and C-type neurons. These results were obtained by adjusting model parameters determining the maximal ion-channel conductances. The observed variation in the model parameters are hypothesized to correspond to physiological differences between A- and C-type neurons. In agreement with published experimental observations, our simulations suggest that a twofold lower potassium conductance in C-type neurons is responsible for the observed sustained basal firing, where as a tenfold higher mechanosensitive conductance is responsible for the greater firing rate observed in A-type neurons. A better understanding of the difference between the two neuron types can potentially be used to gain more insight about pathophysiology and treatment of diseases related to baroreflex function, e.g. in patients with autonomic failure, a syndrome that is difficult to diagnose in terms of its pathophysiology.

Effect of phenytoin on sodium conductances in rat hippocampal CA1 pyramidal neurons

The antiepileptic drug phenytoin (PHT) is thought to reduce the excitability of neural tissue by stabilizing sodium channels (Na_V) in inactivated states. It has been suggested the fast-inactivated state (I_F) is the main target, although slow inactivation (I_S) has also been implicated. Other studies on local anesthetics with similar effects on sodium channels have implicated the Na_V voltage sensor interactions. In this study, we reexamined the effect of PHT in both equilibrium and dynamic transitions between fast and slower forms of inactivation in rat hippocampal CA1 pyramidal neurons. The effects of PHT were observed on fast and slow inactivation processes, as well as on another identified "intermediate" inactivation process. The effect of enzymatic removal of I_F was also studied, as well as effects on the residual persistent sodium current (I_NaP). A computational model based on a gating charge interaction was derived that reproduced a range of PHT effects on Na_V equilibrium and state transitions. No effect of PHT on I_F was observed; rather, PHT appeared to facilitate the occupancy of other closed states, either through enhancement of slow inactivation or through formation of analogous drug-bound states. The overall significance of these observations is that our data are inconsistent with the commonly held view that the archetypal Na_V channel inhibitor PHT stabilizes fast inactivation states, and we demonstrate that conventional slow activation "I_S" and the more recently identified intermediate-duration inactivation process "I_I" are the primary functional targets of PHT. In addition, we show that the traditional explanatory frameworks based on the "modulated receptor hypothesis" can be substituted by simple, physiologically plausible interactions with voltage sensors. Additionally, I_NaP was not preferentially inhibited compared with peak I_Na at short latencies (50 ms) by PHT.

Qualitative causal analyses of biosimulation models

We describe an approach for performing qualitative, systems-level causal analyses on biosimulation models that leverages semantics-based modeling formats, formal ontology, and automated inference. The approach allows users to quickly investigate how a qualitative perturbation to an element within a model's network (an increment or decrement) propagates throughout the modeled system. To support such analyses, we must interpret and annotate the semantics of the models, including both the physical properties modeled and the dependencies that relate them. We build from prior work understanding the semantics of biological properties, but here, we focus on the semantics for dependencies, which provide the critical knowledge necessary for causal analysis of biosimulation models. We describe augmentations to the Ontology of Physics for Biology, via OWL axioms and SWRL rules, and demonstrate that a reasoner can then infer how an annotated model's physical properties influence each other in a qualitative sense. Our goal is to provide researchers with a tool that helps bring the systems-level network dynamics of biosimulation models into perspective, thus facilitating model development, testing, and application.

The Pathway for Oxygen: Tutorial Modelling on Oxygen Transport from Air to Mitochondrion: The Pathway for Oxygen

The 'Pathway for Oxygen' is captured in a set of models describing quantitative relationships between fluxes and driving forces for the flux of oxygen from the external air source to the mitochondrial sink at cytochrome oxidase. The intervening processes involve convection, membrane permeation, diffusion of free and heme-bound O2 and enzymatic reactions. While this system's basic elements are simple: ventilation, alveolar gas exchange with blood, circulation of the blood, perfusion of an organ, uptake by tissue, and consumption by chemical reaction, integration of these pieces quickly becomes complex. This complexity led us to construct a tutorial on the ideas and principles; these first PathwayO2 models are simple but quantitative and cover: (1) a 'one-alveolus lung' with airway resistance, lung volume compliance, (2) bidirectional transport of solute gasses like O2 and CO2, (3) gas exchange between alveolar air and lung capillary blood, (4) gas solubility in blood, and circulation of blood through the capillary syncytium and back to the lung, and (5) blood-tissue gas exchange in capillaries. These open-source models are at Physiome.org and provide background for the many respiratory models there.

