A sensitivity analysis of a personalized pulse wave propagation model for arteriovenous fistula surgery. Part B: Identification of possible generic model parameters

Decision-making in vascular access surgery for hemodialysis can be supported by a pulse wave propagation model that is able to simulate pressure and flow changes induced by the creation of a vascular access. To personalize such a model, patient-specific input parameters should be chosen. However, the number of input parameters that can be measured in clinical routine is limited. Besides, patient data are compromised with uncertainty. Incomplete and uncertain input data will result in uncertainties in model predictions. In part A, we analyzed how the measurement uncertainty in the input propagates to the model output by means of a sensitivity analysis. Of all 73 input parameters, 16 parameters were identified to be worthwhile to measure more accurately and 51 could be fixed within their measurement uncertainty range, but these latter parameters still needed to be measured. Here, we present a methodology for assessing the model input parameters that can be taken constant and therefore do not need to be measured. In addition, a method to determine the value of this parameter is presented. For the pulse wave propagation model applied to vascular access surgery, six patient-specific datasets were analyzed and it was found that 47 out of 73 parameters can be fixed on a generic value. These model parameters are not important for personalization of the wave propagation model. Furthermore, we were able to determine a generic value for 37 of the 47 fixable model parameters.     

A pulse wave propagation model to support decision-making in vascular access planning in the clinic

The preferred vascular access for hemodialysis is an autologous arteriovenous fistula (AVF) in the arm: a surgically created connection between an artery and vein. The surgeon selects the AVF location based on experience and preoperative diagnostics. However, 20-50% of all lower arm AVFs are hampered by a too low access flow, whereas complications associated with too high flows are observed in 20% of all upper arm AVFs. We hypothesize that a pulse wave propagation model fed by patient-specific data has the ability to assist the surgeon in selecting the optimal AVF configuration by predicting direct postoperative flow. Previously, a 1D wave propagation model (spectral elements) was developed in which an approximated velocity profile was assumed based on boundary layer theory. In this study, we derived a distributed lumped parameter implementation of the pulse wave propagation model. The elements of the electrical analog for a segment are based on the approximated velocity profiles and dependent on the Womersley number. We present the application of the lumped parameter pulse wave propagation model to vascular access surgery and show how a patient-specific model is able to predict the hemodynamical impact of AVF creation and might assist in vascular access planning. The lumped parameter pulse wave propagation model was able to select the same AVF configuration as an experienced surgeon in nine out of ten patients. In addition, in six out of ten patients predicted postoperative flows were in the same order of magnitude as measured postoperative flows. Future research should quantify uncertainty in model predictions and measurements.     

Global sensitivity analysis of a wave propagation model for arm arteries

Wave propagation models of blood flow and blood pressure in arteries play an important role in cardiovascular research. For application of these models in patient-specific simulations a number of model parameters, that are inherently subject to uncertainties, are required. The goal of this study is to identify with a global sensitivity analysis the model parameters that influence the output the most. The improvement of the measurement accuracy of these parameters has largest consequences for the output statistics. A patient specific model is set up for the major arteries of the arm. In a Monte-Carlo study, 10 model parameters and the input blood volume flow (BVF) waveform are varied randomly within their uncertainty ranges over 3000 runs. The sensitivity in the output for each system parameter was evaluated with the linear Pearson and ranked Spearman correlation coefficients. The results show that model parameter and input BVF uncertainties induce large variations in output variables and that most output variables are significantly influenced by more than one system parameter. Overall, the Young's modulus appears to have the largest influence and arterial length the smallest. Only small differences were obtained between Spearman's and Pearson's tests, suggesting that a high monotonic association given by Spearman's test is associated with a high linear corelation between the inputs and output parameters given by Pearson's test.     

Role of total arterial compliance and peripheral resistance in the determination of systolic and diastolic aortic pressure.

