An integrated mathematical model of the human cardiopulmonary system: model development

Unanticipated evolution of cardio-respiratory interactions with cognitive load during a Go-NoGo shooting task in virtual reality

The cardiovascular system interacts continuously with the respiratory system to maintain the vital balance of oxygen and carbon dioxide in our body. The interplay between the sympathetic and parasympathetic branches of the autonomic nervous system regulates the aforesaid involuntary functions. This study analyzes the dynamics of the cardio-respiratory (CR) interactions using RR Intervals (RRI), Systolic Blood Pressure (SBP), and Respiration signals after first-order differencing to make them stationary. It investigates their variation with cognitive load induced by a virtual reality (VR) based Go-NoGo shooting task with low and high levels of task difficulty. We use Pearson's correlation-based linear and mutual information-based nonlinear measures of association to indicate the reduction in RRI-SBP and RRI-Respiration interactions with cognitive load. However, no linear correlation difference was observed in SBP-Respiration interactions with cognitive load, but their mutual information increased. A couple of open-loop autoregressive models with exogenous input (ARX) are estimated using RRI and SBP, and one closed-loop ARX model is estimated using RRI, SBP, and Respiration. The impulse responses (IRs) are derived for each input-output pair, and a reduction in the positive and negative peak amplitude of all the IRs is observed with cognitive load. Some novel parameters are derived by representing the IR as a double exponential curve with cosine modulation and show significant differences with cognitive load compared to other measures, especially for the IR between SBP and Respiration.

Comparing physiological impacts of positive pressure ventilation versus self-breathing via a versatile cardiopulmonary model incorporating a novel alveoli opening mechanism

Mathematical models can be used to generate high-fidelity simulations of the cardiopulmonary system. Such models, when applied to real patients, can provide valuable insights into underlying physiological processes that are hard for clinicians to observe directly. In this work, we propose a novel modelling strategy capable of generating scenario-specific cardiopulmonary simulations to replicate the vital physiological signals clinicians use to determine the state of a patient. This model is composed of a tree-like pulmonary system that features a novel, non-linear alveoli opening strategy, based on the dynamics of balloon inflation, that interacts with the cardiovascular system via the thorax. A baseline simulation of the model is performed to measure the response of the system during spontaneous breathing which is subsequently compared to the same system under mechanical ventilation. To test the new lung opening mechanics and systematic recruitment of alveolar units, a positive end-expiratory pressure (PEEP) test is performed and its results are then compared to simulations of a deep spontaneous breath. The system displays a marked decrease in tidal volume as PEEP increases, replicating a sigmoidal curve relationship between volume and pressure. At high PEEP, cardiovascular function is shown to be visibly impaired, in contrast to the deep breath test where normal function is maintained.

Building Digital Twins for Cardiovascular Health: From Principles to Clinical Impact

The past several decades have seen rapid advances in diagnosis and treatment of cardiovascular diseases and stroke, enabled by technological breakthroughs in imaging, genomics, and physiological monitoring, coupled with therapeutic interventions. We now face the challenge of how to (1) rapidly process large, complex multimodal and multiscale medical measurements; (2) map all available data streams to the trajectories of disease states over the patient's lifetime; and (3) apply this information for optimal clinical interventions and outcomes. Here we review new advances that may address these challenges using digital twin technology to fulfill the promise of personalized cardiovascular medical practice. Rooted in engineering mechanics and manufacturing, the digital twin is a virtual representation engineered to model and simulate its physical counterpart. Recent breakthroughs in scientific computation, artificial intelligence, and sensor technology have enabled rapid bidirectional interactions between the virtual-physical counterparts with measurements of the physical twin that inform and improve its virtual twin, which in turn provide updated virtual projections of disease trajectories and anticipated clinical outcomes. Verification, validation, and uncertainty quantification builds confidence and trust by clinicians and patients in the digital twin and establishes boundaries for the use of simulations in cardiovascular medicine. Mechanistic physiological models form the fundamental building blocks of the personalized digital twin that continuously forecast optimal management of cardiovascular health using individualized data streams. We present exemplars from the existing body of literature pertaining to mechanistic model development for cardiovascular dynamics and summarize existing technical challenges and opportunities pertaining to the foundation of a digital twin.

Closed-loop baroreflex model with biophysically detailed afferent pathway

In this work, we couple a lumped-parameter closed-loop model of the cardiovascular system with a physiologically-detailed mathematical description of the baroreflex afferent pathway. The model features a classical Hodgkin-Huxley current-type model for the baroreflex afferent limb (primary neuron) and for the second-order neuron in the central nervous system. The pulsatile arterial wall distension triggers a frequency-modulated sequence of action potentials at the afferent neuron. This signal is then integrated at the brainstem neuron model. The efferent limb, representing the sympathetic and parasympathetic nervous system, is described as a transfer function acting on heart and blood vessel model parameters in order to control arterial pressure. Three in silico experiments are shown here: a step increase in the aortic pressure to evaluate the functionality of the reflex arch, a hemorrhagic episode and an infusion simulation. Through this model, it is possible to study the biophysical dynamics of the ionic currents proposed for the afferent limb components of the baroreflex during the cardiac cycle, and the way in which currents dynamics affect the cardiovascular function. Moreover, this system can be further developed to study in detail each baroreflex loop component, helping to unveil the mechanisms involved in the cardiovascular afferent information processing.

A Lumped-Parameter Model of the Cardiovascular System Response for Evaluating Automated Fluid Resuscitation Systems

Physiological closed-loop controlled (PCLC) medical devices, such as those designed for blood pressure regulation, can be tested for safety and efficacy in real-world clinical settings. However, relying solely on limited animal and clinical studies may not capture the diverse range of physiological conditions. Credible mathematical models can complement these studies by allowing the testing of the device against simulated patient scenarios. This research involves the development and validation of a low-order lumped-parameter mathematical model of the cardiovascular system's response to fluid perturbation. The model takes rates of hemorrhage and fluid infusion as inputs and provides hematocrit and blood volume, heart rate, stroke volume, cardiac output and mean arterial blood pressure as outputs. The model was calibrated using data from 27 sheep subjects, and its predictive capability was evaluated through a leave-one-out cross-validation procedure, followed by independent validation using 12 swine subjects. Our findings showed small model calibration error against the training dataset, with the normalized root-mean-square error (NRMSE) less than 10% across all variables. The mathematical model and virtual patient cohort generation tool demonstrated a high level of predictive capability and successfully generated a sufficient number of subjects that closely resembled the test dataset. The average NRMSE for the best virtual subject, across two distinct samples of virtual subjects, was below 12.7% and 11.9% for the leave-one-out cross-validation and independent validation dataset. These findings suggest that the model and virtual cohort generator are suitable for simulating patient populations under fluid perturbation, indicating their potential value in PCLC medical device evaluation.

Parametric analysis of an integrated cardio-respiratory model in preterm newborns during apnea

The analysis of the complex interactions involved in the acute physiological response to apnea-bradycardia events in preterm newborns remains a challenging task. This paper presents a novel integrated model of cardio-respiratory interactions, adapted to preterm newborns. A sensitivity analysis, based Morris' screening method, was applied to study the effects of physiological parameters on heart rate and desaturation, during the simulation of a 15-seconds apnea-bradycardia episode. The most sensitive parameters are associated with fundamental, integrative physiological mechanisms involving: (i) respiratory mechanics (intermediate airways and lung compliance), (ii) fraction of inspired oxygen, (iii) metabolic rates (oxygen consumption rate), (iv) heart rate regulation and (v) chemoreflex (gain). Results highlight the relevant influence of physiological variables, involved in preterm apnea-bradycardia events.

