Influence of angiotensin II and telmisartan on in vivo high-resolution renal arterial impedance in rats.

Angiotensin II (ANG II) is known to play an important role in regulating renal hemodynamics. We sought to quantify this effect in an in vivo rat model with high-resolution renal arterial (RA) impedance. This study examines the effects of ANG II and its type 1 receptor blocker telmisartan (TELM) on RA impedance. In baroreflex-deactivated rats, we measured RA pressure (Pr) and blood flow (Fr) during random ventricular pacing to induce pressure fluctuation at three different mean Pr (60, 80, and 100 mmHg). We then estimated RA impedance as the transfer function from Fr to Pr. The RA impedance was found to align with a three-element Windkessel model consisting of proximal (Rp) and distal (Rd) resistance and compliance (C). Our study showed Rd reflected the composite characteristics of afferent and efferent arterioles. Rd increased with increasing Pr under the baseline condition with a slope of 1.03 ± 0.21 (× 10-1) min·mL-1. ANG II significantly increased the slope by 0.72 ± 0.29 (× 10-1) min·mL-1 (P < 0.05) without affecting the intercept. TELM significantly reduced the intercept by 34.49 ± 4.86 (× 10-1) mmHg·min·mL-1 (P < 0.001) from the baseline value of 37.93 ± 13.36 (× 10-1) mmHg·min·mL-1, whereas it did not affect the slope. In contrast, Rp was less sensitive than Rd to ANG II or TELM, suggesting Rp may represent the characteristics of elastic large arteries. Our findings provide valuable insights into the influence of ANG II on the dynamics of the renal vasculature.NEW & NOTEWORTHY This present method of quantifying high-resolution renal arterial impedance could contribute to elucidating the characteristics of renal vasculature influenced by physiological mechanisms, renal diseases, or pharmacological effects. The present findings help construct a lumped-parameter renal hemodynamic model that reflects the influence of angiotensin II.

Transient Performance Analysis of Centrifugal Left Ventricular Assist Devices Coupled With Windkessel Model: Large Eddy Simulations Study on Continuous and Pulsatile Flow Operation.

Computational fluid dynamics (CFD) simulations are widely used to develop and analyze blood-contacting medical devices such as left ventricular assist devices (LVADs). This work presents an analysis of the transient behavior of two centrifugal LVADs with different designs: HeartWare VAD and HeartMate3. A scale-resolving methodology is followed through Large Eddy Simulations, which allows for the visualization of turbulent structures. The three-dimensional (3D) LVAD models are coupled to a zero-dimensional (0D) 2-element Windkessel model, which accounts for the vascular resistance and compliance of the arterial system downstream of the device. Furthermore, both continuous- and pulsatile-flow operation modes are analyzed. For the pulsatile conditions, the artificial pulse of HeartMate3 is imposed, leading to a larger variation of performance variables in HeartWare VAD than in HeartMate3. Moreover, CFD results of pulsatile-flow simulations are compared to those obtained by accessing the quasi-steady maps of the pumps. The quasi-steady approach is a predictive tool used to provide a preliminary approximation of the pulsatile evolution of flow rate, pressure head, and power, by only imposing a speed pulse and vascular parameters. This preliminary quasi-steady solution can be useful for deciding the characteristics of the pulsatile speed law before running a transient CFD simulation, as the former entails a significant reduction in computational cost in comparison to the latter.

An interdisciplinary computational model for predicting traumatic brain injury: Linking biomechanics and functional neural networks.