The goal of the study was to define the major arterial parameters that determine aortic systolic (Ps) and diastolic (Pd) pressure in the dog. Measured aortic flows were used as input to the two-element windkessel model of the arterial system, with peripheral resistance calculated as mean pressure over mean flow and total arterial compliance calculated from the decay time in diastole. The windkessel model yielded an aortic pressure wave from which we obtained the predicted systolic (Ps, wk) and diastolic (Pd, wk) pressure. These predicted pressures were compared with the measured systolic and diastolic pressures. The measurements and calculations were carried out in 7 dogs in control conditions, during aortic occlusion at four locations (the trifurcation, between trifurcation and diaphragm, the diaphragm and the proximal descending thoracic aorta) and during occlusion of both carotid arteries. Under all conditions studied the predicted systolic and diastolic pressure matched the experimental ones very well: Ps, wk = (1.000 +/- 0.0055) Ps with r = 0.958 and Pd, wk = (1.024 +/- 0.0035) Pd with r = 0.995. Linear regression for pulse pressure gave PPwk = (0.99 +/- 0.016) PP (r = 0.911). We found the accuracy of prediction equally good under control conditions and in presence of aortic or carotid artery occlusions. Multiple regression between pulse pressure and arterial resistance and total arterial compliance yielded a poor regression constant (r2 = 0.19) suggesting that the two arterial parameters alone cannot explain pulse pressure and that flow is an important determinant as well. We conclude that, for a given ejection pattern (aortic flow), two arterial parameters, total arterial resistance and total arterial compliance are sufficient to accurately describe systolic and diastolic aortic pressure.     

Computational model for estimating the short- and long-term cardiac response to arteriovenous fistula creation for hemodialysis

Creation of an arteriovenous fistula (AVF) for hemodialysis may result in cardiac failure due to dramatic increases in cardiac output. To investigate the quantitative relations between AVF flow, changes in cardiac output, myocardial stress and strain and resulting left ventricular adaptation, a computational model is developed. The model combines a one-dimensional pulse wave propagation model of the arterial network with a zero-dimensional one-fiber model of cardiac mechanics and includes adaptation rules to capture the effect of the baro-reflex and long-term structural remodelling of the left ventricle. Using generic vascular and cardiac parameters based on literature, simulations are done that illustrate the model??s ability to quantitatively reproduce the clinically observed increase in brachial flow and cardiac output as well as occurence of eccentric hypertrophy. Patient-specific clinical data is needed to investigate the value of the computational model for personalized predictions.     

基于传输线模型的脉搏波传播数值仿真及参数分析

目的通过提出一种传输线模型和输入阻抗递归算法的计算方法,数值仿真人体动脉树中脉搏波的传播过程,分析个体差异性和动脉树各参数对脉搏波的影响,为动脉树生理和病理变化分析提供参考。方法利用由大中动脉构成的55段人体动脉树建立传输线模型,采用递归算法计算动脉树各点的输入阻抗,仿真计算动脉树中各段血压和血流的分布图。在此基础上比较不同身高、心率、每搏量、内径、壁厚等参数对脉搏波传播和血压分布的影响。结果仿真结果和一般脉搏波传播规律相一致,验证了该方法的有效性。不同参数对动脉树中脉搏波传播的影响有较大差异且呈现各自特征。结论基于传输线模型和递归算法的计算方法能有效仿真动脉树中脉搏波的传播过程,并准确反映个体差异性和动脉树血液动力学参数的变化对脉搏波的影响,是人体动脉树生理病理分析和诊断的重要辅助手段。     

Computer identification of models for the arterial tree input impedance: Comparison between two new simple models and first experimental results

Two new simple models for the arterial tree input impedance are presented. The first is a 4-element windkessel model, obtained by paralleling the characteristic resistance of the 3-element windkessel model (Westerhof, 1968) with an inductance. The second is a tube model with a complex load, which is characterised by four parameters also. The parameters of these models are estimated from aortic root pressure and flow, which are either simulated by a complex numerical model of the peripheral arterial tree or measured in dogs. The parameter estimation is carried out using an automatic procedure based on the Powell optimisation algorithm. The importance of the evaluation of the achievable accuracy in the estimation of parameters and its relationship to model identifiability is emphasised.     

Identification of the three-element windkessel model incorporating a pressure-dependent compliance

A new one-step computational procedure is presented for estimating the parameters of the nonlinear three-element windkessel model of the arterial system incorporating a pressure-dependent compliance. The data required are pulsatile aortic pressure and flow. The basic assumptions are a steadystate periodic regime and a purely elastic compliant element. By stating two conditions, zero mean flow and zero mean power in the compliant element, peripheral and characteristic resistances are determined through simple closed form formulas as functions of mean values of the square of aortic pressure, the square of aortic flow, and the product of aortic pressure with aortic flow. The pressure across as well as the flow through the compliant element can be then obtained so allowing the calculation of volume variation and compliance as functions of pressure. The feasibility of this method is studied by applying it to both simulated and experimental data relative to different circulatory conditions and comparing the results with those obtained by an iterative parameter optimization algorithm and with the actual values when available. The conclusion is that the proposed method appears to be effective in identifying the three-element windkessel even in the case of nonlinear compliance.     