A mathematical model to assess the effects of COVID-19 on the cardiocirculatory system

Impaired cardiac function has been described as a frequent complication of COVID-19-related pneumonia. To investigate possible underlying mechanisms, we represented the cardiovascular system by means of a lumped-parameter 0D mathematical model. The model was calibrated using clinical data, recorded in 58 patients hospitalized for COVID-19-related pneumonia, to make it patient-specific and to compute model outputs of clinical interest related to the cardiocirculatory system. We assessed, for each patient with a successful calibration, the statistical reliability of model outputs estimating the uncertainty intervals. Then, we performed a statistical analysis to compare healthy ranges and mean values (over patients) of reliable model outputs to determine which were significantly altered in COVID-19-related pneumonia. Our results showed significant increases in right ventricular systolic pressure, diastolic and mean pulmonary arterial pressure, and capillary wedge pressure. Instead, physical quantities related to the systemic circulation were not significantly altered. Remarkably, statistical analyses made on raw clinical data, without the support of a mathematical model, were unable to detect the effects of COVID-19-related pneumonia in pulmonary circulation, thus suggesting that the use of a calibrated 0D mathematical model to describe the cardiocirculatory system is an effective tool to investigate the impairments of the cardiocirculatory system associated with COVID-19.

Evaluation of vascular aging on measures of cardiac function and mechanical efficiency: insights from in-silico modeling

Introduction

This study evaluated the hypothesis that vascular aging (VA) reduces ventricular contractile function and mechanical efficiency (ME) using the left ventricular pressure-volume (PV) construct.

Methods

A previously published in-silico computational model (CM) was modified to evaluate the hypothesis in two phases. In phase I, the CM included five settings of aortic compliance (CA) from normal to stiff, studied at a heart rate of 80 bpm, and phase II included the normal to stiff CA settings evaluated at 60, 100, and 140 bpm. The PV construct provided steady-state and transient data through a simulated vena caval occlusion (VCO). The steady-state data included left ventricular volumes (EDV and ESV), stroke work (SW), and VCO provided the PV area (PVA) data in addition to the three measures of contractile state (CS): end-systolic pressure-volume relationship (ESPVR), dP/dtmax-EDV and preload recruitable stroke work (PRSW). Finally, ME was calculated with the SW/PVA parameter.

Results

In phase I, EDV and ESV increased, as did SW and PVA. The impact on the CS parameters demonstrated a small decrease in ESPVR, no change in dP/dtmax-EDV, and a large increase in PRSW. ME decreased from 71.5 to 60.8%, respectively. In phase II, at the normal and stiff CA settings, across the heart rates studied, EDV and ESV decreased, ESPVR and dP/dtmax-EDV increased and PRSW decreased. ME decreased from 76.4 to 62.6% at the normal CA and 65.8 to 53.2% at the stiff CA.

Discussion

The CM generated new insights regarding how the VA process impacts the contractile state of the myocardium and ME.

Heart Rate Variability Monitoring Based on Doppler Radar Using Deep Learning

The potential of microwave Doppler radar in non-contact vital sign detection is significant; however, prevailing radar-based heart rate (HR) and heart rate variability (HRV) monitoring technologies often necessitate data lengths surpassing 10 s, leading to increased detection latency and inaccurate HRV estimates. To address this problem, this paper introduces a novel network integrating a frequency representation module and a residual in residual module for the precise estimation and tracking of HR from concise time series, followed by HRV monitoring. The network adeptly transforms radar signals from the time domain to the frequency domain, yielding high-resolution spectrum representation within specified frequency intervals. This significantly reduces latency and improves HRV estimation accuracy by using data that are only 4 s in length. This study uses simulation data, Frequency-Modulated Continuous-Wave radar-measured data, and Continuous-Wave radar data to validate the model. Experimental results show that despite the shortened data length, the average heart rate measurement accuracy of the algorithm remains above 95% with no loss of estimation accuracy. This study contributes an efficient heart rate variability estimation algorithm to the domain of non-contact vital sign detection, offering significant practical application value.

Systems Engineering Approach to Modeling and Analysis of Chronic Obstructive Pulmonary Disease Part II: Extension for Variable Metabolic Rates

Recently, we developed a systems engineering model of the human cardiorespiratory system [Kurian et al. ACS Omega2023, 8 (23), 20524-20535. DOI: 10.1021/acsomega.3c00854] based on existing models of physiological processes and adapted it for chronic obstructive pulmonary disease (COPD)-an inflammatory lung disease with multiple manifestations and one of the leading causes of death in the world. This control engineering-based model is extended here to allow for variable metabolic rates established at different levels of physical activity. This required several changes to the original model: the model of the controller was enhanced to include the feedforward loop that is responsible for cardiorespiratory control under varying metabolic rates (activity level, characterized as metabolic equivalent of the task-Rm-and normalized to one at rest). In addition, a few refinements were made to the cardiorespiratory mechanics, primarily to introduce physiological processes that were not modeled earlier but became important at high metabolic rates. The extended model is verified by analyzing the impact of exercise (Rm > 1) on the cardiorespiratory system of healthy individuals. We further formally justify our previously proposed adaptation of the model for COPD patients through sensitivity analysis and refine the parameter tuning through the use of a parallel tempering stochastic global optimization method. The extended model successfully replicates experimentally observed abnormalities in COPD-the drop in arterial oxygen tension and dynamic hyperinflation under high metabolic rates-without being explicitly trained on any related data. It also supports the prospects of remote patient monitoring in COPD.

An enhanced respiratory mechanics model based on double-exponential and fractional calculus

We address mathematical modelling of respiratory mechanics and put forward a model based on double-exponential and fractional calculus for parameter estimation, model simulation, and evaluation based on actual data. Our model has been implemented on a publicly available executable code with adjustable parameters, making it suitable for different applications. Our analysis represents the first application of fractional calculus and double-exponential modelling to respiratory mechanics, and allows us to propose a hybrid model fitting experimental data in different ventilation modes. Furthermore, our model can be used to study the mechanical features of the respiratory system, improve the safety of ventilation techniques, reduce ventilation damages, and provide strong support for fast and adaptive determination of ventilation parameters.

Evaluation of Potential Effects of Increased Outdoor Temperatures Due to Global Warming on Cerebral Blood Flow Rate and Respiratory Function in Chronic Obstructive Disease and Anemia

Global warming due to increased outdoor carbon dioxide (CO2) levels may cause several health problems such as headaches, cognitive impairment, or kidney dysfunction. It is predicted that further increases in CO2 levels will increase the morbidity and mortality of patients affected by a variety of diseases. For instance, patients with Chronic Obstructive Pulmonary Disease (COPD) may suffer cognitive impairments or intracranial bleeding due to an increased cerebral blood flow rate. Predicting the harmful effects of global warming on human health will help to take measures for potential problems. Therefore, the quantification of physiological parameters is an essential step to investigate the effects of global warming on human health. In this study, the effects of increased outdoor temperatures due to climate change on cerebral blood flow rate and respiratory function in healthy subjects and COPD patients with anemia and respiratory acidosis are evaluated utilizing numerical simulations. The numerical model simulates cardiac function and blood circulation in systemic, pulmonary and cerebral circulations, cerebral autoregulatory functions, respiratory function, alveolar gas exchange, oxygen (O2) and CO2 contents, and hemoglobin levels in the blood. The simulation results show that although the cardiovascular function is not significantly altered, the respiratory function and cerebral blood flow rates are altered remarkably.

