A multiformalism and multiresolution modelling environment: application to the cardiovascular system and its regulation

Modeling Patient-Specific Apnea-Bradycardia Patterns in Preterm Newborn

OBJECTIVE

Preterm infants are particularly exposed to severe cardio-respiratory events, associating apnea with bradycardia and oxygen desaturation. A patient-specific and event-specific model-based approach is proposed in this work to analyze the acute heart rate response to apnea-bradycardia events in preterm newborn.

METHODS

A novel model integrating the main cardio-respiratory interactions which are specific to the neonatal period is proposed. An evolutionary algorithm is applied to estimate patient-specific model parameters from a database of 37 apnea-bradycardia episodes acquired from 10 preterm newborns. Unsupervised clustering (K-means) was applied to the identified parameters to define phenogroups of cardio-respiratory responses to apnea.

RESULTS

A significant correspondence was observed between simulated and experimental heart rate series in all identifications (median RMSE = 8.85 bpm). Three clusters of parameters were found and were associated to three different pathophysiological dynamics related to apnea-bradycardia.

CONCLUSION AND SIGNIFICANCE

The proposed method, based on patient and event-specific model parameter identification, provides a novel approach to characterize bradycardia dynamics in response to apnea, opening the way to the proposal of new personalized diagnosis and treatment possibilities in this particularly sensitive population.

Mathematical modelling of the influence of ACE I/D polymorphism on blood pressure and antihypertensive therapy

The angiotensin-converting enzyme (ACE) gene (ACE) insertion/deletion (I/D) polymorphism raises the possibility of personalising ACE inhibitor therapy to optimise its efficiency and reduce side effects in genetically distinct subgroups. However, the extent of its influence among these subgroups is unknown. Therefore, we extended our computational model of blood pressure regulation to investigate the effect of the ACE I/D polymorphism on haemodynamic parameters in humans undergoing antihypertensive therapy. The model showed that the dependence of blood pressure on serum ACE activity is a function of saturation and therefore, the lack of association between ACE I/D and blood pressure levels may be due to high ACE activity in specific populations. Additionally, in an extended model simulating the effects of different classes of antihypertensive drugs, we explored the relationship between ACE I/D and the efficacy of inhibitors of the renin-angiotensin-aldosterone system. The model predicted that the response of cardiovascular and renal parameters to treatment directly depends on ACE activity. However, significant differences in parameter changes were observed only between groups with high and low ACE levels, while different ACE I/D genotypes within the same group had similar changes in absolute values. We conclude that a single genetic variant is responsible for only a small fraction of heredity in treatment success and its predictive value is limited.

Thoroughly Calibrated Modular Agent-Based Model of the Human Cardiovascular and Renal Systems for Blood Pressure Regulation in Health and Disease

Here we present a modular agent-based mathematical model of the human cardiovascular and renal systems. It integrates the previous models primarily developed by A. C. Guyton, F. Karaaslan, K. M. Hallow, and Y. V. Solodyannikov. We performed the model calibration to find an equilibrium state within the normal vital sign ranges for a healthy adult. We verified the model's abilities to reproduce equilibrium states with abnormal physiological values related to different combinations of cardiovascular diseases (such as systemic hypertension, chronic heart failure, pulmonary hypertension, etc.). For the model creation and validation, we involved over 200 scientific studies covering known models of the human cardiovascular and renal functions, biosimulation platforms, and clinical measurements of physiological quantities in normal and pathological conditions. We compiled detailed documentation describing all equations, parameters and variables of the model with justification of all formulas and values. The model is implemented in BioUML and available in the web-version of the software.

Modeling patient-specific desaturation patterns in sleep apnea

OBJECTIVE

The physiological mechanisms involved in cardio-respiratory responses to sleep apnea events are not yet fully elucidated. A model-based approach is proposed to analyse the acute desaturation response to obstructive apneas.

