Tuning Multidomain Hemodynamic Simulations to Match Physiological Measurements

In recent years, considerable progress has been made in creating more realistic models of the cardiovascular system, often based on patient-specific anatomic data, whereas comparatively little progress has been made on incorporating measured physiological data. We have developed a method to systematically adjust the parameters of three-element windkessel outlet boundary conditions of three-dimensional blood flow models such that desired features of pressure and flow waveforms are achieved. This tuning method was formulated as the solution of a nonlinear system of equations and employed a quasi-Newton method that was informed by a reduced-order model. The three-dimensional hemodynamic models were solved using a stabilized finite-element method incorporating deformable vessel walls. The tuning method was applied to an idealized common carotid artery, an idealized iliac arterial bifurcation, and a patient-specific abdominal aorta. The objectives for the abdominal aortic model were values of the maximum and minimum of the pressure waveform, an indicator of the pressure waveform’s shape, and the mean, amplitude, and diastolic mean of the flow waveform for an infrarenal measurement plane. The hemodynamic models were automatically generated and tuned by custom software with minimal user input. This approach enables efficient development of cardiovascular models for applications including detailed evaluation of cardiovascular mechanics, simulation-based design of medical devices, and patient-specific treatment planning.     

Pulse pressure waveform estimation using distension profiling with contactless optical probe

The pulse pressure waveform has, for long, been known as a fundamental biomedical signal and its analysis is recognized as a non-invasive, simple, and resourceful technique for the assessment of arterial vessels condition observed in several diseases. In the current paper, waveforms from non-invasive optical probe that measures carotid artery distension profiles are compared with the waveforms of the pulse pressure acquired by intra-arterial catheter invasive measurement in the ascending aorta. Measurements were performed in a study population of 16 patients who had undergone cardiac catheterization. The hemodynamic parameters: area under the curve (AUC), the area during systole (AS) and the area during diastole (AD), their ratio (AD/AS) and the ejection time index (ETI), from invasive and non-invasive measurements were compared. The results show that the pressure waveforms obtained by the two methods are similar, with 13% of mean value of the root mean square error (RMSE). Moreover, the correlation coefficient demonstrates the strong correlation. The comparison between the AUCs allows the assessment of the differences between the phases of the cardiac cycle. In the systolic period the waveforms are almost equal, evidencing greatest clinical relevance during this period. Slight differences are found in diastole, probably due to the structural arterial differences. The optical probe has lower variability than the invasive system (13% vs 16%). This study validates the capability of acquiring the arterial pulse waveform with a non-invasive method, using a non-contact optical probe at the carotid site with residual differences from the aortic invasive measurements.     

动脉压力波形分析在麻醉诱导期的应用

为探索动脉波形分析方法的临床意义，使用波形分离法与储存压力波模型对采集到的25例进行全麻手术的高龄患者的动脉压力波形进行波形分析，在获得[Pf]、[Pb]以及[Pe]、[Pr]等波形形态参数后，将诱导前后的参数变化量与临床生命指标变化量进行相关性分析。在本文的研究群体中，波形分离法与储存压力波模型的参数均与诱导中的血压和心率变化量有相关性，其中△[Pe]与临床指标△PP相关系数最高（r=0.926）。从生理病理学的角度对波形参数的变化进行解读，旨在探索波形分析在诱导期对全麻患者麻醉水平的应用价值，可为动脉压力波形分析及其应用提供新的理论基础和技术方案。     

Continuous Left Ventricular Ejection Fraction Monitoring by Aortic Pressure Waveform Analysis

We developed a technique to monitor left ventricular ejection fraction (EF) by model-based analysis of the aortic pressure waveform. First, the aortic pressure waveform is represented with a lumped parameter circulatory model. Then, the model is fitted to each beat of the waveform to estimate its lumped parameters to within a constant scale factor equal to the arterial compliance (C _a). Finally, the proportional parameter estimates are utilized to compute beat-to-beat absolute EF by cancelation of the C _a scale factor. In this way, in contrast to conventional imaging, EF may be continuously monitored without any ventricular geometry assumptions. Moreover, with the proportional parameter estimates, relative changes in beat-to-beat left ventricular end-diastolic volume (EDV), cardiac output (CO), and maximum left ventricular elastance (E _max) may also be monitored. To evaluate the technique, we measured aortic pressure waveforms, reference EF and EDV via standard echocardiography, and other cardiovascular variables from six dogs during various pharmacological influences and total intravascular volume changes. Our results showed overall EF and calibrated EDV root-mean-squared-errors of 5.6% and 4.1 mL, and reliable estimation of relative E _max and beat-to-beat CO changes. These results demonstrate, perhaps for the first time, the feasibility of estimating EF from only a blood pressure waveform.     

