Reduced-order modeling of blood flow for noninvasive functional evaluation of coronary artery disease

Biomechanics and Modeling in Mechanobiology - We present a novel computational approach, based on a parametrized reduced-order model, for accelerating the calculation of pressure drop along blood...     

Venous occlusion plethysmography reduces arterial diameter and flow velocity

The measurement of peripheral blood flow by plethysmography assumes that the cuff pressure required for venous occlusion does not decrease arterial inflow. However, studies in five normal subjects suggested that calf blood flow measured with a plethysmograph was less than arterial inflow calculated from Doppler velocity measurements. We hypothesized that the pressure required for venous occlusion may have decreased arterial velocity. Further studies revealed that systolic diameter of the superficial femoral artery under a thigh cuff decreased from 7.7 +/- 0.4 to 5.6 +/- 0.7 mm (P less than 0.05) when the inflation pressure was increased from 0 to 40 mmHg. Cuff inflation to 40 mmHg also reduced mean velocity 38% in the common femoral artery and 47% in the popliteal artery. Inflation of a cuff on the arm reduced mean velocity in the radial artery 22% at 20 mmHg, 26% at 40 mmHg, and 33% at 60 mmHg. We conclude that inflation of a cuff on an extremity to low pressures for venous occlusion also caused a reduction in arterial diameter and flow velocity.     

Influence of noninvasive peripheral arterial blood pressure measurements on assessment of dynamic cerebral autoregulation.

Assessment of dynamic cerebral autoregulation (CA) requires continuous recording of arterial blood pressure (ABP). In humans, noninvasive ABP recordings with the Finapres device have often been used for this purpose. We compared estimates of dynamic CA derived from Finapres with those from invasive recordings in the aorta. Measurements of finger noninvasive ABP (Finapres), intra-aortic ABP (Millar catheter), surface ECG, transcutaneous CO2, and bilateral cerebral blood flow velocity (CBFV) in the middle cerebral arteries were simultaneously and continuously recorded in 27 patients scheduled for percutaneous coronary interventions. Phase, gain, coherence, and CBFV step response from both the Finapres and intra-arterial catheter were estimated by transfer function analysis. A dynamic autoregulation index (ARI) was also calculated. For both hemispheres, the ARI index and the CBFV step response recovery at 4 s were significantly greater for the Finapres-derived estimates than for the values obtained from aortic pressure. The transfer function gain for frequencies <0.1 Hz was significantly smaller for the Finapres estimates. The phase frequency response was significantly greater for the Finapres estimates at frequencies >0.1 Hz, but not at lower frequencies. The Finapres gives higher values for the efficiency of dynamic CA compared with values derived from aortic pressure measurements, as indicated by biases in the ARI index, CBFV step response, gain, and phase. Despite the significance of these biases, their relatively small amplitude indicates a good level of agreement between indexes of CA derived from the Finapres compared with corresponding estimates obtained from invasive measurements of aortic ABP.     

Training increases muscle blood flow in rats with peripheral arterial insufficiency

This study investigated the effect of physical training on muscle blood flow (BF) in rats with peripheral arterial insufficiency during treadmill running. Bilateral stenosis of the femoral artery of adult rats (300-350 g) was performed to reduce exercise hyperemia in the hindlimb but not limit resting muscle BF. Rats were divided into normal sedentary, acute stenosed (stenosed 3 days before the experiment), stenosed sedentary (limited to cage activity), and stenosed trained (run on a treadmill by a progressively intense program, up to 50-60 min/day, 5 days/wk for 6-8 wk). Hindlimb BF was determined with 85Sr- and 141Ce-labeled microspheres at a low (20 m/min) and high treadmill speed (30-40 m/min depending on ability). Maximal hindlimb BF was reduced to approximately 50% normal in the acute stenosed group. Total hindlimb BF (81 +/- 5 ml.min-1.100 g-1) did not change in stenosed sedentary animals with 6-8 wk of cage activity, but a redistribution of BF occurred within the hindlimb. Two factors contributed to a higher BF to the distal limb muscle of the trained animals. A redistribution BF within the hindlimb occurred in stenosed trained animals; distal limb BF increased to approximately 80% (P less than 0.001) of the proximal tissue. In addition, an increase in total hindlimb BF with training indicates that collateral BF has been enhanced (P less than 0.025). The associated increase in oxygen delivery to the relatively ischemic muscle probably contributed to the markedly improved exercise tolerance evident in the trained animals.     