METHODS

An integrated model of cardio-respiratory interactions was proposed and parameters were identified, using an evolutionary algorithm, on a database composed of 107 obstructive apneas acquired from 10 patients (HYPNOS clinical study). Unsupervised clustering was applied to the identified parameters in order to characterize the phenotype of each response to obstructive apneas.

RESULTS

A close match was observed between simulated oxygen saturation (SaO2) and experimental SaO2 in all identifications (median RMSE = 1.3892%). Two clusters of parameters, associated with different dynamics related to sleep apnea and periodic breathing were obtained.

CONCLUSION AND SIGNIFICANCE

The proposed patient and event-specific model-based analysis provides understanding on specific desaturation patterns, consequent to apnea events, with potential applications for personalized diagnosis and treatment.

Parametric Analysis of an Integrated Model of Cardio-respiratory Interactions in Adults in the Context of Obstructive Sleep Apnea

An original integrated model of cardio-respiratory interactions is presented in this paper with the objective of studying the acute physiological responses evoked by obstructive sleep apnea events in adults. A comprehensive sensitivity analysis of the model is proposed during the simulation of a 20 s obstructive apnea episode using the Morris' screening method and local sensitivity analysis. The more relevant parameters are related to the following mechanisms of the physiology: (i) the fraction of oxygen in inspired air, (ii) metabolic rates (oxygen consumption rate, CO₂ production rate); (iii) chemoreflex (gains and time constants) (iv) respiratory mechanics (lung compliance and unstressed volume of air in the alveoli). These results highlight significant physiological variables that may be particularly useful for the development of novel diagnostic and therapeutic strategies, integrating a virtual patient approach.

Towards a Reduced In Silico Model Predicting Biochemical Recurrence After Radiotherapy in Prostate Cancer

OBJECTIVE

Purposes of this work were i) to develop an in silico model of tumor response to radiotherapy, ii) to perform an exhaustive sensitivity analysis in order to iii) propose a simplified version and iv) to predict biochemical recurrence with both the comprehensive and the reduced model.

METHODS

A multiscale computational model of tumor response to radiotherapy was developed. It integrated the following radiobiological mechanisms: oxygenation, including hypoxic death; division of tumor cells; VEGF diffusion driving angiogenesis; division of healthy cells and oxygen-dependent response to irradiation, considering, cycle arrest and mitotic catastrophe. A thorough sensitivity analysis using the Morris screening method was performed on 21 prostate computational tissues. Tumor control probability (TCP) curves of the comprehensive model and 15 reduced versions were compared. Logistic regression was performed to predict biochemical recurrence after radiotherapy on 76 localized prostate cancer patients using an output of the comprehensive and the reduced models.

RESULTS

No significant difference was found between the TCP curves of the comprehensive and a simplified version which only considered oxygenation, division of tumor cells and their response to irradiation. Biochemical recurrence predictions using the comprehensive and the reduced models improved those made from pre-treatment imaging parameters (AUC = 0.81 ± 0.02 and 0.82 ± 0.02 vs. 0.75 ± 0.03, respectively).

CONCLUSION

A reduced model of tumor response to radiotherapy able to predict biochemical recurrence in prostate cancer was obtained.

SIGNIFICANCE

This reduced model may be used in the future to optimize personalized fractionation schedules.

Model-based analysis of the autonomic response to head-up tilt testing in Brugada syndrome

The etiology of Brugada syndrome (BS) is complex and multifactorial, making risk stratification in this population a major challenge. Since changes in the autonomic modulation of these patients are commonly related to arrhythmic events, we analyze in this work whether the response to head-up tilt (HUT) testing on this population may provide useful, complementary information for risk stratification. In order to perform this analysis, a coupled physiological model integrating the cardiac electrical activity, the cardiovascular system and the baroreceptors reflex control of the autonomic function, in response to HUT is proposed. A sensitivity analysis was performed, based on a screening method, evidencing the influence of cardiovascular parameters on blood pressure and of baroreflex regulation on heart rate. The most sensitive parameters have been identified on a set of 20 subjects (8 controls and 12 BS patients), so as to assess subject-specific model parameters. According to the results, controls showed an increased sympathetic modulation after tilting, as well as a reduced left ventricular contractility was observed in symptomatic, with respect to asymptomatic BS patients. These results provide new insights regarding the autonomic mechanisms regulating the cardiovascular system in BS which might be used as a complementary source of information, along with classical electrophysiological parameters, for BS risk stratification.