Doppler flow velocity waveforms of human fetal ductus arteriosus and branch pulmonary artery.

Doppler waveforms of the human fetal ductus arteriosus and the branch pulmonary artery are distinct in their shape and might reflect fetal cardiovascular hemodynamics and vessel wall characteristics. The waveform of ductus arteriosus had two peaks, a higher one in systole and a lower one in diastole. Both peaks had slow acceleration and deceleration and looked like two narrow base isosceles triangles. This unique waveform might be due to vessel wall characteristics and an instantaneous pressure gradient between the main pulmonary artery and descending aorta. The waveform of the branch pulmonary artery showed very steep acceleration with the onset of ejection followed by steep decline, then low velocity flow during diastole. The characteristic shape of the branch pulmonary artery might be related to high vascular resistance, decreased capacitance and the earlier reflection wave of pulmonary vessels.     

Mathematical model for interpretation of doppler velocity waveform indices

Various empirical indices such as the pulsatility index (PI) are widely used for quantitative analysis of Doppler ultrasound velocity waveforms. The physical interpretation of these indices was studied using a mathematical model. Although the method has more general applicability, this particular study was concerned with the umbilical-placental circulation. A lumped element electrical circuit equivalent was used, with each arterial branch represented by a resistor and a capacitor. The placental villous bed was modelled by a two-step parallel branching structure. Placental vascular disease was modelled either as obliteration of a fraction of the terminal branches, or as a fractional decrease in the radius of the vessels. The main features of both normal and abnormal umbilical artery waveforms can be reproduced by this simple model. Theoretical relationships between the velocity waveform indices and the lumped resistances and capacitance of the system were obtained for different input pressure functions. Over a wide range of physically reasonable conditions, the umbilical artery PI is approximately proportional to the ratio of the placental resistance to the umbilial artery resistance. The PI also depends on the pulsatility of the input pressure waveform. The Fourier pulsatility index was evaluated for an arbitrary pressure function, and shown to behave like (PI)² for the umbilical artery waveform.     

Time domain analysis of the arterial pulse in clinical medicine

The arterial pulse at any site is created by an impulse generated by the left ventricle as it ejects blood into the aorta, together with multiple impulses travelling in the opposite direction from reflecting sites in the peripheral circulation. The compound wave at any site depends on the pattern of ventricular ejection, the properties of large arteries, particularly their stiffness (which determines rate of propagation) and the distance to and impedance mismatch at reflecting sites. Physicians are familiar with waveform analysis in the time domain, as in the electrocardiogram (ECG) where the principal features are explicable on the basis of atrial depolarisation followed by ventricular depolarisation, then repolarisation. Effects of cardiac functional and structural disease can be inferred from the ECG. It is more difficult to make similar interpretations from the pulse waveform and clinicians usually use this only to count heart rate, extremes of the pressure pulse to express systolic and diastolic pressure, and (sometimes) time from wave foot to incisural notch to measure time of systole and diastole. More information can be gleaned from the shape of the arterial pressure wave through consideration of the factors which create it—on stiffening of large arteries with age, effects of drugs on smallest arteries, and changes in such arterial properties on left ventricular load and function. Such is a major challenge to future physicians. It is aided by better and more accurate methods for measuring flow and diameter as well as pressure waveforms, and by appropriate use of other analytic techniques such as analysis of the pulse in the frequency domain. Michael F. O’Rourke is a founding director of AtCor Medical, manufacturer of systems for analysing the arterial pulse.     

Adaptive neuro-fuzzy inference systems for analysis of internal carotid arterial Doppler signals

In this study, a new approach based on adaptive neuro-fuzzy inference system (ANFIS) was presented for detection of internal carotid artery stenosis and occlusion. The internal carotid arterial Doppler signals were recorded from 130 subjects that 45 of them suffered from internal carotid artery stenosis, 44 of them suffered from internal carotid artery occlusion and the rest of them were healthy subjects. The three ANFIS classifiers were used to detect internal carotid artery conditions (normal, stenosis and occlusion) when two features, resistivity and pulsatility indices, defining changes of internal carotid arterial Doppler waveforms were used as inputs. To improve diagnostic accuracy, the fourth ANFIS classifier (combining ANFIS) was trained using the outputs of the three ANFIS classifiers as input data. The proposed ANFIS model combined the neural network adaptive capabilities and the fuzzy logic qualitative approach. Some conclusions concerning the impacts of features on the detection of internal carotid artery stenosis and occlusion were obtained through analysis of the ANFIS. The performance of the ANFIS model was evaluated in terms of classification accuracies and the results confirmed that the proposed ANFIS classifiers have some potential in detecting the internal carotid artery stenosis and occlusion. The ANFIS model achieved accuracy rates which were higher than that of the stand-alone neural network model.     