Semantics-Based Composition of Integrated Cardiomyocyte Models Motivated by Real-World Use Cases

Semantics-based model composition is an approach for generating complex biosimulation models from existing components that relies on capturing the biological meaning of model elements in a machine-readable fashion. This approach allows the user to work at the biological rather than computational level of abstraction and helps minimize the amount of manual effort required for model composition. To support this compositional approach, we have developed the SemGen software, and here report on SemGen's semantics-based merging capabilities using real-world modeling use cases. We successfully reproduced a large, manually-encoded, multi-model merge: the "Pandit-Hinch-Niederer" (PHN) cardiomyocyte excitation-contraction model, previously developed using CellML. We describe our approach for annotating the three component models used in the PHN composition and for merging them at the biological level of abstraction within SemGen. We demonstrate that we were able to reproduce the original PHN model results in a semi-automated, semantics-based fashion and also rapidly generate a second, novel cardiomyocyte model composed using an alternative, independently-developed tension generation component. We discuss the time-saving features of our compositional approach in the context of these merging exercises, the limitations we encountered, and potential solutions for enhancing the approach.

Dynamic contrast-enhanced MRI: Study of inter-software accuracy and reproducibility using simulated and clinical data

PURPOSE

To test the reproducibility and accuracy of pharmacokinetic parameter measurements on five analysis software packages (SPs) for dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), using simulated and clinical data.

MATERIALS AND METHODS

This retrospective study was Institutional Review Board-approved. Simulated tissues consisted of pixel clusters of calculated dynamic signal changes for combinations of Tofts model pharmacokinetic parameters (volume transfer constant [K(trans) ], extravascular extracellular volume fraction [ve ]), longitudinal relaxation time (T1 ). The clinical group comprised 27 patients treated for rectal cancer, with 36 3T DCE-MR scans performed between November 2012 and February 2014, including dual-flip-angle T1 mapping and a dynamic postcontrast T1 -weighted, 3D spoiled gradient-echo sequence. The clinical and simulated images were postprocessed with five SPs to measure K(trans) , ve , and the initial area under the gadolinium curve (iAUGC). Modified Bland-Altman analysis was conducted, intraclass correlation coefficients (ICCs) and within-subject coefficients of variation were calculated.

RESULTS

Thirty-one examinations from 23 patients were of sufficient technical quality and postprocessed. Measurement errors were observed on the simulated data for all the pharmacokinetic parameters and SPs, with a bias ranging from -0.19 min(-1) to 0.09 min(-1) for K(trans) , -0.15 to 0.01 for ve , and -0.65 to 1.66 mmol.L(-1) .min for iAUGC. The ICC between SPs revealed moderate agreement for the simulated data (K(trans) : 0.50; ve : 0.67; iAUGC: 0.77) and very poor agreement for the clinical data (K(trans) : 0.10; ve : 0.16; iAUGC: 0.21).

CONCLUSION

Significant errors were found in the calculated DCE-MRI pharmacokinetic parameters for the perfusion analysis SPs, resulting in poor inter-software reproducibility. J. Magn. Reson. Imaging 2016;43:1288-1300.

Semi-automated Modular Program Constructor for physiological modeling: Building cell and organ models

The Modular Program Constructor (MPC) is an open-source Java based modeling utility, built upon JSim's Mathematical Modeling Language (MML) ( http://www.physiome.org/jsim/) that uses directives embedded in model code to construct larger, more complicated models quickly and with less error than manually combining models. A major obstacle in writing complex models for physiological processes is the large amount of time it takes to model the myriad processes taking place simultaneously in cells, tissues, and organs. MPC replaces this task with code-generating algorithms that take model code from several different existing models and produce model code for a new JSim model. This is particularly useful during multi-scale model development where many variants are to be configured and tested against data. MPC encodes and preserves information about how a model is built from its simpler model modules, allowing the researcher to quickly substitute or update modules for hypothesis testing. MPC is implemented in Java and requires JSim to use its output. MPC source code and documentation are available at http://www.physiome.org/software/MPC/.