A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems

Current mathematical models of the cardiovascular system that are based on systems of ordinary differential equations are limited in their ability to mimic important features of measured patient data, such as variable heart rates (HR). Such limitations present a significant obstacle in the use of such models for clinical decision-making, as it is the variations in vital signs such as HR and systolic and diastolic blood pressure that are monitored and recorded in typical critical care bedside monitoring systems. In this paper, novel extensions to well-established multi-compartmental models of the cardiovascular and respiratory systems are proposed that permit the simulation of variable HR. Furthermore, a correction to current models is also proposed to stabilize the respiratory behaviour and enable realistic simulation of vital signs over the longer time scales required for clinical management. The results of the extended model developed here show better agreement with measured bio-signals, and these extensions provide an important first step towards estimating model parameters from patient data, using methods such as neural ordinary differential equations. The approach presented is generalizable to many other similar multi-compartmental models of the cardiovascular and respiratory systems.

Systems Engineering Approach to Modeling and Analysis of Chronic Obstructive Pulmonary Disease

Chronic obstructive pulmonary disease (COPD) is a progressive lung disease characterized by airflow limitation. This study develops a systems engineering framework for representing important mechanistic details of COPD in a model of the cardiorespiratory system. In this model, we present the cardiorespiratory system as an integrated biological control system responsible for regulating breathing. Four engineering control system components are considered: sensor, controller, actuator, and the process itself. Knowledge of human anatomy and physiology is used to develop appropriate mechanistic mathematical models for each component. Following a systematic analysis of the computational model, we identify three physiological parameters associated with reproducing clinical manifestations of COPD: changes in the forced expiratory volume, lung volumes, and pulmonary hypertension. We quantify the changes in these parameters (airway resistance, lung elastance, and pulmonary resistance) as the ones that result in a systemic response that is diagnostic of COPD. A multivariate analysis of the simulation results reveals that the changes in airway resistance have a broad impact on the human cardiorespiratory system and that the pulmonary circuit is stressed beyond normal under hypoxic environments in most COPD patients.

A numerical study of the hemodynamic behavior and gas transport in cardiovascular systems with severe cardiac or cardiopulmonary failure supported by venoarterial extracorporeal membrane oxygenation

Venoarterial extracorporeal membrane oxygenation (VA-ECMO) has been extensively demonstrated as an effective means of bridge-to-destination in the treatment of patients with severe ventricular failure or cardiopulmonary failure. However, appropriate selection of candidates and management of patients during Extracorporeal membrane oxygenation (ECMO) support remain challenging in clinical practice, due partly to insufficient understanding of the complex influences of extracorporeal membrane oxygenation support on the native cardiovascular system. In addition, questions remain as to how central and peripheral venoarterial extracorporeal membrane oxygenation modalities differ with respect to their hemodynamic impact and effectiveness of compensatory oxygen supply to end-organs. In this work, we developed a computational model to quantitatively address the hemodynamic interaction between the extracorporeal membrane oxygenation and cardiovascular systems and associated gas transport. Model-based numerical simulations were performed for cardiovascular systems with severe cardiac or cardiopulmonary failure and supported by central or peripheral venoarterial extracorporeal membrane oxygenation. Obtained results revealed that: 1) central and peripheral venoarterial extracorporeal membrane oxygenation modalities had a comparable capacity for elevating arterial blood pressure and delivering oxygenated blood to important organs/tissues, but induced differential changes of blood flow waveforms in some arteries; 2) increasing the rotation speed of extracorporeal membrane oxygenation pump (ω) could effectively improve arterial blood oxygenation, with the efficiency being especially high when ω was low and cardiopulmonary failure was severe; 3) blood oxygen indices (i.e., oxygen saturation and partial pressure) monitored at the right radial artery could be taken as surrogates for diagnosing potential hypoxemia in other arteries irrespective of the modality of extracorporeal membrane oxygenation; and 4) Left ventricular (LV) overloading could occur when ω was high, but the threshold of ω for inducing clinically significant left ventricular overloading depended strongly on the residual cardiac function. In summary, the study demonstrated the differential hemodynamic influences while comparable oxygen delivery performance of the central and peripheral venoarterial extracorporeal membrane oxygenation modalities in the management of patients with severe cardiac or cardiopulmonary failure and elucidated how the status of arterial blood oxygenation and severity of left ventricular overloading change in response to variations in ω. These model-based findings may serve as theoretical references for guiding the application of venoarterial extracorporeal membrane oxygenation or interpreting in vivo measurements in clinical practice.

A Novel Strategy to Fit and Validate Physiological Models: A Case Study of a Cardiorespiratory Model for Simulation of Incremental Aerobic Exercise

Applying complex mathematical models of physiological systems is challenging due to the large number of parameters. Identifying these parameters through experimentation is difficult, and although procedures for fitting and validating models are reported, no integrated strategy exists. Additionally, the complexity of optimization is generally neglected when the number of experimental observations is restricted, obtaining multiple solutions or results without physiological justification. This work proposes a fitting and validation strategy for physiological models with many parameters under various populations, stimuli, and experimental conditions. A cardiorespiratory system model is used as a case study, and the strategy, model, computational implementation, and data analysis are described. Using optimized parameter values, model simulations are compared to those obtained using nominal values, with experimental data as a reference. Overall, a reduction in prediction error is achieved compared to that reported for model building. Furthermore, the behavior and accuracy of all the predictions in the steady state were improved. The results validate the fitted model and provide evidence of the proposed strategy's usefulness.

Proposed cardio-pulmonary model to investigate the effects of COVID-19 on the cardiovascular system

In this paper, we propose a new mathematical model of cardiovascular system coupled with a respiratory system to study the effects of COVID-19 on global blood circulation parameters using the lumped parameters model. We use the fourth-order Runge-Kutta method for solving the sets of equations of motion. We validate our model by showing that the simulated flows in pulmonary and aortic valves corroborate, respectively, the results established by Smith et al. [IFAC Proceedings Volumes, 39 (2006) 453-458]. Then we examine the effects of the new coronavirus (covid-19) on the cardiopulmonary system through the impact of the high respiratory frequency and the variation of the alveoli volume. To achieve this aim, we propose a new exponential law for the time varying of the pulmonary resistance. It appears that when the respiratory frequency grows, the delay between the systemic artery flow and the flow in the pulmonary artery diminishes. Therefore, the efficiency of the cardiac pump is reduced. Moreover, our results also show that variations of the alveoli volume cause the increment of the pleural pressure in the vascular cavities that induces an exponential growth of the pulmonary resistance. Furthermore, this growth of the pulmonary resistance provokes the augmentation of pressure in some organs and its reduction in others. We found that patient with covid-19 having a prior history of cardiovascular diseases is exposed to a severe case of inflammation/damage of certain organs than those with no history of cardiovascular disease.