The brain is a complex network consisting of neuron cell bodies in the gray matter and their axonal projections, forming the white matter tracts. These neurons are supported by an equally complex vascular network as well as glial cells. Traumatic brain injury (TBI) can lead to the disruption of the structural and functional brain networks due to disruption of both neuronal cell bodies in the gray matter as well as their projections and supporting cells. To explore how an impact can alter the function of brain networks, we integrated a finite element (FE) brain mechanics model with linked models of brain dynamics (Kuramoto oscillator) and vascular perfusion (Balloon-Windkessel) in this study. We used empirical resting-state functional magnetic resonance imaging (MRI) data to optimize the fit of our brain dynamics and perfusion models to clinical data. Results from the FE model were used to mimic injury in these optimized brain dynamics models: injury to the nodes (gray matter) led to a decrease in the nodal oscillation frequency, while damage to the edges (axonal connections/white matter) progressively decreased coupling among connected nodes. A total of 53 cases, including 33 non-injurious and 20 concussive head impacts experienced by professional American football players were simulated using this integrated model. We examined the correlation of injury outcomes with global measures of structural connectivity, neural dynamics, and functional connectivity of the brain networks when using different lesion methods. Results show that injurious head impacts cause significant alterations in global network topology regardless of lesion methods. Changes between the disrupted and healthy functional connectivity (measured by Pearson correlation) consistently correlated well with injury outcomes (AUC≥0.75), although the predictive performance is not significantly different (p>0.05) to that of traditional kinematic measures (angular acceleration). Intriguingly, our lesion model for gray matter damage predicted increases in global efficiency and clustering coefficient with increases in injury risk, while disrupting axonal connections led to lower network efficiency and clustering. When both injury mechanisms were combined into a single injury prediction model, the injury prediction performance depended on the thresholds used to determine neurodegeneration and mechanical tolerance for axonal injury. Together, these results point towards complex effects of mechanical trauma to the brain and provide a new framework for understanding brain injury at a causal mechanistic level and developing more effective diagnostic methods and therapeutic interventions.

[Effect of lower limb amputation level on aortic hemodynamics: a numerical study].

It has been found that the incidence of cardiovascular disease in patients with lower limb amputation is significantly higher than that in normal individuals, but the relationship between lower limb amputation and the episodes of cardiovascular disease has not been studied from the perspective of hemodynamics. In this paper, numerical simulation was used to study the effects of amputation on aortic hemodynamics by changing peripheral impedance and capacitance. The final results showed that after amputation, the aortic blood pressure increased, the time averaged wall shear stress of the infrarenal abdominal aorta decreased and the oscillatory shear index of the left and right sides was asymmetrically distributed, while the time averaged wall shear stress of the iliac artery decreased and the oscillatory shear index increased. The changes above were more significant with the increase of amputation level, which will result in a higher incidence of atherosclerosis and abdominal aortic aneurysm. These findings preliminarily revealed the influence of lower limb amputation on the occurrence of cardiovascular diseases, and provided theoretical guidance for the design of rehabilitation training and the optimization of cardiovascular diseases treatment.

Vasodilatation by carbon dioxide and sodium nitroglycerin reduces compliance of the cerebral arteries in humans.

NEW FINDINGS: What is the central question of this study? Vascular compliance importantly contributes to the regulation of cerebral perfusion and complex mechanisms are known to influence compliance of a vascular bed: while vasodilatation mediates changes in vascular resistance, does it also affect compliance, particularly in the cerebral vasculature? What is the main finding and its importance? Cerebral vasodilatation, elicited by hypercapnia and sodium nitroglycerin administration, reduced cerebrovascular compliance by approximately 26% from baseline. This study provides new insight into mechanisms mediating cerebrovascular compliance. ABSTRACT: Changes in vascular resistance and vascular compliance contribute to the regulation of cerebral perfusion. While changes in vascular resistance are known to be mediated by vasodilatation, the mechanisms contributing to changes in vascular compliance are complex. In particular, whether vasodilatation affects compliance of the vasculature within the cranium remains unknown. Therefore, the present study examined the impact of two vasodilatation pathways on cerebrovascular compliance in humans. Fifteen young, healthy adults (26 ± 5 years, seven females) completed two protocols: (i) sublingual sodium nitroglycerin (SNG; 0.4 mg) and (ii) hypercapnia (5-6% carbon dioxide gas mixture for 4 min). Blood pressure waveforms (finger photoplethysmography) and middle cerebral artery blood velocity waveforms (transcranial Doppler ultrasound) were input into a modified Windkessel model and an index of cerebrovascular compliance (Ci) was calculated. During the SNG protocol, Ci decreased 24 ± 17% from baseline ((5.0 ± 2.3) × 10-4  cm s-1  mmHg-1 ) to minute 10 ((3.6 ± 1.2) × 10-4  cm s-1  mmHg-1 ; P = 0.009). During the hypercapnia protocol, Ci decreased 28 ± 9% from baseline ((4.4 ± 1.9) × 10-4  cm s-1  mmHg-1 ) to minute 4 ((3.1 ± 1.4) × 10-4  cm s-1  mmHg-1 ; P < 0.001). Cerebral vasodilatory stimuli induced by nitric oxide and carbon dioxide mechanisms reduced compliance of the cerebral vascular bed by approximately 26% from supine baseline values.

