Modelling in the study of interaction of Hemopump device and artificial ventilation

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.

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.

CARDIOSIM©: The First Italian Software Platform for Simulation of the Cardiovascular System and Mechanical Circulatory and Ventilatory Support

This review is devoted to presenting the history of the CARDIOSIM^© software simulator platform, which was developed in Italy to simulate the human cardiovascular and respiratory systems. The first version of CARDIOSIM^© was developed at the Institute of Biomedical Technologies of the National Research Council in Rome. The first platform version published in 1991 ran on a PC with a disk operating system (MS-DOS) and was developed using the Turbo Basic language. The latest version runs on PC with Microsoft Windows 10 operating system; it is implemented in Visual Basic and C++ languages. The platform has a modular structure consisting of seven different general sections, which can be assembled to reproduce the most important pathophysiological conditions. One or more zero-dimensional (0-D) modules have been implemented in the platform for each section. The different modules can be assembled to reproduce part or the whole circulation according to Starling’s law of the heart. Different mechanical ventilatory and circulatory devices have been implemented in the platform, including thoracic artificial lungs, ECMO, IABPs, pulsatile and continuous right and left ventricular assist devices, biventricular pacemakers and biventricular assist devices. CARDIOSIM^© is used in clinical and educational environments.

Mock circulatory loops used for testing cardiac assist devices: A review of computational and experimental models

Heart failure is a major health risk, and with limited availability of donor organs, there is an increasing need for developing cardiac assist devices (CADs). Mock circulatory loops (MCL) are an important in-vitro test platform for CAD's performance assessment and optimisation. The MCL is a lumped parameter model constructed out of hydraulic and mechanical components aiming to simulate the native cardiovascular system (CVS) as closely as possible. Further development merged MCLs and numerical circulatory models to improve flexibility and accuracy of the system; commonly known as hybrid MCLs. A total of 128 MCLs were identified in a literature research until 25 September 2020. It was found that the complexity of the MCLs rose over the years, recent MCLs are not only capable of mimicking the healthy and pathological conditions, but also implemented cerebral, renal and coronary circulations and autoregulatory responses. Moreover, the development of anatomical models made flow visualisation studies possible. Mechanical MCLs showed excellent controllability and repeatability, however, often the CVS was overly simplified or lacked autoregulatory responses. In numerical MCLs the CVS is represented with a higher order of lumped parameters compared to mechanical test rigs, however, complex physiological aspects are often simplified. In hybrid MCLs complex physiological aspects are implemented in the hydraulic part of the system, whilst the numerical model represents parts of the CVS that are too difficult to represent by mechanical components per se. This review aims to describe the advances, limitations and future directions of the three types of MCLs.

A model-based analysis of autonomic nervous function in response to the Valsalva maneuver

The Valsalva maneuver (VM) is a diagnostic protocol examining sympathetic and parasympathetic activity in patients with autonomic dysfunction (AD) impacting cardiovascular control. Because direct measurement of these signals is costly and invasive, AD is typically assessed indirectly by analyzing heart rate and blood pressure response patterns. This study introduces a mathematical model that can predict sympathetic and parasympathetic dynamics. Our model-based analysis includes two control mechanisms: respiratory sinus arrhythmia (RSA) and the baroreceptor reflex (baroreflex). The RSA submodel integrates an electrocardiogram-derived respiratory signal with intrathoracic pressure, and the baroreflex submodel differentiates aortic and carotid baroreceptor regions. Patient-specific afferent and efferent signals are determined for 34 control subjects and 5 AD patients, estimating parameters fitting the model output to heart rate data. Results show that inclusion of RSA and distinguishing aortic/carotid regions are necessary to model the heart rate response to the VM. Comparing control subjects to patients shows that RSA and baroreflex responses are significantly diminished. This study compares estimated parameter values from the model-based predictions to indices used in clinical practice. Three indices are computed to determine adrenergic function from the slope of the systolic blood pressure in phase II [α (a new index)], the baroreceptor sensitivity (β), and the Valsalva ratio (γ). Results show that these indices can distinguish between normal and abnormal states, but model-based analysis is needed to differentiate pathological signals. In summary, the model simulates various VM responses and, by combining indices and model predictions, we study the pathologies for 5 AD patients.NEW & NOTEWORTHY We introduce a patient-specific model analyzing heart rate and blood pressure during a Valsalva maneuver (VM). The model predicts autonomic function incorporating the baroreflex and respiratory sinus arrhythmia (RSA) control mechanisms. We introduce a novel index (α) characterizing sympathetic activity, which can distinguish control and abnormal patients. However, we assert that modeling and parameter estimation are necessary to explain pathologies. Finally, we show that aortic baroreceptors contribute significantly to the VM and RSA affects early VM.