基于容积脉搏波血流动力学检测的血流动力学参数的临床验证

目的 改进脉搏波无创检测仪的检测方式,考虑到桡动脉检测的操作复杂,因而选择操作简便的指脉检测.方法 通过大量的临床数据分析,确定指脉检测方式与桡动脉检测方式之间的转换关系,计算基于容积脉搏波的部分血流动力学参数,并和超声心动检测结果进行对比.结果 用指端容积脉搏血流方法同步检测的血流参数和超声心动检测血流参数的结果对比,差异没有统计学意义.结论 所得结果表明,在应用指端容积脉搏血流方法检测心输出量及其他血流参数是可行的.     

基于桡动脉脉搏波血流动力学检测的心输出量计算修正

目的心输出量是评估心血管功能的重要参数.长期以来,心输出量作为常规的心血管血流参数已被临床医生、药剂师和生理学家所接受.北京工业大学罗志昌等人通过多年研究,获得了心输出量的临床实用公式,但此公式中的一些近似是以正常健康人的生理条件为基准,在长期的实验中,发现由此得出的心输出量在一些情况下失真,因此有必要对这种失真进行修正.方法通过大量临床实验,用线性回归的方法,通过修正系数,对心输出量计算公式进行修正.结果修正系数与脉搏波特征参数K、年龄、血压和心率有关,修正后的公式计算的心输出量较为接近实际值.结论在没有经过心外科手术的无心瓣膜缺损、主动脉瘤、心衰、心率不齐等疾病的患者,以及健康的孕妇、运动员和普通的健康人中,通过脉搏波特征参数K、年龄、血压和心率计算心输出量是比较可靠的.     

Physiological interpretation of inductance and low-resistance terms in four-element windkessel models: assessment by generalized sensitivity function analysis

Physiological relevance of parameters of three arterial models, denominated W4P, W4S and IVW, was assessed by computation of parameter-related generalized sensitivity functions (GSFs), which allow the definition of heart-cycle time intervals where the information content of experimental data, useful for estimation of each model parameter, is concentrated. The W4P and W4S are derived from the three-element windkessel by connecting an inductance, L, in parallel or in series, respectively, with aortic characteristic impedance, R(c). In the IVW, L is placed in series at the input of a viscoelastic windkessel, incorporating a Voigt cell (a resistor, R(d), in series with a capacitor, C). Pressure and flow measured in the ascending aorta of five ferrets and five dogs were used to estimate all model parameters, by fitting to pressure. For each model structure, parameter-related GSFs were generated. Focusing on controversial L, R(c) and R(d) physical meaning, our GSF analysis yielded the conclusion that, in both the W4S and the IVW, but not in the W4P, the L-term is suitable to represent the inertial properties of blood motion. Moreover, the meaning of aortic characteristic impedance ascribed to R(c) is questionable; while R(d) is likely to account for viscous losses of arterial wall motion.     

Simple and accurate way for estimating total and segmental arterial compliance: The pulse pressure method

We derived and tested a new, simple, and accurate method to estimate the compliance of the entire arterial tree and parts thereof. The method requires the measurements of pressure and flow and is based on fitting the pulse pressure (systolic minus diastolic pressure) predicted by the two-element windkessel model to the measured pulse pressure. We show that the two-element windkessel model accurately describes the modulus of the input impedance at low harmonics (0–4th) of the heart rate so that the gross features of the arterial pressure wave, including pulse pressure, are accounted for. The method was tested using a distributed nonlinear model of the human systemic arterial tree. Pressure and flow were calculated in the ascending aorta, thoracic aorta, common carotid, and iliac artery. In a linear version of the systemic model the estimated compliance was within 1% of the compliance at the first three locations. In the iliac artery an error of 7% was found. In a nonlinear version, we compared the estimates of compliance with the average compliance over the cardiac cycle and the compliance at the mean working pressure. At the first three locations we found the estimated and “actual” compliance to be within 12% of each other. In the iliac artery the error was larger. We also investigated an increase and decrease in heart rate, a decrease in wall elasticity and exercise conditions. In all cases the estimated total arterial compliance was within 10% of mean compliance. Thus, the errors result mainly from the nonlinearity of the arterial system. Segmental compliance can be obtained by subtraction of compliance determined at two locations.     