Development and validation of a mathematical model of heart rate response to fluid perturbation

Physiological closed-loop controlled (PCLC) medical devices monitor and automatically adjust the patient's condition by using physiological variables as feedback, ideally with minimal human intervention to achieve the target levels set by a clinician. PCLC devices present a challenge when it comes to evaluating their performance, where conducting large clinical trials can be expensive. Virtual physiological patients simulated by validated mathematical models can be utilized to obtain pre-clinical evidence of safety and assess the performance of the PCLC medical device during normal and worst-case conditions that are unlikely to happen in a limited clinical trial. A physiological variable that plays a major role during fluid resuscitation is heart rate (HR). For in silico assessment of PCLC medical devices regarding fluid perturbation, there is currently no mathematical model of HR validated in terms of its predictive capability performance. This paper develops and validates a mathematical model of HR response using data collected from sheep subjects undergoing hemorrhage and fluid infusion. The model proved to be accurate in estimating the HR response to fluid perturbation, where averaged between 21 calibration datasets, the fitting performance showed a normalized root mean square error (NRMSE) of [Formula: see text]. The model was also evaluated in terms of model predictive capability performance via a leave-one-out procedure (21 subjects) and an independent validation dataset (6 subjects). Two different virtual cohort generation tools were used in each validation analysis. The generated envelope of virtual subjects robustly met the defined acceptance criteria, in which [Formula: see text] of the testing datasets presented simulated HR patterns that were within a deviation of 50% from the observed data. In addition, out of 16000 and 18522 simulated subjects for the leave-one-out and independent datasets, the model was able to generate at least one virtual subject that was close to the real subject within an error margin of [Formula: see text] and [Formula: see text] NRMSE, respectively. In conclusion, the model can generate valid virtual HR physiological responses to fluid perturbation and be incorporated into future non-clinical simulated testing setups for assessing PCLC devices intended for fluid resuscitation.

An Efficient Heart Rate Measurement System Using Medical Radar and LSTM Neural Network

This research proposes a noncontact heart rate measurement method using medical radar and artificial intelligence techniques. This technique has a significant role in the design and development of a wireless system that monitors the body’s vital signs. Firstly, based on a signal model describing chest surface movement, we propose a method to create a dataset for the training process using the long-short-term memory model. Secondly, a novel method to extract chest motion from the received radar signal is proposed. Finally, the heart rate will be estimated by using the obtained model and the received motion signal. The performance of the proposed method is evaluated through the root mean square error parameter as well as compared with other methods. Experimental results evaluated according to Bland–Altman achieved an accuracy of 96.67%.

Automated model calibration with parallel MCMC: Applications for a cardiovascular system model

Computational physiological models continue to increase in complexity, however, the task of efficiently calibrating the model to available clinical data remains a significant challenge. One part of this challenge is associated with long calibration times, which present a barrier for the routine application of model-based prediction in clinical practice. Another aspect of this challenge is the limited available data for the unique calibration of complex models. Therefore, to calibrate a patient-specific model, it may be beneficial to verify that task-specific model predictions have acceptable uncertainty, rather than requiring all parameters to be uniquely identified. We have developed a pipeline that reduces the set of fitting parameters to make them structurally identifiable and to improve the efficiency of a subsequent Markov Chain Monte Carlo (MCMC) analysis. MCMC was used to find the optimal parameter values and to determine the confidence interval of a task-specific prediction. This approach was demonstrated on numerical experiments where a lumped parameter model of the cardiovascular system was calibrated to brachial artery cuff pressure, echocardiogram volume measurements, and synthetic cerebral blood flow data that approximates what can be obtained from 4D-flow MRI data. This pipeline provides a cerebral arterial pressure prediction that may be useful for determining the risk of hemorrhagic stroke. For a set of three patients, this pipeline successfully reduced the parameter set of a cardiovascular system model from 12 parameters to 8–10 structurally identifiable parameters. This enabled a significant (>4×) efficiency improvement in determining confidence intervals on predictions of pressure compared to performing a naive MCMC analysis with the full parameter set. This demonstrates the potential that the proposed pipeline has in helping address one of the key challenges preventing clinical application of such models. Additionally, for each patient, the MCMC approach yielded a 95% confidence interval on systolic blood pressure prediction in the middle cerebral artery smaller than ±10 mmHg (±1.3 kPa). The proposed pipeline exploits available high-performance computing parallelism to allow straightforward automation for general models and arbitrary data sets, enabling automated calibration of a parameter set that is specific to the available clinical data with minimal user interaction.

Initial clinical validation of a hybrid in silico—in vitro cardiorespiratory simulator for comprehensive testing of mechanical circulatory support systems

Simulators are expected to assume a prominent role in the process of design—development and testing of cardiovascular medical devices. For this purpose, simulators should capture the complexity of human cardiorespiratory physiology in a realistic way. High fidelity simulations of pathophysiology do not only allow to test the medical device itself, but also to advance practically relevant monitoring and control features while the device acts under realistic conditions. We propose a physiologically controlled cardiorespiratory simulator developed in a mixed in silico-in vitro simulation environment. As inherent to this approach, most of the physiological model complexity is implemented in silico while the in vitro system acts as an interface to connect a medical device. As case scenarios, severe heart failure was modeled, at rest and at exercise and as medical device a left ventricular assist device (LVAD) was connected to the simulator. As initial validation, the simulator output was compared against clinical data from chronic heart failure patients supported by an LVAD, that underwent different levels of exercise tests with concomitant increase in LVAD speed. Simulations were conducted reproducing the same protocol as applied in patients, in terms of exercise intensity and related LVAD speed titration. Results show that the simulator allows to capture the principal parameters of the main adaptative cardiovascular and respiratory processes within the human body occurring from rest to exercise. The simulated functional interaction with the LVAD is comparable to the one clinically observed concerning ventricular unloading, cardiac output, and pump flow. Overall, the proposed simulation system offers a high fidelity in silico-in vitro representation of the human cardiorespiratory pathophysiology. It can be used as a test bench to comprehensively analyze the performance of physically connected medical devices simulating clinically realistic, critical scenarios, thus aiding in the future the development of physiologically responding, patient-adjustable medical devices. Further validation studies will be conducted to assess the performance of the simulator in other pathophysiological conditions.

Computational modeling of orthostatic intolerance for travel to Mars

Astronauts in a microgravity environment will experience significant changes in their cardiopulmonary system. Up until now, there has always been the reassurance that they have real-time contact with experts on Earth. Mars crew however will have gaps in their communication of 20 min or more. In silico experiments are therefore needed to assess fitness to fly for those on future space flights to Mars. In this study, we present an open-source controlled lumped mathematical model of the cardiopulmonary system that is able simulate the short-term adaptations of key hemodynamic parameters to an active stand test after being exposed to microgravity. The presented model is capable of adequately simulating key cardiovascular hemodynamic changes—over a short time frame—during a stand test after prolonged spaceflight under different gravitational conditions and fluid loading conditions. This model can form the basis for further exploration of the ability of the human cardiovascular system to withstand long-duration space flight and life on Mars.