How can LVAD support influence ventricular energetics parameters in advanced heart failure patients? A retrospective study

BACKGROUND AND OBJECTIVE

Here we present a retrospective analysis of six heart failure patients previously discussed at a multidisciplinary team meeting. Only three out of six patients underwent LVAD insertion as the most appropriate management option.

METHODS

We sought to reproduce the baseline conditions of these patients on hospital admission using our cardiovascular software simulator (CARDIOSIM^©). Subsequently, we simulated the effects of LVAD support and drug administration on left and right ventricular energetics parameters. LVAD assistance was delivered by CARDIOSIM^© based on the module reproducing the behaviour of the Berlin Heart INCOR pump.

RESULTS

The results of our simulations were in agreement with the multidisciplinary team meeting outcome. The analysis of ventricular energetics parameters based on external work and pressure volume area confirmed LVAD support as a beneficial therapeutic option for the three patients considered eligible for this type of treatment. The effects induced by LVAD support and drugs administration showed specific patterns between the two groups of patients.

CONCLUSION

A quantitative approach with the ability to predict outcome during patient's assessment may well be an aid and not a substitute for clinical decision-making.

Simulation as a preoperative planning approach in advanced heart failure patients. A retrospective clinical analysis

BACKGROUND

Modelling and simulation may become clinically applicable tools for detailed evaluation of the cardiovascular system and clinical decision-making to guide therapeutic intervention. Models based on pressure-volume relationship and zero-dimensional representation of the cardiovascular system may be a suitable choice given their simplicity and versatility. This approach has great potential for application in heart failure where the impact of left ventricular assist devices has played a significant role as a bridge to transplant and more recently as a long-term solution for non eligible candidates.

RESULTS

We sought to investigate the value of simulation in the context of three heart failure patients with a view to predict or guide further management. CARDIOSIM^© was the software used for this purpose. The study was based on retrospective analysis of haemodynamic data previously discussed at a multidisciplinary meeting. The outcome of the simulations addressed the value of a more quantitative approach in the clinical decision process.

CONCLUSIONS

Although previous experience, co-morbidities and the risk of potentially fatal complications play a role in clinical decision-making, patient-specific modelling may become a daily approach for selection and optimisation of device-based treatment for heart failure patients. Willingness to adopt this integrated approach may be the key to further progress.

Lung assist devices influence cardio-energetic parameters: Numerical simulation study

We aim at an analysis of the effects mechanical ventilators (MVs) and thoracic artificial lungs (TALs) will have on the cardiovascular system, especially on important quantities, such as left and right ventricular external work (EW), pressure-volume area (PVA) and cardiac mechanical efficiency (CME). Our analyses are based on simulation studies which were carried out by using our CARDIOSIM(©) software simulator. At first, we carried out simulation studies of patients undergoing mechanical ventilation (MV) without a thoracic artificial lung (TAL). Subsequently, we conducted simulation studies of patients who had been provided with a TAL, but did not undergo MV. We aimed at describing the patient's physiological characteristics and their variations with time, such as EW, PVA, CME, cardiac output (CO) and mean pulmonary arterial/venous pressure (PAP/PVP). We were starting with a simulation run under well-defined initial conditions which was followed by simulation runs for a wide range of mean intrathoracic pressure settings. Our simulations of MV without TAL showed that for mean intrathoracic pressure settings from negative (-4 mmHg) to positive (+5 mmHg) values, the left and right ventricular EW and PVA, right ventricular CME and CO decreased, whereas left ventricular CME and the PAP increased. The simulation studies of patients with a TAL, comprised all the usual TAL arrangements, viz. configurations "in series" and in parallel with the natural lung and, moreover, hybrid configurations. The main objective of the simulation studies was, as before, the assessment of the hemodynamic response to the application of a TAL. We could for instance show that, in case of an "in series" configuration, a reduction (an increase) in left (right) ventricular EW and PVA values occurred, whereas the best performance in terms of CO can be achieved in the case of an in parallel configuration.

Interactive simulator for e-Learning environments: a teaching software for health care professionals

There is an established tradition of cardiovascular simulation tools, but the application of this kind of technology in the e-Learning arena is a novel approach. This paper presents an e-Learning environment aimed at teaching the interaction of cardiovascular and lung systems to health-care professionals. Heart-lung interaction must be analyzed while assisting patients with severe respiratory problems or with heart failure in intensive care unit. Such patients can be assisted by mechanical ventilatory assistance or by thoracic artificial lung.

“In silico” cardiovascular simulator was experimented during a training course given to graduate students of the School of Specialization in Cardiology at ‘Sapienza’ University in Rome.

The training course employed CARDIOSIM^©: a numerical simulator of the cardiovascular system. Such simulator is able to reproduce pathophysiological conditions of patients affected by cardiovascular and/or lung disease. In order to study the interactions among the cardiovascular system, the natural lung and the thoracic artificial lung (TAL), the numerical model of this device has been implemented. After having reproduced a patient’s pathological condition, TAL model was applied in parallel and hybrid model during the training course.

