Subject-specific pulse wave propagation modeling: Towards enhancement of cardiovascular assessment methods

Abstract

Cardiovascular diseases are the leading cause of death worldwide. Pulse wave analysis (PWA) technique, which reconstructs and analyses aortic pressure waveform based on non-invasive peripheral pressure recording, became an important bioassay for cardiovascular assessment in a general population. The aim of our study was to establish a pulse wave propagation modeling framework capable of matching clinical PWA data from healthy individuals on a per-subject basis. Radial pressure profiles from 20 healthy individuals (10 males, 10 females), with mean age of 42 ± 10 years, were recorded using applanation tonometry (SphygmoCor, AtCor Medical, Australia) and used to estimate subject-specific parameters of mathematical model of blood flow in the system of fifty-five arteries. The model was able to describe recorded pressure profiles with high accuracy (mean absolute percentage error of 1.87 ± 0.75%) when estimating only 6 parameters for each subject. Cardiac output (CO) and stroke volume (SV) have been correctly identified by the model as lower in females than males (CO of 3.57 ± 0.54 vs. 4.18 ± 0.72 L/min with p-value < 0.05; SV of 49.5 ± 10.1 vs. 64.2 ± 16.8 ml with p-value = 0.076). Moreover, the model identified age related changes in the heart function, i.e. that the cardiac output at rest is maintained with age (r = 0.23; p-value = 0.32) despite the decreasing heart rate (r = −0.49; p-value < 0.05), because of the increase in stroke volume (r = 0.46; p-value < 0.05). Central PWA indices derived from recorded waveforms strongly correlated with those obtained using corresponding model-predicted radial waves (r > 0.99 and r > 0.97 for systolic (SP) and diastolic (DP) pressures, respectively; r > 0.77 for augmentation index (AI); all p—values < 0.01). Model-predicted central waveforms, however, had higher SP than those reconstructed by PWA using recorded radial waves (5.6 ± 3.3 mmHg on average). From all estimated subject-specific parameters only the time to the peak of heart ejection profile correlated with clinically measured AI. Our study suggests that the proposed model may serve as a tool to computationally investigate virtual patient scenarios mimicking different cardiovascular abnormalities. Such a framework can augment our understanding and help with the interpretation of PWA results.

Patient-specific pulse wave propagation model identifies cardiovascular risk characteristics in hemodialysis patients

“…Basic volunteers characteristics are shown in Table 1 . The data about 20 out of those 32 healthy individuals have been published previously in [ 20 ]. Participants were enrolled from June 2014 through February 2018.…”

“…We use our previously published model [ 20 ] that allows to simulate the blood flow in a bifurcating binary tree of fifty-five larger systemic arteries in which individual vessels are axisymmetric elastic cylinders tapering along their length. The model describes spatiotemporal changes in the pressure and blood flow, under the assumption that each vessel is impermeable and blood is an incompressible fluid with given density and viscosity.…”

“…Here, as in [ 20 ], we use the model to estimate six patient-specific parameters: k 1 and k 3 being hyperparameters describing stiffness of small and large arteries, respectively; cardiac output (CO); moment of the heart ejection peak ( τ ); and scaling constants of resistances ( S R ) and compliances ( S C ) of capillary beds ( Fig 2B ). Equation describing stiffness of an artery ( F ) has the following form where k 2 = 22.53 and r 0 ( x ) is the assumed vessel diameter at the reference pressure (97 mmHg) and distance x from the vessel’s inlet [ 20 , 27 ]. Therefore, larger vessels’ ( r 0 > > 1) stiffness is governed primarily by parameter k 3 whereas for smaller vessels ( r 0 < < 1) stiffness F is related to k 1 + k 3 .…”

“…However, despite some studies showing validity of this assumption [ 12 – 14 ], there are still significant concerns about the robustness of aortic wave reconstruction [ 15 – 19 ]. Moreover, it is not completely clear what the major determinants of PWA-derived indices are as the waveform can be attributed to those cardiovascular properties that determine the wave propagation and reflection, such as, among other, arterial geometry, elasticity of the vessel wall, systemic resistance, heart frequency, cardiac output [ 20 ]. Nevertheless, one of the PWA-derived indices, i.e.…”

“…Here, in a detailed study of pulse wave propagation properties using our previously published model [ 20 ], we aimed to check whether the cardiovascular risk factors for hemodialysis patients, such as arterial stiffness, can be derived from a single, quick and non-invasive peripheral wave recording and thus, overcome the PWA and PWV limitations. Moreover, we try to decipher what are the major determinants of PWA-derived indices and how they relate to the predicted pulse wave velocity.…”