基于深度学习的指-桡端脉搏波信号转换方法

针对目前市面上大多数脉搏波检测仪器检测的是指端脉搏波信号,提出一种基于卷积神经网络的指-桡端脉搏波信号转换方法,在仅获取指端脉搏波信号的情况下得到对应的桡动脉脉搏波信号。该方法主要由一维卷积神经网络通过端到端的训练实现,模型包含编码器、解码器和跳跃连接3个部分,通过编码器网络提取指端脉搏波信号的特征,再通过解码器网络将特征图进行扩展,并且利用跳跃连接的方式实现特征图的融合。采集60份指端和桡端的脉搏波信号进行实验,并与传递函数模型和弹性腔模型进行对比。实验结果表明,该模型转换所得的桡端脉搏波信号在MAE和PRD的指标上分别达到1.4%±0.3%和3.6%±1.2%,优于其他模型。研究表明,该模型能够较精确地实现指端脉搏波信号到桡端脉搏波信号的转化。     

Estimation of distributed arterial mechanical properties using a wave propagation model in a reverse way

To estimate arterial stiffness, different methods based either on distensibility, pulse wave velocity or a pressure-velocity loop, have been proposed. These methods can be employed to determine the arterial mechanical properties either locally or globally, e.g. averaged over an entire arterial segment. The aim of this study was to investigate the feasibility of a new method that estimates distributed arterial mechanical properties non-invasively. This new method is based on a wave propagation model and several independent ultrasound and pressure measurements. Model parameters (including arterial mechanical properties) are obtained from a reverse method in which differences between modeling results and measurements are minimized using a fitting procedure based on local sensitivity indices. This study evaluates the differences between in vivo measured and simulated blood pressure and volume flow waveforms at the brachial, radial and ulnar arteries of 6 volunteers. The estimated arterial Young's modulus range from 1.0 to 6.0 MPa with an average of (3.8 ± 1.7) MPa at the brachial artery and from 1.2 to 7.8 MPa with an average of (4.8 ± 2.2) MPa at the radial artery. A good match between measured and simulated waveforms and the realistic stiffness parameters indicate a good in vivo suitability.     

桡动脉内压力波的微创伤测定法及其意义的探讨

我们应用22号血管套管针穿刺桡动脉、留置微导管,描记压力波形,研究正常青年组(Ⅰ)、肺心病Ⅱ型呼衰的老年组(Ⅱ)及老年对照组(Ⅲ)桡动脉压力波,对比桡动脉内压力波与脉象图。结果表明,Ⅰ组多呈三峰波形、Ⅱ组呈单峰高尖波,Ⅲ组呈主波宽园、园钝波形。Ⅰ组与Ⅲ组波形图主要参数h_4/h_1、w/t_4、A_d/A_T差别显著或非常显著(分别P<0.05,P<0.001,P<0.001),A_T差别不显著。两组动脉血气分析pH、PaCO_2无显著差别,PaO_2均在正常范围。Ⅱ组与Ⅲ组h_4/h_1、w/t_4、A_T、A_d/A_T差别均非常显著(P相似文献   

一种桡动脉脉搏信号的自动检波算法

现有的基于桡动脉脉搏波的心血管功能参数检测仪能够无创地检测心血管参数,但要求使用者具备一定的医学知识,需人工判断用于检测心血管功能参数的脉搏波波形,从而降低了仪器的普适性.本文利用小波变换对脉搏波进行分析,实现了一种新的基于连续小波变换的桡动脉脉搏波检波算法.实验结果表明:该算法准确性好,能有效提高心血管功能参数检测的智能化程度,降低操作难度,有利于心血管功能检测仪在家庭医疗保健中的推广使用.     