Why Reduced Inspiratory Pressure Could Determine Success of Non-Invasive Ventilation in Acute Hypoxic Respiratory Failure

The magnitude of inspiratory effort relief within the first 2 hours of non-invasive ventilation for hypoxic respiratory failure was shown in a recent exploratory clinical study to be an early and accurate predictor of outcome at 24 hours. We simulated the application of non-invasive ventilation to three patients whose physiological and clinical characteristics match the data in that study. Reductions in inspiratory effort corresponding to reductions of esophageal pressure swing greater than 10 cmH₂O more than halved the values of total lung stress, driving pressure, power and transpulmonary pressure swing. In the absence of significant reductions in inspiratory pressure, multiple indicators of lung injury increased after application of non-invasive ventilation. Clinical Relevance- We show using computer simulation that reduced inspiratory pressure after application of noninvasive ventilation translates directly into large reductions in multiple well-established indicators of lung injury, providing a potential physiological explanation for recent clinical findings.

A model of the pulmonary acinar circulatory system with gas exchange function to explore the influence of alveolar diameter

Lung diseases such as acute respiratory distress syndrome affect the patient's lung compliance, which in turn affects the ability of gas exchange. Changes in alveolar diameter relate to local lung compliance. How alveolar diameter affects gas exchange, particularly oxygen concentrations in alveolar capillaries, is a topic of concern for researchers, and can be studied using mathematical models. The level of small-scale mathematical models of the pulmonary circulatory system was the alveolar capillaries, but existing models do not consider the gas-exchange function and fail to reflect the influence of alveolar diameter. Therefore, we proposed a pulmonary acinar capillary model with gas exchange function, and most importantly, introduced alveolar diameter into the model, to analyze the effect of alveolar diameter on the gas exchange function of the pulmonary acini. The model was tested by three respiratory function simulation experiments. According to the simulation results of changing diameter, we found that the alveolar diameter mainly affects the alveolar gas exchange function of lung acinar inlets and the middle section compared with the peripheral section.

Modeling Mechanical Ventilation In Silico-Potential and Pitfalls

Computer simulation offers a fresh approach to traditional medical research that is particularly well suited to investigating issues related to mechanical ventilation. Patients receiving mechanical ventilation are routinely monitored in great detail, providing extensive high-quality data-streams for model design and configuration. Models based on such data can incorporate very complex system dynamics that can be validated against patient responses for use as investigational surrogates. Crucially, simulation offers the potential to "look inside" the patient, allowing unimpeded access to all variables of interest. In contrast to trials on both animal models and human patients, in silico models are completely configurable and reproducible; for example, different ventilator settings can be applied to an identical virtual patient, or the same settings applied to different patients, to understand their mode of action and quantitatively compare their effectiveness. Here, we review progress on the mathematical modeling and computer simulation of human anatomy, physiology, and pathophysiology in the context of mechanical ventilation, with an emphasis on the clinical applications of this approach in various disease states. We present new results highlighting the link between model complexity and predictive capability, using data on the responses of individual patients with acute respiratory distress syndrome to changes in multiple ventilator settings. The current limitations and potential of in silico modeling are discussed from a clinical perspective, and future challenges and research directions highlighted.

Contactless radar-based breathing monitoring of premature infants in the neonatal intensive care unit

Vital sign monitoring systems are essential in the care of hospitalized neonates. Due to the immaturity of their organs and immune system, premature infants require continuous monitoring of their vital parameters and sensors need to be directly attached to their fragile skin. Besides mobility restrictions and stress, these sensors often cause skin irritation and may lead to pressure necrosis. In this work, we show that a contactless radar-based approach is viable for breathing monitoring in the Neonatal intensive care unit (NICU). For the first time, different scenarios common to the NICU daily routine are investigated, and the challenges of monitoring in a real clinical setup are addressed through different contributions in the signal processing framework. Rather than just discarding measurements under strong interference, we present a novel random body movement mitigation technique based on the time-frequency decomposition of the recovered signal. In addition, we propose a simple and accurate frequency estimator which explores the harmonic structure of the breathing signal. As a result, the proposed radar-based solution is able to provide reliable breathing frequency estimation, which is close to the reference cabled device values most of the time. Our findings shed light on the strengths and limitations of this technology and lay the foundation for future studies toward a completely contactless solution for vital signs monitoring.

OpenModelica-based virtual simulator for the cardiovascular and respiratory physiology of a neonate

There is a lack of medical simulation tools that can be understood and used, at the same time, by researchers, teachers, clinicians and students. Regarding this issue, in this work we report a virtual simulator (developed in OpenModelica) that allow to experiment with the fundamental variables of the cardiovascular and respiratory system of a neonate. We extended a long-tested lumped parameter model that represents the cardiovascular and respiratory physiology of a neonate. From this model, we implemented a physiological simulator using Modelica. The fidelity and versatility of the reported simulator were evaluated by simulating seven physiological scenarios: two of them representing a healthy infant (newborn and 6-months old) and five representing newborns affected by different heart diseases. The simulator properly and consistently represented the quantitative and qualitative behaviour of the seven physiological scenarios when compared with existing clinical data. Results allow us to consider the simulator reported here as a reliable tool for researching, training and learning. The advanced modelling features of Modelica and the friendly graphical user interface of OpenModelica make the simulator suitable to be used by a broad community of users. Furthermore, it can be easily extended to simulate many clinical scenarios.

The effect of apnea length on vital parameters in apnea of prematurity - Hybrid observations from clinical data and simulation in a mathematical model

Apnea of prematurity (AOP) is a critical condition for preterm infants which can lead to several adverse outcomes. Despite its relevance, mechanisms underlying AOP are still unclear. In this work we aimed at improving the understanding of AOP and its physiologic responses by analyzing and comparing characteristics of real infant data and model-based simulations of AOP. We implemented an existing algorithm to extract apnea events originating from the central nervous system from a population of 26 premature infants (1248 h of data in total) and investigated oxygen saturation (SpO₂) and heart rate (HR) of the infants around these events. We then extended a previously developed cardio-vascular model to include the lung mechanics and gas exchange. After simulating the steady state of a preterm infant, which successfully replicated results described in previous literature studies, the extended model was used to simulate apneas with different lengths caused by a stop in respiratory muscles. Apneas identified by the algorithm and simulated by the model showed several similarities, including a far deeper decrease in SpO₂, with the minimum reached later in time, in case of longer apneas. Results also showed some differences, either due to how measures are performed in clinical practice in our neonatal intensive care unit (e.g. delayed detection of decline in SpO₂ after apnea onset due to signal averaging) or to the limited number of very long apneas (≥80 s) identified in our dataset.

MATHEMATICAL MODELS OF HUMAN RESPIRATORY AND BLOOD CIRCULATORY SYSTEMS

Aim. To analyze modern approaches to mathematical modeling of human respiratory and blood circulatory systems. Methods. Comprehensive review of scientific literature sources extracted from domestic and international resources databases. Results. Historical information and modern data concerning mathematical modeling of human functional respiratory and blood circulatory systems were summarized and analyzed in present ¬review; current trends in approaches to the construction of these models were revealed. Conclusions. Currently, two main approaches to the mathematical modeling of respiratory and blood circulatory systems exist. One of them is the construction of models of the mechanics of respiration and blood circulation. They are based on the models of mechanics of solid deformable body, thermomechanics, hydromechanics, and continuum mechanics. This approach uses complex mathematical apparatus, including Navier-Stokes equation, which makes it possible to obtain a number of theoretical results, but it is hardly usable for real problems solutions at present time. The second approach is based on the model of F. Grodins, who represented the process of breathing as a controlled dynamic system, described by ordinary differential equations, in which the process control is carried out according to the feedback principle. There is a significant number of modifications of this model, which made it possible to simulate various disturbing influences, such as physical activity, hypoxia and hyperemia, and to predict parameters characterizing functional respiratory system under these disturbing influences.