A hybrid Windkessel-Womersley model for blood flow in arteries.

A hybrid Windkessel-Womersley (WK-W) coupled mathematical model for the study of pulsatile blood flow in the arterial system is proposed in this article. The model consists of the Windkessel-type proximal and distal compartments connected by a tube to represent the aorta. The blood flow in the aorta is described by the Womersley solution of the simplified Navier-Stokes equations. In addition, we defined a 6-elements Windkessel model (WK6) in which the blood flow in the connecting tube is modeled by the one-dimensional unsteady Bernoulli equation. Both models have been applied and validated using several aortic pressure and flow rate data acquired from different species such as, humans, dogs and pigs. The results have shown that, both models were able to accurately reconstruct arterial input impedance, however, only the WK-W model was able to calculate the radial distribution of the axial velocity in the aorta and consequently the model predicts the time-varying wall shear stress, and frictional pressure drop during the cardiac cycle more accurately. Additionally, the hybrid WK-W model has the capability to predict the pulsed wave velocity, which is also not possible to obtain when using the classical Windkessel models. Moreover, the values of WK-W model parameters have found to fall in the physiologically realistic range of values, therefore it seems that this hybrid model shows a great potential to be used in clinical practice, as well as in the basic cardiovascular mechanics research.

A Primary Computational Fluid Dynamics Study of Pre- and Post-TEVAR With Intentional Left Subclavian Artery Coverage in a Type B Aortic Dissection.

The impact of left subclavian artery (LSA) coverage during thoracic endovascular aortic repair (TEVAR) on the circulatory system is not fully understood. Here, we coupled a single-phase non-Newtonian model with fluid-structure interaction (FSI) technique to simulate blood flow in an acute type B aortic dissection. Three-element Windkessel model was implemented to reproduce physiological pressure waves, where a new workflow was designed to determine model parameters with the absence of measured data. Simulations were carried out in three geometric models to demonstrate the consequence of TEVAR with the LSA coverage; case A: pre-TEVAR aorta; case B: post-TEVAR aorta with the disappearance of LSA; case C: post-TEVAR aorta with virtually adding LSA. Results show that the blood flow through the compressed true lumen is only 8.43%, which may lead to ischemia in related organs. After TEVAR, the wall pressure on the stented segment increases and blood flow in the supra-aortic branches and true lumen is improved. Meantime, the average deformation of the aorta is obviously reduced due to the implantation of the stent graft. After virtually adding LSA, significant changes in the distribution of blood flow and two indices based on wall shear stress are observed. Moreover, the movement of residual false lumen becomes stable, which could contribute to patient recovery. Overall, this study quantitatively evaluates the efficacy of TEVAR for acute type B aortic dissection and demonstrates that the coverage of LSA has a considerable impact on the important hemodynamic parameters.

Windkessel model of hemodynamic state supported by a pulsatile ventricular assist device in premature ventricle contraction.