Pressure and volume measurements from the eye for detecting possible arterial obstruction

Detection and evaluation of functionally significant carotid occlusive disease are effectively achieved by noninvasive pressure and/or volume measurements from the eye. Ocular arterial blood pressure is measured by applying either direct compression or suction to evaluate intraocular pressure to the point of arterial collapse. Carotid blood flow is evaluated as it affects ocular volume waveforms, which result from the difference between pulsatile arterial flow and relatively constant venous flow. The relationship between noninvasive measurements from the eyes and carotid blood flow can be predicted using simple models of the cervical-cerebral circulatory system. Proper models verify clinically observed correlations between pressure and volume measurements from the eye and the underlying carotid occlusive disease. Electrical analog circuits provide a method for varying model parameters to simulate abnormalities, producing waveforms with good similarity to waveforms recorded from patients with known vascular or ophthalmic pathology. Further model refinements can be contributed by interested investigators. By using the improved models the strengths and weaknesses of current tests and techniques can then be better defined. Techniques that have been widely used for screening and evaluating potential stroke patients can thereby be modified to give improved functional analysis of these patients.     

The influence of a nonlinear resistance element upon in vitro aortic pressure tracings and aortic valve motions

In vitro testing of biological heart valves requires pressure and flow waveforms closely simulating natural conditions, which are mainly influenced by the characteristics of the vascular system. Simulation of the arterial function in artificial circulations was mostly performed by the useful Windkessel model but sometimes failed by generating inadequate systolic pressures. The integration of a novel nonlinear resistance element may improve the Windkessel function. Native porcine aortic valves were studied in a mock circulation with a novel nonlinear resistance element combined with the Windkessel compared with an aperture plate resistance. Pressure and flow measurements were performed at varying heart rates and stroke volumes and analyzed in the time and frequency domain. Aortic valve motions were evaluated using high speed video recording. With the classical afterload configuration including an aperture plate resistance, the pressure tracings showed a nonphysiologic decrease of pressure during systole after early peak pressure. By integration of the novel nonlinear resistance, peak systolic pressure occured later, peak pressure was higher, and the pressure waveform was more physiologically shaped. Leaflet motions of the aortic valves were less oscillatory and compared well with in vivo characteristics. In conclusion, a novel nonlinear resistance element in a mock circulation has the potential to provide more physiologic aortic pressure waveforms as influencing aortic valve dynamics and thus may be a helpful tool for investigation of biological heart valves.     

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.     

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.     

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.     

Mechanical principles. Arterial stiffness and wave reflection.

Arterial (and predominantly aortic) stiffening with age is now acknowledged as the cause of isolated systolic hypertension, and the predominant cause of cardiac failure in the elderly. Aortic stiffening is gauged clinically from increase in brachial pulse pressure, but this underestimates change with age, since aortic pulse pressure increases far more than brachial (on account of substantial amplification of the peripheral arterial pressure pulse in young adults). Aortic stiffness can be measured as pulse wave velocity, but this too underestimates ill effects on the heart and central vessels, since the direct effect is amplified by early return of wave reflection. Ill effects of arterial stiffening can best be assessed through analysis of pressure wave contour from the carotid or radial site. Exploitation of relatively constant brachial transfer function enables the central aortic pressure wave to be synthesised from the radial pulse. This new clinical approach links traditional sphygmography (originally introduced in France) with conventional cuff sphygmomanometry, and is being evaluated in clinical and epidemiological studies.     

Non-invasive pulsatile arterial pressure and stroke volume changes from the human finger

In this paper we review recent developments in the methodology of non-invasive finger arterial pressure measurement and the information about arterial flow that can be obtained from it. Continuous measurement of finger pressure based on the volume-clamp method was introduced in the early 1980s both for research purposes and for clinical medicine. Finger pressure tracks intra-arterial pressure but the pressure waves may differ systematically both in shape and magnitude. Such bias can, at least partly, be circumvented by reconstruction of brachial pressure from finger pressure by using a general inverse anti-resonance model correcting for the difference in pressure waveforms and an individual forearm cuff calibration. The Modelflow method as implemented in the Finometer computes an aortic flow waveform from peripheral arterial pressure by simulating a non-linear three-element model of the aortic input impedance. The methodology tracks fast changes in stroke volume (SV) during various experimental protocols including postural stress and exercise. If absolute values are required, calibration against a gold standard is needed. Otherwise, Modelflow-measured SV is expressed as change from control with the same precision in tracking. Beat-to-beat information on arterial flow offers important and clinically relevant information on the circulation beyond what can be detected by arterial pressure.     