Two heads are better than one: current landscape of integrating QSP and machine learning : An ISoP QSP SIG white paper by the working group on the integration of quantitative systems pharmacology and machine learning

Quantitative systems pharmacology (QSP) modeling is applied to address essential questions in drug development, such as the mechanism of action of a therapeutic agent and the progression of disease. Meanwhile, machine learning (ML) approaches also contribute to answering these questions via the analysis of multi-layer 'omics' data such as gene expression, proteomics, metabolomics, and high-throughput imaging. Furthermore, ML approaches can also be applied to aspects of QSP modeling. Both approaches are powerful tools and there is considerable interest in integrating QSP modeling and ML. So far, a few successful implementations have been carried out from which we have learned about how each approach can overcome unique limitations of the other. The QSP + ML working group of the International Society of Pharmacometrics QSP Special Interest Group was convened in September, 2019 to identify and begin realizing new opportunities in QSP and ML integration. The working group, which comprises 21 members representing 18 academic and industry organizations, has identified four categories of current research activity which will be described herein together with case studies of applications to drug development decision making. The working group also concluded that the integration of QSP and ML is still in its early stages of moving from evaluating available technical tools to building case studies. This paper reports on this fast-moving field and serves as a foundation for future codification of best practices.

Treatment of Cheyne-Stokes Respiration in Heart Failure with Adaptive Servo-Ventilation: An Integrative Model

The SERVE-HF (Treatment of Predominant Central Sleep Apnea by Adaptive Servo Ventilation in Patients with Heart Failure) multicenter trial found a small but significant increase in all-cause and cardiovascular mortality in patients assigned to adaptive servo-ventilation (ASV) versus guideline-based medical treatment. To better understand the physiological underpinnings of this clinical outcome, we employ an integrative computer model to simulate congestive heart failure with Cheyne-Stokes respiration (CHF-CSR) in subjects with a broad spectrum of underlying pathogenetic mechanisms, as well as to determine the in silico changes in cardiopulmonary and autonomic physiology resulting from ASV. Our simulation results demonstrate that while the elimination of CSR through ASV can partially restore cardiorespiratory and autonomic physiology toward normality in the vast majority of CHF phenotypes, the degree of restoration can be highly variable, depending on the combination of CHF mechanisms in play. The group with the lowest left ventricular ejection fraction (LVEF) appears to be most vulnerable to the potentially adverse effects of ASV, but the level of pulmonary capillary wedge pressure (PCWP) plays an important role in determining the nature of these effects.

Using a Human Circulation Mathematical Model to Simulate the Effects of Hemodialysis and Therapeutic Hypothermia

Background: We developed a hemodynamic mathematical model of human circulation coupled to a virtual hemodialyzer. The model was used to explore mechanisms underlying our clinical observations involving hemodialysis. Methods: The model consists of whole body human circulation, baroreflex feedback control, and a hemodialyzer. Four model populations encompassing baseline, dialysed, therapeutic hypothermia treated, and simultaneous dialysed with hypothermia were generated. In all populations atrial fibrillation and renal failure as co-morbidities, and exercise as a treatment were simulated. Clinically relevant measurables were used to quantify the effects of each in silico experiment. Sensitivity analysis was used to uncover the most relevant parameters. Results: Relative to baseline, the modelled dialysis increased the population mean diastolic blood pressure by 5%, large vessel wall shear stress by 6%, and heart rate by 20%. Therapeutic hypothermia increased systolic blood pressure by 3%, reduced large vessel shear stress by 15%, and did not affect heart rate. Therapeutic hypothermia reduced wall shear stress by 15% in the aorta and 6% in the kidneys, suggesting a potential anti-inflammatory benefit. Therapeutic hypothermia reduced cardiac output under atrial fibrillation by 12% and under renal failure by 20%. Therapeutic hypothermia and exercise did not affect dialyser function, but increased water removal by approximately 40%. Conclusions: This study illuminates some mechanisms of the action of therapeutic hypothermia. It also suggests clinical measurables that may be used as surrogates to diagnose underlying diseases such as atrial fibrillation.

Effect of Ventricular Elasticity Due to Congenital Hydrocephalus

Cerebrospinal fluid (CSF) is a symmetric flow transport that surrounds brain and central nervous system (CNS). Congenital hydrocephalusis is an asymmetric and unusual cerebrospinal fluid flow during fetal development. This dumping impact enhances the elasticity over the ventricle wall. Henceforth, compression change influences the force of brain tissues. This paper presents a mathematical model to establish the effects of ventricular elasticity through a porous channel. The current model is good enough for immediate use by a neurosurgeon. The mathematical model is likely to be a powerful tool for the better treatment of hydrocephalus and other brain biomechanics. The non-linear dimensionless governing equations are solved using a perturbation technique, and the outcome is portrayed graphically with the aid of MATLAB.

Identification of an optimal CPR chest compression protocol

In this study, we used a high-fidelity integrated computational model of the respiratory and cardiovascular systems to investigate cardiopulmonary resuscitation (CPR) after cardiac arrest in a virtual healthy subject. For the purpose of this work, a newly developed thoracic model has been integrated to the current model, to study the influence of external chest compressions upon the arrested circulation during CPR. We evaluated the chest compression (CC) parameters, namely, end compression force, compression rate, and duty cycle to optimize the coronary perfusion pressure and the systolic blood pressure, using a genetic algorithm. While the sternal displacement associated with the CC force agreed with the ERC guidelines, the CC rate and duty cycle were respectively higher and lower than the ones recommended by the ERC guidelines. The effect of these CC parameters on cardiac output (CO) were also assessed. The end compression force was the parameter with the largest impact on CO, while the compression rate and duty cycle scarcely influence it.Relevance- Our results may aid in understanding the underlying pathophysiology of cardiac arrest and help guide research into the refinement of CPR strategies, without sacrificing animals or conducting clinical trials, which are difficult to undertake in crisis scenarios.

Integrated cardiorespiratory system model with short timescale control mechanisms

A compartmental model of the cardiorespiratory system featuring pulsatile blood flow and gas transport, as well as closed loop mechanisms of cardiorespiratory regulation is presented. Short timescale regulatory action includes baroreflex, peripheral and central chemoreflex feedback. The cardiorespiratory model is composed by compartments to describe blood flow and gas exchange in the major systemic and pulmonic regions. The control systems include formulations to afferent activity of arterial baroreceptor and peripheral and central chemoreceptors. Simulations described here include situations of hypoxia, hypercapnia, and hemorrhage. The overall responses of our simulations agree with physiological (experimental) and theoretical data. Our results suggest that the present model could be used to further understand the interplay among major regulatory mechanisms in the functioning of the cardiovascular and respiratory systems in cases of normal and abnormal physiological conditions.

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.