BACKGROUND: Counter-pulsation control (CPC) by ventricular assist devices (VADs) is believed to reduce cardiac load and increase coronary perfusion. However, patients with VADs have a higher risk of arrhythmia, which may cause the CPC to fail. Consequently, CPC has not been applied by VADs in clinical practice. The phase-locked loop (PLL) algorithm for CPC is readily implemented in VADs; however, it requires a normal, consistent heartbeat for adequate performance. When an arrhythmia occurs, the algorithm maintains a constant pumping rate despite the unstable heartbeat. Therefore, to apply the PLL algorithm to CPC, the hemodynamic effects of abnormal heartbeats must be analyzed. OBJECTIVES: This study sought to predict the hemodynamic effects in patients undergoing CPC using VADs, based on electrocardiogram (ECG) data, including a wide range of heart rate (HR) changes caused by premature ventricular contraction (PVC) or other reasons. METHODS: A four-element Windkessel hemodynamic model was used to reproduce the patient's aortic blood pressure in this study. ECG data from 15 patients with severe congestive heart failure were used to assess the effect of the CPC on the patients' hemodynamic state. The input and output flow characteristics of the pulsatile VAD (LibraHeart I, Cervika, Korea) were measured using an ultrasound blood flow meter (TS410, Transonic, USA), with the aortic pressure maintained at 80-120 mmHg. All other patient conditions were also reproduced. RESULTS: In patients with PVCs or normal heartbeats, CPC controlled by a VAD reduced the cardiac load by 20 and 40%, respectively. When the HR was greater for other reasons, such as sinus tachycardia, simultaneous ejection from the heart and VAD was observed; however, the cardiac load was not increased by rapid cardiac contractions resulting from decreased left ventricle volume. These data suggest that the PLL algorithm reduces the cardiac load and maintains consistent hemodynamic changes.

Improved pressure contour analysis for estimating cardiac stroke volume using pulse wave velocity measurement.

BACKGROUND: Pressure contour analysis is commonly used to estimate cardiac performance for patients suffering from cardiovascular dysfunction in the intensive care unit. However, the existing techniques for continuous estimation of stroke volume (SV) from pressure measurement can be unreliable during hemodynamic instability, which is inevitable for patients requiring significant treatment. For this reason, pressure contour methods must be improved to capture changes in vascular properties and thus provide accurate conversion from pressure to flow. METHODS: This paper presents a novel pressure contour method utilizing pulse wave velocity (PWV) measurement to capture vascular properties. A three-element Windkessel model combined with the reservoir-wave concept are used to decompose the pressure contour into components related to storage and flow. The model parameters are identified beat-to-beat from the water-hammer equation using measured PWV, wave component of the pressure, and an estimate of subject-specific aortic dimension. SV is then calculated by converting pressure to flow using identified model parameters. The accuracy of this novel method is investigated using data from porcine experiments (N = 4 Pietrain pigs, 20-24.5 kg), where hemodynamic properties were significantly altered using dobutamine, fluid administration, and mechanical ventilation. In the experiment, left ventricular volume was measured using admittance catheter, and aortic pressure waveforms were measured at two locations, the aortic arch and abdominal aorta. RESULTS: Bland-Altman analysis comparing gold-standard SV measured by the admittance catheter and estimated SV from the novel method showed average limits of agreement of ±26% across significant hemodynamic alterations. This result shows the method is capable of estimating clinically acceptable absolute SV values according to Critchely and Critchely. CONCLUSION: The novel pressure contour method presented can accurately estimate and track SV even when hemodynamic properties are significantly altered. Integrating PWV measurements into pressure contour analysis improves identification of beat-to-beat changes in Windkessel model parameters, and thus, provides accurate estimate of blood flow from measured pressure contour. The method has great potential for overcoming weaknesses associated with current pressure contour methods for estimating SV.

Development of a servo pump system for in vivo loading of pathological pulmonary artery impedance on the right ventricle of normal rats.