Recursive identification of an arterial baroreflex model for the evaluation of cardiovascular autonomic modulation

The evaluation of the time-varying vagal and sympathetic contributions to heart rate remains a challenging task because the observability of the baroreflex is generally limited and the time-varying properties are difficult to take into account, especially in non-stationnary conditions. The objective is to propose a model-based approach to estimate the autonomic modulation during a pharmacological challenge. A recursive parameter identification method is proposed and applied to a mathematical model of the baroreflex, in order to estimate the time-varying vagal and sympathetic contributions to heart rate modulation during autonomic maneuvers. The model-based method was evaluated with data from five newborn lambs, which were acquired during injection of vasodilator and vasoconstrictor drugs, on normal conditions and under beta-blockers, so as to quantify the effect of the pharmacological sympathetic blockade on the estimated parameters. After parameter identification, results show a close match between experimental and simulated signals for the five lambs, as the mean relative root mean squared error is equal to 0.0026 (± 0.003). The error, between simulated and experimental signals, is significantly reduced compared to a batch identification of parameters. The model-based estimation of vagal and sympathetic contributions were consistent with physiological knowledge and, as expected, it was possible to observe an alteration of the sympathetic response under beta-blockers. The simulated vagal modulation illustrates a response similar to traditional heart rate variability markers during the pharmacological maneuver. The model-based method, proposed in the paper, highlights the advantages of using a recursive identification method for the estimation of vagal and sympathetic modulation.

A model-based approach for the evaluation of vagal and sympathetic activities in a newborn lamb

This paper proposes a baroreflex model and a recursive identification method to estimate the time-varying vagal and sympathetic contributions to heart rate variability during autonomic maneuvers. The baroreflex model includes baroreceptors, cardiovascular control center, parasympathetic and sympathetic pathways. The gains of the global afferent sympathetic and vagal pathways are identified recursively. The method has been validated on data from newborn lambs, which have been acquired during the application of an autonomic maneuver, without medication and under beta-blockers. Results show a close match between experimental and simulated signals under both conditions. The vagal and sympathetic contributions have been simulated and, as expected, it is possible to observe different baroreflex responses under beta-blockers compared to baseline conditions.

Sensitivity analysis and parameter estimation of a coronary circulation model for triple-vessel disease

Mathematical models of the coronary circulation have been shown to provide useful information for the analysis of intracoronary blood flow and pressure measurements acquired during coronary artery bypass graft (CABG) surgery. Although some efforts towards the patient-specific estimation of model parameters have been presented in this context, they are based on simplifying hypotheses about the collateral circulation and do not take advantage of the whole set of data acquired during CABG. In order to overcome these limitations, this paper presents an exhaustive parameter sensitivity analysis and a multiobjective patient-specific parameter estimation method, applied to a model of the coronary circulation of patients with triple vessel disease. The results of the sensitivity analysis highlighted the importance of capillary and collateral development. On the other hand, the estimation method was applied to intraoperative clinical data from ten patients obtained during CABG, which permitted to assess patient-specific collateral vessel situations. These approaches provide new insights regarding the heterogeneous configuration of the collateral circulation.

