Physical modelling of the arterial wall. Part 1: Testing of tubes of various materials

Blood Pressure Measurement: From Cuff-Based to Contactless Monitoring

Blood pressure (BP) determines whether a person has hypertension and offers implications as to whether he or she could be affected by cardiovascular disease. Cuff-based sphygmomanometers have traditionally provided both accuracy and reliability, but they require bulky equipment and relevant skills to obtain precise measurements. BP measurement from photoplethysmography (PPG) signals has become a promising alternative for convenient and unobtrusive BP monitoring. Moreover, the recent developments in remote photoplethysmography (rPPG) algorithms have enabled new innovations for contactless BP measurement. This paper illustrates the evolution of BP measurement techniques from the biophysical theory, through the development of contact-based BP measurement from PPG signals, and to the modern innovations of contactless BP measurement from rPPG signals. We consolidate knowledge from a diverse background of academic research to highlight the importance of multi-feature analysis for improving measurement accuracy. We conclude with the ongoing challenges, opportunities, and possible future directions in this emerging field of research.

A structural approach to 3D-printing arterial phantoms with physiologically comparable mechanical characteristics: Preliminary observations

Pulse wave behavior is important in cardiovascular pathophysiology and arterial phantoms are valuable for studying arterial function. The ability of phantoms to replicate complex arterial elasticity and anatomy is limited by available materials and techniques. The feasibility of improving phantom performance using functional structure designs producible with practical 3D printing technologies was investigated. A novel corrugated wall approach to separate phantom function from material properties was investigated with a series of designs printed from polyester-polyurethane using a low-cost open-source fused filament fabrication 3D printer. Nonpulsatile pressure-diameter data was collected, and a mock circulatory system was used to observe phantom pulse wave behavior and obtain pulse wave velocities. The measured range of nonpulsatile Peterson elastic strain modulus was 5.6–19 to 12.4–33.0 kPa over pressures of 5–35 mmHg for the most to least compliant designs respectively. Pulse wave velocities of 1.5–5 m s⁻¹ over mean pressures of 7–55 mmHg were observed, comparing favorably to reported in vivo pulmonary artery measurements of 1–4 m s⁻¹ across mammals. Phantoms stiffened with increasing pressure in a manner consistent with arteries, and phantom wall elasticity appeared to vary between designs. Using a functional structure approach, practical low-cost 3D-printed production of simple arterial phantoms with mechanical properties that closely match the pulmonary artery is possible. Further functional structure design development to expand the pressure range and physiologic utility of dir"ectly 3D-printed phantoms appears warranted.

Wave propagation through a viscous fluid-filled elastic tube under initial pressure: theoretical and biophysical model

The velocity of propagation of pulse waves through the arteries is one of the indicators of the health of the cardiovascular system. By measuring the pulse wave velocity, cardiologists estimate the elasticity of the blood vessel walls and the changes that occur with aging. When the Moens-Korteweg equation is used in analysis, it leads to an erroneous assessment. This paper presents the solution of Navier-Stokes equations for propagation of pulse waves through an elastic tube filled with viscous fluid under initial pressure. The equation for pulse wave velocity depending on viscosity, density and initial fluid pressure, density and elasticity of the wall and geometry of the tube is derived. The results of the equation were compared with experimental results measured using a biophysical model of the cardiovascular system.

In Vitro Validation of 4D Flow MRI for Local Pulse Wave Velocity Estimation

PURPOSE

Arterial stiffness has predictive value for cardiovascular disease (CVD). Local artery stiffness can provide insight on CVD pathology and may be useful for diagnosis and prognosis. However, current methods are invasive, require real-time expertise for measurement, or are limited by arterial region. 4D Flow MRI can non-invasively measure local stiffness by estimating local pulse wave velocity (PWV). This technique can be applied to vascular regions, previously accessible only by invasive stiffness measurement methods. MRI PWV data can also be analyzed post-exam. However, 4D Flow MRI requires validation before it is used in vivo to measure local PWV.

METHODS

PWV, calculated from 4D Flow MRI and a benchtop experiment, was compared with petersons elastic modulus (PEM) of in vitro models. PEM was calculated using high-speed camera images and pressure transducers. Three transit-time algorithms were analyzed for PWV measurement accuracy and precision.

RESULTS

PWV from 4D Flow MRI and reference benchtop experiments show strong correlation with PEM (R² = 0.99). The cross correlation transit-time algorithm showed the lowest percent difference between 4D Flow MRI and benchtop experiments (4-7%), and the point to point of 50% upstroke algorithm had the highest transit-time vs. distance data average R² (0.845).

CONCLUSION

4D Flow MRI is a feasible method for estimating local PWV in simple in vitro models and is a viable tool for clinical analysis. In addition, choice in transit-time algorithm depends on flow waveform shape and arterial region. This study strengthens the validity of 4D Flow MRI local PWV measurement in simple models. However, this technique requires validation in more complex models before it is used in vivo.