Pulmonary artery (PA) impedance provides detailed information on right ventricular (RV) afterload in pulmonary hypertension (PH). This study aimed to examine PA impedance in a rat model of monocrotaline-induced PH (MCT-PH) and to develop an experimental system for in vivo loading of pathological PA impedance on the RV of normal rats. PA impedance was quantified in normal (n= 10) and MCT-PH rats (n= 10) using a three-element Windkessel (3-WK) model. Compared with normal rats, MCT-PH rats had higher characteristic impedance (ZC) and peripheral pulmonary resistance (RP) (ZC: 0.121 ± 0.039 vs. 0.053 ± 0.017 mmHg·min·ml(-1), P< 0.001; RP: 0.581 ± 0.334 vs. 0.252 ± 0.105 mmHg·min·ml(-1), P= 0.013) and lower pulmonary artery compliance (CP) (0.242 ± 0.131 vs. 0.700 ± 0.186 ml/mmHg, P< 0.001). In another group of 10 normal rats, a computer-controlled servo pump was connected to the left PA for loading PA impedance with parameters in pathological ranges designed by the 3-WK model. Activation of the servo pump decreased the error of measured vs. target PA impedance (modulus: from 0.047 ± 0.020 without pump activation to 0.019 ± 0.007 with pump activation,P< 0.001; phase: 0.085 ± 0.028 to 0.043 ± 0.012 radians,P< 0.001). In conclusion, MCT-PH increases ZC and RP and decreases CP Our servo pump system, which is capable of imposing arbitrary PA impedance with pathological parameters, may offer a unique opportunity to delineate the pathological significance of PA impedance in PH.

Reducing the number of parameters in 1D arterial blood flow modeling: less is more for patient-specific simulations.

Patient-specific one-dimensional (1D) blood flow modeling requires estimating model parameters from available clinical data, ideally acquired noninvasively. The larger the number of arterial segments in a distributed 1D model, the greater the number of input parameters that need to be estimated. We investigated the effect of a reduction in the number of arterial segments in a given distributed 1D model on the shape of the simulated pressure and flow waveforms. This is achieved by systematically lumping peripheral 1D model branches into windkessel models that preserve the net resistance and total compliance of the original model. We applied our methodology to a model of the 55 larger systemic arteries in the human and to an extended 67-artery model that contains the digital arteries that perfuse the fingers. Results show good agreement in the shape of the aortic and digital waveforms between the original 55-artery (67-artery) and reduced 21-artery (37-artery) models. Reducing the number of segments also enables us to investigate the effect of arterial network topology (and hence reflection sites) on the shape of waveforms. Results show that wave reflections in the thoracic aorta and renal arteries play an important role in shaping the aortic pressure and flow waves and in generating the second peak of the digital pressure and flow waves. Our novel methodology is important to simplify the computational domain while maintaining the precision of the numerical predictions and to assess the effect of wave reflections.

Uncertainty quantification of the pressure waveform using a Windkessel model.

The Windkessel (WK) model is a simplified mathematical model used to represent the systemic arterial circulation. While the WK model is useful for studying blood flow dynamics, it suffers from inaccuracies or uncertainties that should be considered when using it to make physiological predictions. This paper aims to develop an efficient and easy-to-implement uncertainty quantification method based on a local gradient-based formulation to quantify the uncertainty of the pressure waveform resulting from aleatory uncertainties of the WK parameters and flow waveform. The proposed methodology, tested against Monte Carlo simulations, demonstrates good agreement in estimating blood pressure uncertainties due to uncertain Windkessel parameters, but less agreement considering uncertain blood-flow waveforms. To illustrate our methodology's applicability, we assessed the aortic pressure uncertainty generated by Windkessel parameters-sets from an available in silico database representing healthy adults. The results from the proposed formulation align qualitatively with those in the database and in vivo data. Furthermore, we investigated how changes in the uncertainty of the Windkessel parameters affect the uncertainty of systolic, diastolic, and pulse pressures. We found that peripheral resistance uncertainty produces the most significant change in the systolic and diastolic blood pressure uncertainties. On the other hand, compliance uncertainty considerably modifies the pulse pressure standard deviation. The presented expansion-based method is a tool for efficiently propagating the Windkessel parameters' uncertainty to the pressure waveform. The Windkessel model's clinical use depends on the reliability of the pressure in the presence of input uncertainties, which can be efficiently investigated with the proposed methodology. For instance, in wearable technology that uses sensor data and the Windkessel model to estimate systolic and diastolic blood pressures, it is important to check the confidence level in these calculations to ensure that the pressures accurately reflect the patient's cardiovascular condition.

Efficient Cardiovascular Parameters Estimation for Fluid-Structure Simulations Using Gappy Proper Orthogonal Decomposition.