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

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

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

Multiobjective patient-specific estimation of a coronary circulation model for triple vessel disease

Computational models can help understand the hemodynamics of the coronary circulation, which is of the upmost importance to help clinicians before, during and after a coronary artery bypass graft surgery. In this paper, we propose a multiobjective optimization method for parameter estimation of a computational model representing the coronary circulation on patients with a triple vessel disease. This estimation was not based on any assumption regarding the development of the collateral circulation, like in previous works. Indeed, the collateral development of a given patient is estimated through the model parameters. Parameter estimation was performed using clinical data from three patients, obtained before and during an off-pump coronary artery bypass graft surgery (CABG). Results showed a better performance when comparing the simulation with clinical data, since the total error estimation for three patients was reduced by 40 ± 22%. Moreover, the proposed method provides new insight regarding the heterogeneous configuration of the alternative collateral vessels.

Mathematical modeling of respiratory system mechanics in the newborn lamb

In this paper, a mathematical model of the respiratory mechanics is used to reproduce experimental signal waveforms acquired from three newborn lambs. As the main challenge is to determine specific lamb parameters, a sensitivity analysis has been realized to find the most influent parameters, which are identified using an evolutionary algorithm. Results show a close match between experimental and simulated pressure and flow waveforms obtained during spontaneous ventilation and pleural pressure variations acquired during the application of positive pressure, since root mean square errors equal to 0.0119, 0.0052 and 0.0094. The identified parameters were discussed in light of previous knowledge of respiratory mechanics in the newborn.

Virtual patients and sensitivity analysis of the Guyton model of blood pressure regulation: towards individualized models of whole-body physiology

Mathematical models that integrate multi-scale physiological data can offer insight into physiological and pathophysiological function, and may eventually assist in individualized predictive medicine. We present a methodology for performing systematic analyses of multi-parameter interactions in such complex, multi-scale models. Human physiology models are often based on or inspired by Arthur Guyton's whole-body circulatory regulation model. Despite the significance of this model, it has not been the subject of a systematic and comprehensive sensitivity study. Therefore, we use this model as a case study for our methodology. Our analysis of the Guyton model reveals how the multitude of model parameters combine to affect the model dynamics, and how interesting combinations of parameters may be identified. It also includes a "virtual population" from which "virtual individuals" can be chosen, on the basis of exhibiting conditions similar to those of a real-world patient. This lays the groundwork for using the Guyton model for in silico exploration of pathophysiological states and treatment strategies. The results presented here illustrate several potential uses for the entire dataset of sensitivity results and the "virtual individuals" that we have generated, which are included in the supplementary material. More generally, the presented methodology is applicable to modern, more complex multi-scale physiological models.

Regulation of cell behavior and tissue patterning by bioelectrical signals: challenges and opportunities for biomedical engineering

Achieving control over cell behavior and pattern formation requires molecular-level understanding of regulatory mechanisms. Alongside transcriptional networks and biochemical gradients, there functions an important system of cellular communication and control: transmembrane voltage gradients (V(mem)). Bioelectrical signals encoded in spatiotemporal changes of V(mem) control cell proliferation, migration, and differentiation. Moreover, endogenous bioelectrical gradients serve as instructive cues mediating anatomical polarity and other organ-level aspects of morphogenesis. In the past decade, significant advances in molecular physiology have enabled the development of new genetic and biophysical tools for the investigation and functional manipulation of bioelectric cues. Recent data implicate V(mem) as a crucial epigenetic regulator of patterning events in embryogenesis, regeneration, and cancer. We review new conceptual and methodological developments in this fascinating field. Bioelectricity offers a novel way of quantitatively understanding regulation of growth and form in vivo, and it reveals tractable, powerful control points that will enable truly transformative applications in bioengineering, regenerative medicine, and synthetic biology.