Clinical Diagnostic Biomarkers from the Personalization of Computational Models of Cardiac Physiology

Computational modelling of the heart is rapidly advancing to the point of clinical utility. However, the difficulty of parameterizing and validating models from clinical data indicates that the routine application of truly predictive models remains a significant challenge. We argue there is significant value in an intermediate step towards prediction. This step is the use of biophysically based models to extract clinically useful information from existing patient data. Specifically in this paper we review methodologies for applying modelling frameworks for this goal in the areas of quantifying cardiac anatomy, estimating myocardial stiffness and optimizing measurements of coronary perfusion. Using these indicative examples of the general overarching approach, we finally discuss the value, ongoing challenges and future potential for applying biophysically based modelling in the clinical context.

OpenCOR: a modular and interoperable approach to computational biology

Computational biologists have been developing standards and formats for nearly two decades, with the aim of easing the description and exchange of experimental data, mathematical models, simulation experiments, etc. One of those efforts is CellML (cellml.org), an XML-based markup language for the encoding of mathematical models. Early CellML-based environments include COR and OpenCell. However, both of those tools have limitations and were eventually replaced with OpenCOR (opencor.ws). OpenCOR is an open source modeling environment that is supported on Windows, Linux and OS X. It relies on a modular approach, which means that all of its features come in the form of plugins. Those plugins can be used to organize, edit, simulate and analyze models encoded in the CellML format. We start with an introduction to CellML and two of its early adopters, which limitations eventually led to the development of OpenCOR. We then go onto describing the general philosophy behind OpenCOR, as well as describing its openness and its development process. Next, we illustrate various aspects of OpenCOR, such as its user interface and some of the plugins that come bundled with it (e.g., its editing and simulation plugins). Finally, we discuss some of the advantages and limitations of OpenCOR before drawing some concluding remarks.

Diverse Data Sets Can Yield Reliable Information through Mechanistic Modeling: Salicylic Acid Clearance

This is a practical example of a powerful research strategy: putting together data from studies covering a diversity of conditions can yield a scientifically sound grasp of the phenomenon when the individual observations failed to provide definitive understanding. The rationale is that defining a realistic, quantitative, explanatory hypothesis for the whole set of studies, brings about a “consilience” of the often competing hypotheses considered for individual data sets. An internally consistent conjecture linking multiple data sets simultaneously provides stronger evidence on the characteristics of a system than does analysis of individual data sets limited to narrow ranges of conditions. Our example examines three very different data sets on the clearance of salicylic acid from humans: a high concentration set from aspirin overdoses; a set with medium concentrations from a research study on the influences of the route of administration and of sex on the clearance kinetics, and a set on low dose aspirin for cardiovascular health. Three models were tested: (1) a first order reaction, (2) a Michaelis-Menten (M-M) approach, and (3) an enzyme kinetic model with forward and backward reactions. The reaction rates found from model 1 were distinctly different for the three data sets, having no commonality. The M-M model 2 fitted each of the three data sets but gave a reliable estimates of the Michaelis constant only for the medium level data (K_m = 24±5.4 mg/L); analyzing the three data sets together with model 2 gave K_m = 18±2.6 mg/L. (Estimating parameters using larger numbers of data points in an optimization increases the degrees of freedom, constraining the range of the estimates). Using the enzyme kinetic model (3) increased the number of free parameters but nevertheless improved the goodness of fit to the combined data sets, giving tighter constraints, and a lower estimated K_m = 14.6±2.9 mg/L, demonstrating that fitting diverse data sets with a single model improves confidence in the results. This modeling effort is also an example of reproducible science available at html://www.physiome.org/jsim/models/webmodel/NSR/SalicylicAcidClearance

COMBINE archive and OMEX format: one file to share all information to reproduce a modeling project

BACKGROUND

With the ever increasing use of computational models in the biosciences, the need to share models and reproduce the results of published studies efficiently and easily is becoming more important. To this end, various standards have been proposed that can be used to describe models, simulations, data or other essential information in a consistent fashion. These constitute various separate components required to reproduce a given published scientific result.