Subject-specific estimation of central aortic blood pressure via system identification: preliminary in-human experimental study

This paper demonstrates preliminary in-human validity of a novel subject-specific approach to estimation of central aortic blood pressure (CABP) from peripheral circulatory waveforms. In this “Individualized Transfer Function” (ITF) approach, CABP is estimated in two steps. First, the circulatory dynamics of the cardiovascular system are determined via model-based system identification, in which an arterial tree model is characterized based on the circulatory waveform signals measured at the body’s extremity locations. Second, CABP waveform is estimated by de-convolving peripheral circulatory waveforms from the arterial tree model. The validity of the ITF approach was demonstrated using experimental data collected from 13 cardiac surgery patients. Compared with the invasive peripheral blood pressure (BP) measurements, the ITF approach yielded significant reduction in errors associated with the estimation of CABP, including 1.9–2.6 mmHg (34–42 %) reduction in BP waveform errors (p < 0.05) as well as 5.8–9.1 mmHg (67–76 %) and 6.0–9.7 mmHg (78–85 %) reductions in systolic and pulse pressure (SP and PP) errors (p < 0.05). It also showed modest but significant improvement over the generalized transfer function approach, including 0.1 mmHg (2.6 %) reduction in BP waveform errors as well as 0.7 (20 %) and 5.0 mmHg (75 %) reductions in SP and PP errors (p < 0.05).     

Physiological simulation of blood flow in the aorta: Comparison of hemodynamic indices as predicted by 3-D FSI, 3-D rigid wall and 1-D models

Interest in patient-specific blood-flow circulation modeling has increased substantially in recent years. The availability of clinical data for geometric and elastic properties together with efficient numerical methods has now made model rendering feasible. This work uses 3-D fluid–structure interaction (FSI) to provide physiological simulation resulting in modeling with a high level of detail. Comparisons are made between results using FSI and rigid wall models. The relevance of wall compliance in determining parameters of clinical importance, such as wall shear stress, is discussed together with the significance of differences found in the pressure and flow waveforms when using the 1-D model.Patient-specific geometry of the aorta and its branches was based on MRI angiography data. The arterial wall was created with a variable thickness. The boundary conditions for the fluid domain were pressure waveform at the ascending aorta and flow for each outlet. The waveforms were obtained using a 1-D model validated by in vivo measurements performed on the same person. In order to mimic the mechanical effect of surrounding tissues in the simulation, a stress–displacement relation was applied to the arterial wall.The temporal variation and spatial patterns of wall shear stress are presented in the aortic arch and thoracic aorta together with differences using rigid wall and FSI models. A comparison of the 3-D simulations to the 1-D model shows good reproduction of the pressure and flow waveforms.     

Abdominal aortic aneurysm detection by common femoral artery Doppler ultrasound waveform analysis

The aim of this research was to determine the effects of abdominal aortic aneurysm (AAA) on blood flow patterns in the common femoral artery (CFA) and to determine the feasibility of detecting AAA by analysis of the CFA Doppler waveform. CFA Doppler waveforms were measured from 30 patients with AAA and 30 normal patients without significant atherosclerotic disease. On visual inspection of the CFA waveforms five features were noted, predominantly in the AAA group, as being different from a normal CFA waveform: (1) spectral broadening on the systolic down stroke; (2) transient velocity spikes on the systolic down stroke; (3) an irregular reverse flow pattern; (4) simultaneous forward and reverse flow; and (5) waveform elongation with the reverse flow component extending throughout diastole. Based on visual identification of these five features it was possible to predict AAA with 93% sensitivity and 70% specificity in patients without significant atherosclerotic disease.     

Estimation of arterial compliance in aortic regurgitation: three methods evaluated in pigs

Three methods for measuring arterial compliance when aortic regurgitation is present are examined. The first two methods are based on a Windkessel model composed of two elements, compliance C and resistance R. Arterial compliance was estimated from diastolic pressure waveforms and diastolic regurgitant flow for one method, and from systolic aortic pressure waveforms and systolic flow for the other method. The third method was based on a three-element Windkessel model, composed of characteristic resistance r, compliance C and resistance R. In this method arterial compliance was calculated by adjusting the model to the modulus and phase of the first harmonic term of the aortic input impedance. The three methods were compared and validated in six anaesthetised pigs over a broad range of aortic pressures. The three methods were found to give quantitatively similar estimates of arterial compliance at mean aortic pressures above 60 mm Hg. Below 60 mm Hg, estimates of arterial compliance varied widely, probably because of poor validity of the Windkessel models in the low pressure range.