Endotension is Influenced by Aneurysm Volume: Experimental Findings

Purpose:

To investigate in an in vitro model whether and to what extent pressure is influenced by aneurysm size.

Methods:

Latex aneurysms of 3 different volumes (24, 30, and 81 mL) were inserted into an in vitro circulation model. The systemic mean pressure (SPmean) was varied from 50 to 120 mmHg. The aneurysms were excluded using a woven polyethylene graft. Aneurysm sac mean pressure (ASPmean) was measured.

Results:

In the in vitro model, endovascular aneurysm repair created a closed chamber without endoleak but showed a relevant aneurysm sac pressure. At an SPmean of 80 mmHg, the ASPmean was 42.0 ± 0.6 mmHg in the 24-mL aneurysm, 40.5 ± 0.5 mmHg in the 30-mL model, and 19.3 ± 0.5 mmHg in the 81-mL aneurysm (p < 0.05). The ASPmean rose with increasing SPmean and was inversely dependent on the aneurysm volume.

Conclusions:

This in vitro model demonstrated that the sac mean pressure correlated to the systemic pressure and that a greater aneurysm volume reduced aneurysm sac pressure. These data highlight the need for further studies regarding endotension.

Effect of viscosity on the wave propagation: Experimental determination of compression and expansion pulse wave velocity in fluid-fill elastic tube

The velocity by which the disturbance travels through the medium is the wave velocity. Pulse wave velocity is one of the main parameters in hemodynamics. The study of wave propagation through the fluid-fill elastic tube is of great importance for the proper biophysical understanding of the nature of blood flow through of cardiovascular system. The effect of viscosity on the pulse wave velocity is generally ignored. In this paper we present the results of experimental measurements of pulse wave velocity (PWV) of compression and expansion waves in elastic tube. The solutions with different density and viscosity were used in the experiment. Biophysical model of the circulatory flow is designed to perform measurements. Experimental results show that the PWV of the expansion waves is higher than the compression waves during the same experimental conditions. It was found that the change in viscosity causes a change of PWV for both waves. We found a relationship between PWV, fluid density and viscosity.

Pulse Wave Velocity Prediction and Compliance Assessment in Elastic Arterial Segments

Pressure wave velocity (PWV) is commonly used as a clinical marker of vascular elasticity. Recent studies have increased clinical interest in also analyzing the impact of heart rate, blood pressure, and left ventricular ejection time on PWV. In this article we focus on the development of a theoretical one-dimensional model and validation via direct measurement of the impact of ejection time and peak pressure on PWV using an in vitro hemodynamic simulator. A simple nonlinear traveling wave model was developed for a compliant thin-walled elastic tube filled with an incompressible fluid. This model accounts for the convective fluid phenomena, elastic vessel deformation, radial motion, and inertia of the wall. An exact analytical solution for PWV is presented which incorporates peak pressure, ejection time, ejection volume, and modulus of elasticity. To assess arterial compliance, the solution is introduced in an alternative form, explicitly determining compliance of the wall as a function of the other variables. The model predicts PWV in good agreement with the measured values with a maximum difference of 3.0%. The results indicate an inverse quadratic relationship ([Formula: see text]) between ejection time and PWV, with ejection time dominating the PWV shifts (12%) over those observed with changes in peak pressure (2%). Our modeling and validation results both explain and support the emerging evidence that, both in clinical practice and clinical research, cardiac systolic function related variables should be regularly taken into account when interpreting arterial function indices, namely PWV.

Endotension is Influenced by Wall Compliance in a Latex Aneurysm Model

OBJECTIVES

Even though endovascular aneurysm repair (EVAR) creates a closed chamber except for patent branches, the intra-sac pressure is never zero. This study was designed to investigate whether, and to what extent, aneurysm wall compliance influences intra-sac pressure.

DESIGN

In vitro experimental study.

METHODS

Aneurysm models with six and 12 latex layers were produced, resulting in elastic and stiff circumferential compliance (3.5 +/- 0.5 and 0.9 +/- 0.3%/100 mmHg, respectively). The models with an 18 mm internal neck and maximum aneurysm diameter of 60 mm were inserted into an in vitro circulation system. The systemic mean pressure (SPmean) was varied from 50 to 120 mmHg. After the aneurysm was excluded with a knitted polyethylene graft, aneurysm sac mean pressure (ASPmean) and aneurysm sac pulse pressure (ASPpulse) were measured. Data are presented as mean +/- SD. Statistics were performed using repeated measurements of variance; p<0.05 was considered significant.