Total Effective Vascular Compliance of a Global Mathematical Model for the Cardiovascular System

In this work, we determined the total effective vascular compliance of a global closed-loop model for the cardiovascular system by performing an infusion test of 500 mL of blood in four minutes. Our mathematical model includes a network of arteries and veins where blood flow is described by means of a one-dimensional nonlinear hyperbolic PDE system and zero-dimensional models for other cardiovascular compartments. Some mathematical modifications were introduced to better capture the physiology of the infusion test: (1) a physiological distribution of vascular compliance and total blood volume was implemented, (2) a nonlinear representation of venous resistances and compliances was introduced, and (3) main regulatory mechanisms triggered by the infusion test where incorporated into the model. By means of presented in silico experiment, we show that effective total vascular compliance is the result of the interaction between the assigned constant physical vascular compliance and the capacity of the cardiovascular system to adapt to new situations via regulatory mechanisms.

A mathematical model of cardiovascular dynamics for the diagnosis and prognosis of hemorrhagic shock

A variety of mathematical models of the cardiovascular system have been suggested over several years in order to describe the time-course of a series of physiological variables (i.e. heart rate, cardiac output, arterial pressure) relevant for the compensation mechanisms to perturbations, such as severe haemorrhage. The current study provides a simple but realistic mathematical description of cardiovascular dynamics that may be useful in the assessment and prognosis of hemorrhagic shock. The present work proposes a first version of a differential-algebraic equations model, the model dynamical ODE model for haemorrhage (dODEg). The model consists of 10 differential and 14 algebraic equations, incorporating 61 model parameters. This model is capable of replicating the changes in heart rate, mean arterial pressure and cardiac output after the onset of bleeding observed in four experimental animal preparations and fits well to the experimental data. By predicting the time-course of the physiological response after haemorrhage, the dODEg model presented here may be of significant value for the quantitative assessment of conventional or novel therapeutic regimens. The model may be applied to the prediction of survivability and to the determination of the urgency of evacuation towards definitive surgical treatment in the operational setting.

High risk of patient self-inflicted lung injury in COVID-19 with frequently encountered spontaneous breathing patterns: a computational modelling study

BACKGROUND

There is on-going controversy regarding the potential for increased respiratory effort to generate patient self-inflicted lung injury (P-SILI) in spontaneously breathing patients with COVID-19 acute hypoxaemic respiratory failure. However, direct clinical evidence linking increased inspiratory effort to lung injury is scarce. We adapted a computational simulator of cardiopulmonary pathophysiology to quantify the mechanical forces that could lead to P-SILI at different levels of respiratory effort. In accordance with recent data, the simulator parameters were manually adjusted to generate a population of 10 patients that recapitulate clinical features exhibited by certain COVID-19 patients, i.e., severe hypoxaemia combined with relatively well-preserved lung mechanics, being treated with supplemental oxygen.

RESULTS

Simulations were conducted at tidal volumes (VT) and respiratory rates (RR) of 7 ml/kg and 14 breaths/min (representing normal respiratory effort) and at VT/RR of 7/20, 7/30, 10/14, 10/20 and 10/30 ml/kg / breaths/min. While oxygenation improved with higher respiratory efforts, significant increases in multiple indicators of the potential for lung injury were observed at all higher VT/RR combinations tested. Pleural pressure swing increased from 12.0 ± 0.3 cmH2O at baseline to 33.8 ± 0.4 cmH2O at VT/RR of 7 ml/kg/30 breaths/min and to 46.2 ± 0.5 cmH2O at 10 ml/kg/30 breaths/min. Transpulmonary pressure swing increased from 4.7 ± 0.1 cmH2O at baseline to 17.9 ± 0.3 cmH2O at VT/RR of 7 ml/kg/30 breaths/min and to 24.2 ± 0.3 cmH2O at 10 ml/kg/30 breaths/min. Total lung strain increased from 0.29 ± 0.006 at baseline to 0.65 ± 0.016 at 10 ml/kg/30 breaths/min. Mechanical power increased from 1.6 ± 0.1 J/min at baseline to 12.9 ± 0.2 J/min at VT/RR of 7 ml/kg/30 breaths/min, and to 24.9 ± 0.3 J/min at 10 ml/kg/30 breaths/min. Driving pressure increased from 7.7 ± 0.2 cmH2O at baseline to 19.6 ± 0.2 cmH2O at VT/RR of 7 ml/kg/30 breaths/min, and to 26.9 ± 0.3 cmH2O at 10 ml/kg/30 breaths/min.

CONCLUSIONS

Our results suggest that the forces generated by increased inspiratory effort commonly seen in COVID-19 acute hypoxaemic respiratory failure are comparable with those that have been associated with ventilator-induced lung injury during mechanical ventilation. Respiratory efforts in these patients should be carefully monitored and controlled to minimise the risk of lung injury.

High Accuracy Heartbeat Detection from CW-Doppler Radar Using Singular Value Decomposition and Matched Filter

Heart rate measurement using a continuous wave Doppler radar sensor (CW-DRS) has been applied to cases where non-contact detection is required, such as the monitoring of vital signs in home healthcare. However, as a CW-DRS measures the speed of movement of the chest surface, which comprises cardiac and respiratory signals by body motion, extracting cardiac information from the superimposed signal is difficult. Therefore, it is challenging to extract cardiac information from superimposed signals. Herein, we propose a novel method based on a matched filter to solve this problem. The method comprises two processes: adaptive generation of a template via singular value decomposition of a trajectory matrix formed from the measurement signals, and reconstruction by convolution of the generated template and measurement signals. The method is validated using a dataset obtained in two different experiments, i.e., experiments involving supine and seated subject postures. Absolute errors in heart rate and standard deviation of heartbeat interval with references were calculated as 1.93±1.76bpm and 57.0±28.1s for the lying posture, and 9.72±7.86bpm and 81.3±24.3s for the sitting posture.

A Client-Server and Web-Based Graphical User Interface Design for the Mathematical Model of Cardiovascular-Respiratory System

The prediction of cardiac conditions can be done through comparison and analysis of parameters transformed into mathematical model equations. This paper aims to present the design of a web-based graphical user interface of mathematical model of cardiovascular-respiratory system (ICRSMM) as an appropriate displaying tool. The designed system offers an easy way of recording and storing parameters in a database. Those parameters are computerized to generate automatic results in a graphic representation, which is an effective way used in medicine to allow physicians, nurses, and other experienced health personnel to analyze and discuss results. The designed solution provides an adequate and friendly environment that eases the task of recording the results in a graphic representation. This gives a clear picture of analysis to determine a healthy or unhealthy cardiovascular-respiratory system of a person exercising. However, such a complex design solution comes in to put an accent of consideration to an area of research that still needs more discoveries and exploration.

Modeling the cardiac response to hemodynamic changes associated with COVID-19: a computational study

Emerging studies address how COVID-19 infection can impact the human cardiovascular system. This relates particularly to the development of myocardial injury, acute coronary syndrome, myocarditis, arrhythmia, and heart failure. Prospective treatment approach is advised for these patients. To study the interplay between local changes (reduced contractility), global variables (peripheral resistances, heart rate) and the cardiac function, we considered a lumped parameters computational model of the cardiovascular system and a three-dimensional multiphysics model of cardiac electromechanics. Our mathematical model allows to simulate the systemic and pulmonary circulations, the four cardiac valves and the four heart chambers, through equations describing the underlying physical processes. By the assessment of conventionally relevant parameters of cardiac function obtained through our numerical simulations, we propose a computational model to effectively reveal the interactions between the cardiac and pulmonary functions in virtual subjects with normal and impaired cardiac function at baseline affected by mild or severe COVID-19.