As full-scale detailed hemodynamic simulations of the entire vasculature are not feasible, numerical analysis should be focused on specific regions of the cardiovascular system, which requires the identification of lumped parameters to represent the patient behavior outside the simulated computational domain. We present a novel technique for estimating cardiovascular model parameters using gappy Proper Orthogonal Decomposition (g-POD). A POD basis is constructed with FSI simulations for different values of the lumped model parameters, and a linear operator is applied to retain information that can be compared to the available patient measurements. Then, the POD coefficients of the reconstructed solution are computed either by projecting patient measurements or by solving a minimization problem with constraints. The POD reconstruction is then used to estimate the model parameters. In the first test case, the parameter values of a 3-element Windkessel model are approximated using artificial patient measurements, obtaining a relative error of less than 4.2%. In the second case, 4 sets of 3-element Windkessel are approximated in a patient's aorta geometry, resulting in an error of less than 8% for the flow and less than 5% for the pressure. The method shows accurate results even with noisy patient data. It automatically calculates the delay between measurements and simulations and has flexibility in the types of patient measurements that can handle (at specific points, spatial or time averaged). The method is easy to implement and can be used in simulations performed in general-purpose FSI software.

The role of pulse wave analysis indexes for critically ill patients: a narrative review.

Objective.Arterial pulse wave analysis (PWA) is now established as a powerful tool to investigate the cardiovascular system, and several clinical studies have shown how PWA can provide valuable prognostic information over and beyond traditional cardiovascular risk factors. Typically these techniques are applied to chronic conditions, such as hypertension or aging, to monitor the slow structural changes of the vascular system which lead to important alterations of the arterial PW. However, their application to acute critical illness is not currently widespread, probably because of the high hemodynamic instability and acute dynamic alterations affecting the cardiovascular system of these patients.Approach.In this work we propose a review of the physiological and methodological basis of PWA, describing how it can be used to provide insights into arterial structure and function, cardiovascular biomechanical properties, and to derive information on wave propagation and reflection.Main results.The applicability of these techniques to acute critical illness, especially septic shock, is extensively discussed, highlighting the feasibility of their use in acute critical patients and their role in optimizing therapy administration and hemodynamic monitoring.Significance.The potential for the clinical use of these techniques lies in the ease of computation and availability of arterial blood pressure signals, as invasive arterial lines are commonly used in these patients. We hope that the concepts illustrated in the present review will soon be translated into clinical practice.

The origin of intraluminal pressure waves in gastrointestinal tract.

The gastrointestinal (GI) peristalsis is an involuntary wave-like contraction of the GI wall that helps to propagate food along the tract. Many GI diseases, e.g., gastroparesis, are known to cause motility disorders in which the physiological contractile patterns of the wall get disrupted. Therefore, to understand the pathophysiology of these diseases, it is necessary to understand the mechanism of GI motility. We present a coupled electromechanical model to describe the mechanism of GI motility and the transduction pathway of cellular electrical activities into mechanical deformation and the generation of intraluminal pressure (IP) waves in the GI tract. The proposed model consolidates a smooth muscle cell (SMC) model, an actin-myosin interaction model, a hyperelastic constitutive model, and a Windkessel model to construct a coupled model that can describe the origin of peristaltic contractions in the intestine. The key input to the model is external electrical stimuli, which are converted into mechanical contractile waves in the wall. The model recreated experimental observations efficiently and was able to establish a relationship between change in luminal volume and pressure with the compliance of the GI wall and the peripheral resistance to bolus flow. The proposed model will help us understand the GI tract's function in physiological and pathophysiological conditions.

A numerical method to enhance the performance of a cam-type electric motor-driven left ventricular assist device.