RESULTS

In the model EVAR created a closed chamber without endoleak, but with an aneurysm sac pressure related to wall compliance. In the elastic aneurysm model with six latex coats the aneurysm sac mean pressure (ASPmean) and the aneurysm sac pulse pressure (ASPpulse) at all systemic pressures were significantly lower than they were in the stiffer model with 12 latex coats (p<0.05). At a SPmean of 90 mmHg, the ASPmean was 21.0 +/- 0.9 mmHg (six latex coats) and 26.0 +/- 0.2 mmHg (12 latex coats) (p<0.05), the ASPpulse was 5.7 +/- 0.2 mmHg (six latex coats) and 8.8 +/- 0.3 mmHg (12 latex coats) (p<0.05).

CONCLUSIONS

This in vitro model demonstrated that the aneurysm sac mean pressure (ASPmean) and the aneurysm sac pulse pressure (ASPpulse) were significantly influenced by the compliance of the aneurysm wall. These data highlight the need for further studies regarding endotension.

Measurements of wave speed and reflected waves in elastic tubes and bifurcations

Wave intensity analysis is a time domain method for studying waves in elastic tubes. Testing the ability of the method to extract information from complex pressure and velocity waveforms such as those generated by a wave passing through a mismatched elastic bifurcation is the primary aim of this research. The analysis provides a means for separating forward and backward waves, but the separation requires knowledge of the wave speed. The PU-loop method is a technique for determining the wave speed from measurements of pressure and velocity, and investigating the relative accuracy of this method is another aim of this research. We generated a single semi-sinusoidal wave in long elastic tubes and measured pressure and velocity at the inlet, and pressure at the exit of the tubes. In our experiments, the results of the PU-loop and the traditional foot-to-foot methods for determining the wave speed are comparable and the difference is on the order of 2.9+/-0.8%. A single semi-sinusoidal wave running through a mismatched elastic bifurcation generated complicated pressure and velocity waveforms. By using wave intensity analysis we have decomposed the complex waveforms into simple information of the times and magnitudes of waves passing by the observation site. We conclude that wave intensity analysis and the PU-loop method combined, provide a convenient, time-based technique for analysing waves in elastic tubes.

Fixed region of nondistensibility after coarctation repair: in vitro validation of its influence on Doppler peak velocities

After coarctectomy, local loss of distensibility is noted in addition to mild anatomic narrowing. We hypothesize that the increased Doppler peak velocities measured at the aortic isthmus in these patients partly reflect obstruction secondary to the stiff surgical scar. The hypothesis was studied in a pulsatile hydraulic model. Thirty-one patients (13.0 +/- 4.0 years of age), 10.5 +/- 4.7 years after coarctectomy by end-to-end anastomosis, were studied clinically and echocardiographically. Indexes of distensibility were calculated. The effect of isolated increased stiffness was studied in vitro with a stiff and a compliant 1:1 scale latex model of the aorta mounted in a pulsatile full-scale circulation loop. Local stiffening was obtained by a rigid ring mounted around the aorta, fitted to the dimension of the unloaded aorta. For different pressure and flow regimens, pressures and Doppler velocities were measured across the ring. Mean peak velocities at the surgical scar were 2.2 +/- 0.4 m/s. Mild anatomic stenosis was present. All distensibility indexes indicated locally increased stiffness (P <.001). In the stiff latex model, Doppler peak velocities increased from 1.89 +/- 0.04 m/s to 2.32 +/- 0.06 m/s (P <.03); in the compliant model, from 1.15 +/- 0.03 m/s to 1.79 +/- 0.05 m/s (P <.001). The increase of Doppler peak velocities depends on model compliance only and is independent of flow rate, length of the noncompliant segment, and viscosity of the perfusion fluid. Velocities do not change when semicircular stiffening is applied. We have demonstrated in vitro that isolated local nondistensibility leads to vessel narrowing during vascular distension. The relative contribution of local scar stiffness in the increase of Doppler peak velocities after coarctectomy was hereby assessed.

Effects of frictional losses and pulsatile flow on the collapse of stenotic arteries

High-grade stenosis can produce conditions in which the artery may collapse. A one-dimensional numerical model of a compliant stenosis was developed from the collapsible tube theory of Shapiro. The model extends an earlier model by including the effects of frictional losses and unsteadiness. The model was used to investigate the relative importance of several physical parameters present in the in vivo environment. The results indicated that collapse can occur within the stenosis. Frictional loss was influential in reducing the magnitude of collapse. Large separation losses could prevent collapse outright even with low downstream resistances. However, the degree of stenosis was still the primary parameter governing the onset of collapse. Pulsatile solutions demonstrated conditions that produce cyclic collapse within the stenosis. This study predicts certain physiologic conditions in which collapse of arteries may occur for high-grade stenoses.