基于流体网络的人体血液体循环分析

基于中医脉诊原理,研究人体各器官流阻变化对血流动力学参数的影响。建立人体血液体循环流体网络模型,采用10次谐波血流动力学表达式模拟心脏输出。改变各器官流阻,流阻比η分别取值0.5、1.0、1.5、2.0、2.5、3.0,利用平均法求解模型。假设心输出量一定,结果表明:随着流阻增大对应分支流量下降;不同分支流阻增大均能使主动脉平均压力上升,当流阻比η=3.0时,脑、肝、肾、胃、肠、脾分支流阻增大引起主动脉压力较正常值分别增大23.29%、16.42%、14.67%、9.69%、9.59%、7.82%;肝和肾分支流阻变化对桡动脉影响较大,当流阻比η=3.0时,桡动脉压力较正常值分别增大22.85%和11.17%,而其他器官分支流阻变化对桡动脉影响很小;对于桡动脉压力谐波振幅,脑分支流阻变化的影响最大,其次是肝和肾,而胃肠脾的影响很小。可见,该模拟研究方法可以得到人体血流动力学参数与各器官流阻变化之间的理论联系,为中医脉诊提供一些理论依据。     

Probabilistic finite element predictions of the human lower limb model in total knee replacement

The purpose of this paper is to explore both an extended and a reduced set of input parameters of the Finite Element (FE) model of the human lower limb with a Total Knee Replacement (TKR) implant. The most influential parameters in determining the size and the shape of the performance envelopes of eight kinematics and peak contact pressure output variables of the tibio-femoral joint and the patello-femoral joint are sought. The lower limb FE model, which includes bones, TKR implant, soft tissues and applied forces of realistic size, is used in the context of the stair ascent simulation. Two probabilistic methods are used together with the FE model to generate the performance envelopes and to explore the sensitivities of the input parameters of the FE model: the Monte Carlo simulation and the Response Surface Method (RSM). A total of four probabilistic FE analyses assess how the uncertainties in an extended set of 77 input variables and a reduced set of 22 input variables obtained from the RSM/sensitivity analyses affect the performance envelopes. It is shown that the FE model with the reduced set of variables is able to replicate the full FE model. The differences between the Monte Carlo envelopes of performance obtained with the FE model with the full set of variables and the FE model with the reduced set of variables were on average over all output measures under 1.67 mm for translations, 1.75° for rotations and under 2 MPa for peak contact pressures. The differences between the RSM and the Monte Carlo envelopes of performances obtained with the reduced set of input variables were, on average, over all output measures under 0.75 mm for translations, 1.26° for rotations and 2.39 MPa for peak contact pressures. While saving computational time with the reduced set of variables, the findings are especially of high importance to the orthopedic surgeons who would like to know the most important parameters that can influence the performance of the TKR for a given human activity.     

Implication of the systolic hump in systemic arterial pressure waves

The systolic hump in the aortic blood pressure wave is defined as the aorticresistance component proportional to the aortic blood flow superimposed on the windkessel component. An electrical analogue comprising a series resistance (aortic resistance) plus a resistance (peripheral resistance) and capacitance (aortic compliance) in parallel (i.e. windkessel component) is used for analysis. Curve fitting using the leastsquares method is performed on calculated and measured blood pressure waves from dogs under haemodynamical conditions induced by infusion of three drugs (noradrenaline, isoproterenol and acetylcholine). The curve fitting RMS (root mean square) errors are <3% for blood pressure waves and <30% for blood flow waves, with good agreement between measured and calculated blood flow waveforms. Infusion of noradrenaline and acetylcholine is found to induce a significant decrease and increase in the aortic resistance, respectively. Although only a small fraction of the blood pressure wave, the systolic hump has a marked effect on the systolic pressure waveform.     

Hybrid Cardiopulmonary Model for Analysis of Valsalva Maneuver with Radial Artery Pulse

A comprehensive model, which has the advantages of both lumped parameter and distributed parameter, has been developed with the objective of investigating the respiratory influences in radial artery pressure pulse as in photoplethysmography (PPG). It integrates lumped parameter cardiopulmonary (CP) model and transmission line arterial tree model from aorta to radial artery. The cardio-pulmonary interaction is realized by incorporating respiratory-induced variations in intrapleural pressure (Ppl) in circulatory system. The PPG signal of the model is considered as the radial artery pulse. To investigate the interaction Valsalva Maneuver (VM) condition has been simulated for different Ppl magnitude (10, 20, 30, and 40 mmHg) and for different time duration (5, 10, 15, and 20 s), and validated with PPG signal recorded in 10 normal subjects performing VM. The effects of test duration and VM pressure are studied in both the simulation and the experiments with specific focus on the maximal (%∆) changes in Heart Rate (HR), and Mean Arterial Pressure (MAP) during phases II and IV of VM. The correlation coefficients derived from model result have good agreement with experimental results. As radial artery pulse plays important role in both allopathy and alternate medicine systems, this model can serve to study its clinical importance in detecting cardiac and respiratory pathologies.