Circadian Rhythm of Blood Pressure of Dipper and Non-dipper Patients With Essential Hypertension: A Mathematical Modeling Approach

Blood pressure in humans presents a circadian variation profile with a morning increase, a small postprandial valley, and a deeper descent during night-time rest. Under certain conditions, the nocturnal decline in blood pressure can be reduced or even reversed (non-dipper), which is related to a significantly worse prognosis than a normal fall pattern (dipper). Despite several advances in recent years, our understanding of blood pressure's temporal structure, its sources and mechanisms is far from complete. In this work, we developed an ordinary differential equation-based mathematical model capable of capturing the circadian rhythm of blood pressure in dipper and non-dipper patients with arterial hypertension. The model was calibrated by means of global optimization, using 24-h data of systolic and diastolic blood pressure, physical activity, heart rate, blood glucose and norepinephrine, obtained from the literature. After fitting the model, the mean of the normalized error for each data point was <0.2%, and confidence intervals indicate that all parameters were identifiable. Sensitivity analysis allowed identifying the most relevant parameters and therefore inferring the most important blood pressure regulatory mechanisms involved in the non-dipper status, namely, increase in sympathetic over parasympathetic nervous tone, lower influence of physical activity on heart rate and greater influence of physical activity and glucose on the systemic vascular resistance. In summary, this model allows explaining the circadian rhythm of blood pressure and deepening the understanding of the underlying mechanisms and interactions integrating the results of previous works.

An integrated mathematical model of the cardiovascular and respiratory response to exercise: model-building and comparison with reported models

The use of physiological models in medicine allows the evaluation of new hypotheses, development of diagnosis and clinical treatment applications, and development of training and medical education tools, as well as medical device design. Although several mathematical models of physiological systems have been presented in the literature, few of them are able to predict the human cardiorespiratory response under physical exercise stimulus adequately. This paper aims to present the building and comparison of an integrated cardiorespiratory model focused on the prediction of the healthy human response under rest and aerobic exercise. The model comprises cardiovascular circulation, respiratory mechanics, and gas exchange system, as well as cardiovascular and respiratory controllers. Every system is based on previously reported physiological models and incorporates reported mechanisms related to the aerobic exercise dynamics. Experimental data of 30 healthy male volunteers undergoing a cardiopulmonary exercise test and simulated data from two of the most current and complete cardiorespiratory models were used to evaluate the performance of the presented model. Experimental design, processing, and exploratory analysis are described in detail. The simulation results were compared against the experimental data in steady state and in transient regime. The predictions of the proposed model closely mimic the experimental data, showing in overall the lowest prediction error (10.35%), the lowest settling times for cardiovascular and respiratory variables, and in general the fastest and similar responses in transient regime. These results suggest that the proposed model is suitable to predict the cardiorespiratory response of healthy adult humans under rest and aerobic exercise conditions.NEW & NOTEWORTHY This paper presents a new cardiorespiratory model focused on the prediction of the healthy human response under rest and aerobic dynamic exercise conditions. Simulation results of cardiorespiratory variables are compared against experimental data and two of the most current and complete cardiorespiratory models.

Heart-Lung Interactions During Mechanical Ventilation: Analysis via a Cardiopulmonary Simulation Model

Heart-lung interaction mechanisms are generally not well understood. Mechanical ventilation, for example, accentuates such interactions and could compromise cardiac activity. Thereby, assessment of ventilation-induced changes in cardiac function is considered an unmet clinical need. We believe that mathematical models of the human cardiopulmonary system can provide invaluable insights into such cardiorespiratory interactions. In this article, we aim to use a mathematical model to explain heart-lung interaction phenomena and provide physiologic hypotheses to certain contradictory experimental observations during mechanical ventilation. To accomplish this task, we highlight three model components that play a crucial role in heart-lung interactions: 1) pericardial membrane, 2) interventricular septum, and 3) pulmonary circulation that enables pulmonary capillary compression due to lung inflation. Evaluation of the model’s response under simulated ventilation scenarios shows good agreement with experimental data from the literature. A sensitivity analysis is also presented to evaluate the relative impact of the model’s highlighted components on the cyclic ventilation-induced changes in cardiac function.

Alveolar Tissue Fiber and Surfactant Effects on Lung Mechanics—Model Development and Validation on ARDS and IPF Patients

Goal: Alveolar compliance is a main determinant of lung airflow. The compliance of the alveoli is a function of their tissue fiber elasticity, fiber volume, and surface tension. The compliance varies during respiration because of the nonlinear nature of fiber elasticity and the time-varying surface tension coating the alveoli. Respiratory conditions, like acute respiratory distress syndrome (ARDS) and idiopathic pulmonary fibrosis (IPF) affect fiber elasticity, fiber volume and surface tension. In this paper, we study the alveolar tissue fibers and surface tension effects on lung mechanics. Methods: To better understand the lungs, we developed a physiology-based mathematical model to 1) describe the effect of tissue fiber elasticity, fiber volume and surface tension on alveolar compliance, and 2) the effect of time-varying alveolar compliance on lung mechanics for healthy, ARDS and IPF conditions. Results: We first present the model sensitivity analysis to show the effects of model parameters on the lung mechanics variables. Then, we perform model simulation and validate on healthy non-ventilated subjects and ventilated ARDS or IPF patients. Finally, we assess the robustness and stability of this dynamic system. Conclusions: We developed a mathematical model of the lung mechanics comprising alveolar tissue and surfactant properties that generates reasonable lung pressures and volumes compared to healthy, ARDS, and IPF patient data.

Advanced mechanical ventilation modes: design and computer simulations

In this paper, three different advanced mechanical ventilation modes, pressure regulated volume control ventilation (PRVC), proportional assist ventilation (PAV), and adaptive support ventilation (ASV) are designed and simulated on the computer via MATLAB/Simulink. In the algorithms of advanced ventilation modes, a closed-loop control structure is used and recursive least squares method is considered for the estimation of respiratory mechanics. The designed algorithms are then applied to the human respiratory system model for the active and/or passive patient cases. Simulation results show that such algorithms can be designed and simulated on the computer successfully. In addition, the simulation environment helps us to understand the working principles of the advanced modes and to see the results such as ventilator waveforms, the effect of the parameter changes. Moreover, it also allows us to improve and test the algorithms and strategies quickly and efficiently.

In silico study of airway/lung mechanics in normal human breathing

The airway/lung mechanics is usually represented with nonlinear 0-D models based on a pneumatic-electrical analogy. The aim of this work is to provide a detailed description of the human respiratory mechanics in healthy and diseased conditions. The model used for this purpose employs some known constitutive functions of the main components of the respiratory system. We give a detailed mathematical description of these functions and subsequently derive additional key ones. We are interested not only in the main output such as airflow at the mouth or alveolar pressure and volume, but also in other quantities such as resistance and pressure drop across each element of the system and even recoil and compliance of the chest wall. Pathological conditions are simulated by altering the parameters of the constitutive functions. Results show that increased upper airway resistance induces airflow reduction with concomitant narrowing of volume and pressure ranges without affecting lung compliance. Instead, increased elastic recoil leads to low volumes and decreased lung compliance. The model could be used in the study of the interaction between respiratory and cardiovascular systems in pathophysiological conditions.