Fluid dynamics of a partially collapsible stenosis in a flow model of the coronary circulation

The influence of passive vasomotion on the pressure drop-flow (delta P-Q) characteristics of a partially compliant stenosis was studied in an in vitro model of the coronary circulation. Twelve stenosis models of different severities (50 to 90 percent area reduction) and degrees of flexible wall (0 to 1/2 of the wall circumference) were inserted into thin-walled latex tubing and pressure and flow data were collected during simulated cardiac cycles. In general, the pressure drop increased with increasing fraction of flexible wall for a given flow rate and stenosis severity. The magnitude of this effect was directly dependent upon the underlying stenosis severity. The diastolic delta P-Q relationship of severe, compliant models exhibited features of partial collapse with an increase in pressure drop at a decreasing flow rate. It is concluded that passive vasomotion of a normal wall segment at an eccentric stenosis in response to periodic changes in intraluminal pressure causes dimensional changes in the residual lumen area which can strongly affect the hemodynamic characteristics of the stenosis during the cardiac cycle. This mechanism may have important implications for the onset of plaque fracture and the prediction of the functional significance of a coronary stenosis based on quantitative angiogram analysis.

Modeling of the wave transmission properties of large arteries using nonlinear elastic tubes

We propose a new, simple way of constructing elastic tubes which can be used to model the nonlinear elastic properties of large arteries. The tube models are constructed from a silicon elastomer (Sylgard 184, Dow Corning), which exhibits a nonlinear behavior with increased stiffness at high strains. Tests conducted on different tube models showed that, with the proper choice of geometric parameters, the elastic properties, in terms of area-pressure relation and compliance, can be similar to that of real arteries.

Hydraulic input impedance measurements in physical models of the arterial wall

A white noise method was used to measure the hydraulic input impedance and transmission characteristics in physical models of an arterial system made of single, unbranched latex tubes. The experimentally obtained impedance curves show a rise in modulus and a positive phase at high frequencies in the absence of wave reflections. Using the impedance moduli in the presence of wave reflections, wave velocity and attenuation were calculated. The influence of wall nonlinearity on hydraulic impedance was also examined. It is concluded that, in the model used neither wave reflections nor wall nonlinearity can account for the deviations of the experimental impedance curves from the theoretically predicted ones. Impedance moduli in the presence of reflections may be used to study transmission characteristics (wave velocity and attenuation) of the model.

Effect of stenosis on wall motion. A possible mechanism of stroke and transient ischemic attack

The mechanism by which atherosclerotic plaque causes stroke and transient ischemic attack is not fully understood. One possibility is that the plaque stenosis may set up hemodynamic conditions causing local arterial wall collapse. Arterial wall collapse may, in turn, affect the integrity of the plaque. This study was designed to define the effects of stenosis on the production of arterial wall collapse using a latex tube model. Stenoses ranging up to 81% by diameter were tested in a Starling resistor chamber under pulsatile pressure conditions upstream of the tube. Increasing the degree of stenosis progressively decreased the external pressure necessary to produce collapse, from 37 mm Hg with the 0% stenosis to 24 mm Hg for the 81% stenosis. The stenoses greater than 70% produced a new phenomenon of "systolic wall collapse" just distal to the stenosis. The maximum diameter decrease was 2.83 mm from the baseline diameter of 6.41 mm. Cyclic wall motion just downstream of the stenosis increased with the increased degree of stenosis from 0.34 mm at 0% stenosis to -1.28 mm at 75% stenosis. The phenomena are discussed in terms of simplified Bernoulli pressure drops. We conclude that local arterial stenosis can produce conditions favorable for wall collapse and increased wall motion at physiologic pressure and flow. This collapse may be important in the development of atherosclerotic plaque fracture and subsequent thrombosis or distal embolization.

Circumferential and longitudinal viscoelasticity of human iliac arterial segments in vitro

A random noise technique was used to measure the circumferential and longitudinal dynamic elasticity of human common iliac arteries in vitro. For circumferential measurements the frequency ranged from 0.016 to 20 Hz; the phase lag of diameter behind pressure was found to be almost constant (about 5 degrees) and the Young's modulus of elasticity to increase rapidly at first and then more gradually beyond 1-2 Hz. Somewhat similar results were obtained for longitudinal elasticity. Arterial segments were found to be anisotropic when kept at in vivo length and under normal distending pressure.

Physical modelling of the arterial wall. Part 2: Simulation of the non-linear elasticity of the arterial wall

In part 1 it was established that the elasticity of tubes made from natural rubber is, at low pressures, close to that of the arterial wall; in this part a method is described for reinforcing the walls of rubber tubes so that they may be used for simulating arterial elasticity at higher pressures. The technique is versatile in that, within reasonable limits, wall non-linearity can be modified; tubes with non-linear wall elasticity were produced and tested. A modification of the method enabled us to produce geometrically non-uniform rubber tubes which may be useful in the construction of physical models of the arterial system.