RESULTS

We describe the Open Modeling EXchange format (OMEX). Together with the use of other standard formats from the Computational Modeling in Biology Network (COMBINE), OMEX is the basis of the COMBINE Archive, a single file that supports the exchange of all the information necessary for a modeling and simulation experiment in biology. An OMEX file is a ZIP container that includes a manifest file, listing the content of the archive, an optional metadata file adding information about the archive and its content, and the files describing the model. The content of a COMBINE Archive consists of files encoded in COMBINE standards whenever possible, but may include additional files defined by an Internet Media Type. Several tools that support the COMBINE Archive are available, either as independent libraries or embedded in modeling software.

CONCLUSIONS

The COMBINE Archive facilitates the reproduction of modeling and simulation experiments in biology by embedding all the relevant information in one file. Having all the information stored and exchanged at once also helps in building activity logs and audit trails. We anticipate that the COMBINE Archive will become a significant help for modellers, as the domain moves to larger, more complex experiments such as multi-scale models of organs, digital organisms, and bioengineering.

Improving collaboration by standardization efforts in systems biology

Collaborative genome-scale reconstruction endeavors of metabolic networks would not be possible without a common, standardized formal representation of these systems. The ability to precisely define biological building blocks together with their dynamic behavior has even been considered a prerequisite for upcoming synthetic biology approaches. Driven by the requirements of such ambitious research goals, standardization itself has become an active field of research on nearly all levels of granularity in biology. In addition to the originally envisaged exchange of computational models and tool interoperability, new standards have been suggested for an unambiguous graphical display of biological phenomena, to annotate, archive, as well as to rank models, and to describe execution and the outcomes of simulation experiments. The spectrum now even covers the interaction of entire neurons in the brain, three-dimensional motions, and the description of pharmacometric studies. Thereby, the mathematical description of systems and approaches for their (repeated) simulation are clearly separated from each other and also from their graphical representation. Minimum information definitions constitute guidelines and common operation protocols in order to ensure reproducibility of findings and a unified knowledge representation. Central database infrastructures have been established that provide the scientific community with persistent links from model annotations to online resources. A rich variety of open-source software tools thrives for all data formats, often supporting a multitude of programing languages. Regular meetings and workshops of developers and users lead to continuous improvement and ongoing development of these standardization efforts. This article gives a brief overview about the current state of the growing number of operation protocols, mark-up languages, graphical descriptions, and fundamental software support with relevance to systems biology.

A new flexible plug and play scheme for modeling, simulating, and predicting gastric emptying

BACKGROUND

In-silico models that attempt to capture and describe the physiological behavior of biological organisms, including humans, are intrinsically complex and time consuming to build and simulate in a computing environment. The level of detail of description incorporated in the model depends on the knowledge of the system's behavior at that level. This knowledge is gathered from the literature and/or improved by knowledge obtained from new experiments. Thus model development is an iterative developmental procedure. The objective of this paper is to describe a new plug and play scheme that offers increased flexibility and ease-of-use for modeling and simulating physiological behavior of biological organisms.

METHODS

This scheme requires the modeler (user) first to supply the structure of the interacting components and experimental data in a tabular format. The behavior of the components described in a mathematical form, also provided by the modeler, is externally linked during simulation. The advantage of the plug and play scheme for modeling is that it requires less programming effort and can be quickly adapted to newer modeling requirements while also paving the way for dynamic model building.

RESULTS

As an illustration, the paper models the dynamics of gastric emptying behavior experienced by humans. The flexibility to adapt the model to predict the gastric emptying behavior under varying types of nutrient infusion in the intestine (ileum) is demonstrated. The predictions were verified with a human intervention study. The error in predicting the half emptying time was found to be less than 6%.

CONCLUSIONS

A new plug-and-play scheme for biological systems modeling was developed that allows changes to the modeled structure and behavior with reduced programming effort, by abstracting the biological system into a network of smaller sub-systems with independent behavior. In the new scheme, the modeling and simulation becomes an automatic machine readable and executable task.