A tentative taxonomy for predictive models in relation to their falsifiability

The growing importance of predictive models in biomedical research raises some concerns on the correct methodological approach to the falsification of such models, as they are developed in interdisciplinary research contexts between physics, biology and medicine. In each of these research sectors, there are established methods to develop cause-effect explanations for observed phenomena, which can be used to predict: epidemiological models, biochemical models, biophysical models, Bayesian models, neural networks, etc. Each research sector has accepted processes to verify how correct these models are (falsification). But interdisciplinary research imposes a broader perspective, which encompasses all possible models in a general methodological framework of falsification. The present paper proposes a general definition of 'scientific model' that makes it possible to categorize predictive models into broad categories. For each of these categories, generic falsification strategies are proposed, except for the so-called 'abductive' models. For this category, which includes artificial neural networks, Bayesian models and integrative models, the definition of a generic falsification strategy requires further investigation by researchers and philosophers of science.

Embedding a cardiac pulsatile model into an integrated model of the cardiovascular regulation for heart failure followup

The analysis of followup data from patients suffering from heart failure is a difficult task, due to the complex and multifactorial nature of this pathology. In this paper, we present a coupled model, integrating a pulsatile heart into a model of the short to long-term regulations of the cardiovascular system. An interface method is proposed to couple these models, which present significantly different time scales. Results from a sensitivity analysis of the original and integrated models are proposed with simulations reproducing the main effects of the short- and long-term responses of an acute decompensated heart failure episode on a patient undergoing cardiac resynchronization therapy.

A computational model of the circulating renin-angiotensin system and blood pressure regulation

The renin-angiotensin system (RAS) is critical in sodium and blood pressure (BP) regulation, and in cardiovascular-renal (CVR) diseases and therapeutics. As a contribution to SAPHIR project, we present a realistic computer model of renin production and circulating RAS, integrated into Guyton's circulatory model (GCM). Juxtaglomerular apparatus, JGA, and Plasma modules were implemented in C ++/M2SL (Multi-formalism Multi-resolution Simulation Library) for fusion with GCM. Matlab optimization toolboxes were used for parameter identification. In JGA, renin production and granular cells recruitment (GCR) are controlled by perfusion pressure (PP), macula densa (MD), angiotensin II (Ang II), and renal sympathetic activity (RSNA). In Plasma, renin and ACE (angiotensin-converting enzyme) activities are integrated to yield Ang I and II. Model vs. data deviation is given as normalized root mean squared error (nRMSE; n points).

IDENTIFICATION

JGA and Plasma parameters were identified against selected experimental data. After fusion with GCM: (1) GCR parameters were identified against Laragh's PRA-natriuresis nomogram; (2) Renin production parameters were identified against two sets of data ([renin] transients vs. ACE or renin inhibition). Finally, GCR parameters were re-identified vs. Laragh's nomogram (nRMSE 8%, n = 9).

VALIDATION

(1) model BP, PRA and [Ang II] are within reported ranges, and respond physiologically to sodium intake; (2) short-term Ang II infusion induces reported rise in BP and PRA. The modeled circulating RAS, in interaction with an integrated CVR, exhibits a realistic response to BP control maneuvers. This construction will allow for modelling hypertensive and CVR patients, including salt-sensitivity, polymorphisms, and pharmacotherapeutics.

Design of a framework for modeling, integration and simulation of physiological models

Modeling and simulation of physiological processes deal with the challenges of multiscale models in which coupling is very high within and among scales. Information technology approaches together with related analytical and computational tools will help to deal with these challenges. Physiological Model Simulation, Integration and Modeling Framework, Phy-SIM, provides the modeling environment which will help to cultivate various approaches to deal with the inherent problem of multiscale modeling of physiological systems. In this paper, we present the modular design of Phy-SIM. The proposed layered design of Phy-SIM, separates structure from function in physiological processes advocating modular thinking in developing and integrating physiological models. Moreover, the ontology based architecture will improve the modeling process by the mechanisms to attach anatomical and physiological ontological information to the models. The ultimate aim of the proposed approaches is to enhance the physiological model development and integration processes by providing the tools and mechanisms in Phy-SIM.