Pulsatile left ventricular assist devices (LVADs) driven by electric motors have been widely accepted as a treatment of heart failure. Performance enhancement with computer assistance for this kind of LVAD has seldom been reported. In this article, a numerical method is proposed to assist the design of a cam-type pump. The method requires an integrated model of an LVAD system, consisting of a motor, a transmission mechanism, and a cardiovascular circulation. Performance indices, that is, outlet pressure, outlet flow, and pump efficiency, were used to select the best cam profile from six candidates. A prototype pump connected to a mock circulatory loop (MCL) was used to calibrate the friction coefficient of the cam groove and preliminarily evaluate modeling accuracy. In vitro experiments show that the mean outlet pressure and flow can be predicted with high accuracy by the model, and gross geometries of the measurements can also be reproduced. Simulation results demonstrate that as the total peripheral resistance (TPR) is fixed at 1.1 mm Hg.s/mL, the two-cycle 2/3-rise profile is the best. Compared with other profiles, the maximum increases of pressure and flow indices are 75 and 76%, respectively, and the maximum efficiency increase is over 51%. For different TPRs (0.5∼1.5 mm Hg.s/mL) and operation intervals (0.1∼0.4 s) in counterpulsation, the conclusion is also acceptable.

Temporal complexity in photoplethysmography and its influence on blood pressure.

Objective: The temporal complexity of photoplethysmography (PPG) provides valuable information about blood pressure (BP). In this study, we aim to interpret the stochastic PPG patterns with a model-based simulation, which may help optimize the BP estimation algorithms. Methods: The classic four-element Windkessel model is adapted in this study to incorporate BP-dependent compliance profiles. Simulations are performed to generate PPG responses to pulse and continuous stimuli at various timescales, aiming to mimic sudden or gradual hemodynamic changes observed in real-life scenarios. To quantify the temporal complexity of PPG, we utilize the Higuchi fractal dimension (HFD) and autocorrelation function (ACF). These measures provide insights into the intricate temporal patterns exhibited by PPG. To validate the simulation results, continuous recordings of BP, PPG, and stroke volume from 40 healthy subjects were used. Results: Pulse simulations showed that central vascular compliance variation during a cardiac cycle, peripheral resistance, and cardiac output (CO) collectively contributed to the time delay, amplitude overshoot, and phase shift of PPG responses. Continuous simulations showed that the PPG complexity could be generated by random stimuli, which were subsequently influenced by the autocorrelation patterns of the stimuli. Importantly, the relationship between complexity and hemodynamics as predicted by our model aligned well with the experimental analysis. HFD and ACF had significant contributions to BP, displaying stability even in the presence of high CO fluctuations. In contrast, morphological features exhibited reduced contribution in unstable hemodynamic conditions. Conclusion: Temporal complexity patterns are essential to single-site PPG-based BP estimation. Understanding the physiological implications of these patterns can aid in the development of algorithms with clear interpretability and optimal structures.

A Vector Fitting Approach for the Automated Estimation of Lumped Boundary Conditions of 1D Circulation Models.

PURPOSE: The choice of appropriate boundary conditions is a crucial step in the development of cardiovascular models for blood flow simulations. The three-element Windkessel model is usually employed as a lumped boundary condition, providing a reduced order representation of the peripheral circulation. However, the systematic estimation of the Windkessel parameters remains an open problem. Moreover, the Windkessel model is not always adequate to model blood flow dynamics, which often require more elaborate boundary conditions. In this study, we propose a method for the estimation of the parameters of high order boundary conditions, including the Windkessel model, from pressure and flow rate waveforms at the truncation point. Moreover, we investigate the effect of adopting higher order boundary conditions, corresponding to equivalent circuits with more than one storage element, on the accuracy of the model. METHOD: The proposed technique is based on Time-Domain Vector Fitting, a modeling algorithm that, given samples of the input and output of a system, such as pressure and flow waveforms, can derive a differential equation approximating their relation. RESULTS: The capabilities of the proposed method are tested on a 1D circulation model consisting of the 55 largest human systemic arteries, to demonstrate its accuracy and its usefulness to estimate boundary conditions with order higher than the traditional Windkessel models. The proposed method is compared to other common estimation techniques, and its robustness in parameter estimation is verified in presence of noisy data and of physiological changes of aortic flow rate induced by mental stress. CONCLUSION: Results suggest that the proposed method is able to accurately estimate boundary conditions of arbitrary order. Higher order boundary conditions can improve the accuracy of cardiovascular simulations, and Time-Domain Vector Fitting can automatically estimate them.