Comparative plethysmography; evidence for a hydrostatic effect on foot blood flow

Blood flow in the right foot of 11 subjects was measured simultaneously by a strain gauge placed around the mid metatarsal circumference of the foot and a water displacement plethysmograph in which the foot was resting. A close linear correlation (r = 0.88) between the results of the two methods existed over a wide range of blood flows. It was apparent however that blood flow at the mid metatarsal region of the foot was only about 30% of the total foot blood flow measured by the plethysmograph. The likely cause of this finding is the varying proportion of bone to soft tissue along the length of the foot. It was observed that the strain gauge estimates of blood flow increased two to three fold when the plethysmograph was emptied, an effect that was abolished by refilling the plethysmograph. These changes were highly statistically significant (P less than 0.01) in all ten subjects in whom this comparison was made. The application of progressively increasing hydrostatic pressure in a further 4 subjects demonstrated that the reduction in blood flow was proportional to the pressure applied. Explanations for this effect based upon small temperature and pressure changes altering strain gauge performance are excluded. Three mechanisms are proposed, based upon an increase in venous leakage, a reduction in arterial inflow and the consequence of increased capillary filling occurring as a result of hydrostatic pressure within the plethysmograph.     

Comparison of two plethysmography systems in assessment of forearm blood flow.

Venous occlusion plethysmography is widely used to assess forearm blood flow (FBF). We compared the established Hokanson system (HEC4) with a newly developed Filtrass 2001 system (F2001). The HEC4 uses mercury-in-Silastic strain gauges, whereas F2001 detects volume changes with a nonmercury linear displacement device. The aim of this study was to evaluate the new F2001 against the HEC4 in terms of repeatability and systematic bias. Ten subjects were studied on 4 separate days in random order using either the HEC4 on both arms, the F2001 on both arms, the HEC4 on the right arm with the F2001 on the left, or the F2001 on the right arm and the HEC4 on the left. Stroop's colored word conflict test and postocclusive hyperemia were used to increase FBF, and lower body negative pressure was used to lower FBF. Stroop's colored word conflict test and lower body negative pressure increased (24.6 +/- 1.5%, n = 240, P < 0.0001) and decreased (18.7 +/- 0.8%, n = 240, P < 0.0001) FBF, respectively. Postocclusive hyperemia after occlusion times of 5, 8, and 13 min substantially increased FBF by 390 +/- 86, 756 +/- 217, and 851 +/- 132%, respectively. Repeatability was not different between the devices (0.10 +/- 2.37 vs. -0.47 +/- 1.92 l/min, n = 125, P > 0.05), and there was no systematic bias. The F2001 is a newly developed plethysmography system that does not utilize mercury and is suitable for assessing changes of FBF in physiological studies.     

Small disturbance in arterial blood flow

The behaviour of a small disturbance in an arterial blood flow has been studied analytically. The growth equation governing growth or decay of a disturbance has been obtained and solved. The behaviour of wave amplitude has been investigated as the wave propagates in time. The application of results to the human arterial system shows that the shock waves are not expected under normal physiological conditions. In the case of a pathologically increased pressure rise at the root of aorta, shock-like transitions may develop in the periphery. It is observed that the friction effects are to resist the tendency of shock formation in arteries.     

Calf blood flow and posture: Doppler ultrasound calibrated by plethysmography.

A procedure was developed that enables measurement of rapid variations in calf blood flow during voluntary rhythmic contraction of the calf muscles in supine, sitting, and standing positions. During the exercise, maximum blood velocity is measured by Doppler ultrasound equipment in the popliteal artery. The Doppler signals are calibrated by plethysmography to enable calculation of blood flow during exercise in ml.100 ml-1.min-1. Knowledge of the cross-sectional area of the vessel and the angle of insonation is not required in this procedure. Evaluation of the calibration method with 10 healthy volunteers showed that for each subject a new calibration was necessary after a change in posture; the relationship between the blood flow and the maximum Doppler frequency averaged over one heart cycle was linear for each calibration.     

Measurement of pulsatile limb and finger blood flow by electrical impedance plethysmography: Criteria for the diagnosis of abnormal flow

The range of pulsatile arm and finger blood flow, measured by electrical impedance plethysmography, has been investigated in a hospital ward. The range of absolute blood flows, in ml min⁻¹, was found to be too wide to be used as a standard for identifying single blood flow readings as being abnormal. A blood flow ratio was calculated by dividing the blood flow in the right forearm or middle finger by the blood flow in the left forearm or middle finger. This ratio was found to have a clearly defined range. A blood flow in a unilaterally injured or otherwise abnormal arm or finger was considered to be significantly altered if the blood flow ratio fell outside the previously defined normal range. The diagnosis of significantly altered arm and finger blood flow from abnormalities in the blood flow ratio was tested in a series of experiments, in which artificial changes in upper limb flow were created by high elevation of the right hand. The ratio was measured in 11 patients with unilateral upper limb injuries and in 3 patients who required an urgent assessment of the upper limb circulation. Abnormalities in the ratio were identified in 12 out of 18 subjects after high elevation of the hand and in 8 out of the 14 patients.     