Results obtained during the training course show that TAL parallel assistance reduces right ventricular end systolic (diastolic) volume, but increases left ventricular end systolic (diastolic) volume. The percentage changes induced by hybrid TAL assistance on haemodynamic variables are lower than those produced by parallel assistance. Only in the case of the mean pulmonary arterial pressure, there is a percentage reduction which, in case of hybrid assistance, is greater (about 40%) than in case of parallel assistance (20-30%).

At the end of the course, a short questionnaire was submitted to students in order to assess the quality of the course. The feedback obtained was positive, showing good results with respect to the degree of students’ learning and the ease of use of the software simulator.

Mechanical ventilation and thoracic artificial lung assistance during mechanical circulatory support with PUCA pump: in silico study

Patients assisted with left ventricular assist device (LVAD) may require prolonged mechanical ventilatory assistance secondary to postoperative respiratory failure. The goal of this work is the study of the interdependent effects LVAD like pulsatile catheter (PUCA) pump and mechanical ventilatory support or thoracic artificial lung (TAL), by the hemodynamic point of view, using a numerical simulator of the human cardiovascular system. In the simulator, different circulatory sections are described using lumped parameter models. Lumped parameter models have been designed to describe the hydrodynamic behavior of both PUCA pump and thoracic artificial lung. Ventricular behavior atrial and septum functions were reproduced using variable elastance model. Starting from simulated pathological conditions we studied the effects produced on some hemodynamic variables by simultaneous PUCA pump, thoracic artificial lung or mechanical ventilation assistance. Thoracic artificial lung was applied in parallel or in hybrid mode. The effects of mechanical ventilation have been simulated by changing mean intrathoracic pressure value from -4 mmHg to +5 mmHg. The hemodynamic variables observed during the simulations, in different assisted conditions, were: left and right ventricular end systolic (diastolic) volume, systolic/diastolic aortic pressure, mean pulmonary arterial pressure, left and right mean atrial pressure, mean systemic venous pressure and the total blood flow. Results show that the application of PUCA (without mechanical ventilatory assistance) increases the total blood flow, reduces the left ventricular end systolic volume and increases the diastolic aortic pressure. Parallel TAL assistance increases the right ventricular end diastolic (systolic) volume reduction both when PUCA is switched "ON" and both when PUCA is switched "OFF". By switching "OFF" the PUCA pump, it seems that parallel thoracic artificial lung assistance produces a greater cardiac output (respect to hybrid TAL assistance). Results concerning PUCA and TAL interaction produced by simulations cannot be compared with "in vivo" results since they are not presented in literature. But results concerning the effects produced by LVAD and mechanical ventilation have a trend consistent with those presented in literature.

Review of zero-D and 1-D models of blood flow in the cardiovascular system

Background

Zero-dimensional (lumped parameter) and one dimensional models, based on simplified representations of the components of the cardiovascular system, can contribute strongly to our understanding of circulatory physiology. Zero-D models provide a concise way to evaluate the haemodynamic interactions among the cardiovascular organs, whilst one-D (distributed parameter) models add the facility to represent efficiently the effects of pulse wave transmission in the arterial network at greatly reduced computational expense compared to higher dimensional computational fluid dynamics studies. There is extensive literature on both types of models.

Method and Results

The purpose of this review article is to summarise published 0D and 1D models of the cardiovascular system, to explore their limitations and range of application, and to provide an indication of the physiological phenomena that can be included in these representations. The review on 0D models collects together in one place a description of the range of models that have been used to describe the various characteristics of cardiovascular response, together with the factors that influence it. Such models generally feature the major components of the system, such as the heart, the heart valves and the vasculature. The models are categorised in terms of the features of the system that they are able to represent, their complexity and range of application: representations of effects including pressure-dependent vessel properties, interaction between the heart chambers, neuro-regulation and auto-regulation are explored. The examination on 1D models covers various methods for the assembly, discretisation and solution of the governing equations, in conjunction with a report of the definition and treatment of boundary conditions. Increasingly, 0D and 1D models are used in multi-scale models, in which their primary role is to provide boundary conditions for sophisticate, and often patient-specific, 2D and 3D models, and this application is also addressed. As an example of 0D cardiovascular modelling, a small selection of simple models have been represented in the CellML mark-up language and uploaded to the CellML model repository http://models.cellml.org/. They are freely available to the research and education communities.

Conclusion

Each published cardiovascular model has merit for particular applications. This review categorises 0D and 1D models, highlights their advantages and disadvantages, and thus provides guidance on the selection of models to assist various cardiovascular modelling studies. It also identifies directions for further development, as well as current challenges in the wider use of these models including service to represent boundary conditions for local 3D models and translation to clinical application.