Pulsatile spiral blood flow through arterial stenosis

Pulsatile spiral blood flow in a modelled three-dimensional arterial stenosis, with a 75% cross-sectional area reduction, is investigated by using numerical fluid dynamics. Two-equation k-ω model is used for the simulation of the transitional flow with Reynolds numbers 500 and 1000. It is found that the spiral component increases the static pressure in the vessel during the deceleration phase of the flow pulse. In addition, the spiral component reduces the turbulence intensity and wall shear stress found in the post-stenosis region of the vessel in the early stages of the flow pulse. Hence, the findings agree with the results of Stonebridge et al. (2004). In addition, the results of the effects of a spiral component on time-varying flow are presented and discussed along with the relevant pathological issues.     

Measurement of forearm blood flow by venous occlusion plethysmography: influence of hand blood flow during sustained and intermittent isometric exercise

The requirement for using an arterial occlusion cuff at the wrist when measuring forearm blood flows by plethysmography was tested on a total of 8 subjects at rest and during and after sustained and intermittent isometric exercise. The contribution of the venous effluent from the hand to the forearm flow during exercise was challenged by immersing the arm in water at 20, 34, and 40 degrees C. Occlusion of the circulation to the hand reduced the blood flow through the resting forearm at all water temperatures. There was an inverse relationship between the temperature of the water and the proportion in the reduction of forearm blood flow upon inflation of the wrist-cuff, ranging from 45 to 19% at 20 degrees to 40 degrees C, respectively. However, during sustained isometric exercise at 10% of the subjects maximum voluntary contraction (MVC) there was no reduction in the measured forearm flow when an arterial occlusion cuff was inflated aroung the wrist. Similarly, there was no alteration in the blood flow measured 2 s after each of a series of intermittent isometric contractions exerted at 20% or 60% MVC for 2 s whether or not circulation to the hand was occluded nor of the post-exercise hyperemia following 1 min of sustained contraction at 40% MVC. These results indicate that a wrist-cuff is not required for accurate measurement of forearm blood flows during or after isometric exercise.     

Intermittent pneumatic leg compressions enhance muscle performance and blood flow in a model of peripheral arterial insufficiency

Despite the escalating prevalence in the aging population, few therapeutic options exist to treat patients with peripheral arterial disease. Application of intermittent pneumatic leg compressions (IPC) is regarded as a promising noninvasive approach to treat this condition, but the clinical efficacy, as well the mechanistic basis of action of this therapy, remain poorly defined. We tested the hypothesis that 2 wk of daily application of IPC enhances exercise tolerance by improving blood flow and promoting angiogenesis in skeletal muscle in a model of peripheral arterial insufficiency. Male Sprague-Dawley rats were subjected to bilateral ligation of the femoral artery and randomly allocated to treatment or sham groups. Animals were anesthetized daily and exposed to 1-h sessions of bilateral IPC or sham treatment for 14-16 consecutive days. A third group of nonligated rats was also studied. Marked increases in treadmill exercise tolerance (～33%, P < 0.05) and improved muscle performance in situ (～10%, P < 0.05) were observed in IPC-treated animals. Compared with sham-treated controls, blood flow measured with isotope-labeled microspheres during in situ contractions tended to be higher in IPC-treated animals in muscles composed of predominantly fast-twitch white fibers, such as the plantaris (～93%, P = 0.02). Capillary contacts per fiber and citrate synthase activity were not significantly altered by IPC treatment. Collectively, these data indicate that IPC improves exercise tolerance in a model of peripheral arterial insufficiency in part by enhancing blood flow to collateral-dependent tissues.     

The Y2 receptor mediates increases in collateral-dependent blood flow in a model of peripheral arterial insufficiency

We have utilized a rat model of peripheral artery disease (PAD) to examine whether the known angiogenic activity of the Y(2) receptor would translate into a meaningful increase in collateral blood flow. The maximal increase in collateral blood flow capacity of approximately 60% (p<0.001) was obtained with a 10microg/kgday (IA infusion, 14 days) of either PYY or PYY(3-36) and did not differ from that obtained with a maximally angiogenic dose of VEGF(165). Pharmacodynamic modeling based upon single dose pharmacokinetic plasma profiles of both agonists suggests that E(max) is reached when the Y(2) receptor is occupied by >or=50%. Furthermore, for PYY(3-36), occupancy of the Y(2) receptor is sufficient to promote a significant benefit in collateral blood flow.