Functional respiratory imaging as a tool to personalize respiratory treatment in patients with unilateral diaphragmatic paralysis.

A completely different treatment approach was chosen for 2 patients with unilateral diaphragmatic paralysis and complaints of dyspnea despite similar anatomic and physiologic abnormalities. These decisions were supported by results obtained by functional respiratory imaging (FRI). FRI generated functional information on lobar ventilation and local drug deposition. In the first patient, some lobes were poorly ventilated, and drug deposition simulation showed that some regions were undertreated. This patient underwent diaphragmatic plication to restore ventilation. In the second patient, all lobes were still ventilated. A conservative approach with regular follow-ups was chosen to wait for spontaneous recovery of the diaphragmatic function. Both patients improved subjectively and objectively. These cases demonstrate how novel medical imaging techniques such as FRI can be used to personalize respiratory treatment in patients with unilateral diaphragmatic paralysis.

Change in upper airway geometry between upright and supine position during tidal nasal breathing.

BACKGROUND: As the upper airway is the most important limiting factor for the deposition of inhalation medication in the lower airways, it is interesting to assess how its morphology varies between different postures. The goal of this study is to compare the upper airway morphology and functionality of healthy volunteers in the upright and supine positions during tidal nasal breathing and to search for baseline indicators for these changes. This is done by performing three-dimensional measurements on computed tomography (CT) and cone beam computed tomography (CBCT) scans. METHODS: This prospective study was approved by all relevant institutional review boards. All patients gave their signed informed consent. In this study, 20 healthy volunteers (mean age, 62 years; age range, 37-78 years; mean body mass index, 29.26; body mass index range, 21.63-42.17; 16 men, 4 women) underwent a supine low-dose CT scan and an upright CBCT scan of the upper airway. The (local) average (Savg) and minimal (Smin) cross-sectional area, the position of the latter, the concavity, and the airway resistance were examined to determine if they changed from the upright to the supine position. If changes were found, baseline parameters were sought that were indicators for these differences. RESULTS: There were five dropouts due to movement artifacts in the CBCT scans. Savg and Smin were 9.76% and 26.90% larger, respectively, in the CBCT scan than in the CT scan, whereas the resistance decreased by 26.15% in the upright position. The Savg of the region between the hard palate and the bottom of the uvula increased the most (49.85%). In people with a high body mass index, this value changed the least. The airway resistance in men decreased more than in women. CONCLUSIONS: This study demonstrated that there are differences in upper airway morphology and functionality between the supine and upright positions and that there are baseline indicators for these differences.

Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements.

The accuracy of the nonlinear one-dimensional (1-D) equations of pressure and flow wave propagation in Voigt-type visco-elastic arteries was tested against measurements in a well-defined experimental 1:1 replica of the 37 largest conduit arteries in the human systemic circulation. The parameters required by the numerical algorithm were directly measured in the in vitro setup and no data fitting was involved. The inclusion of wall visco-elasticity in the numerical model reduced the underdamped high-frequency oscillations obtained using a purely elastic tube law, especially in peripheral vessels, which was previously reported in this paper [Matthys et al., 2007. Pulse wave propagation in a model human arterial network: Assessment of 1-D numerical simulations against in vitro measurements. J. Biomech. 40, 3476-3486]. In comparison to the purely elastic model, visco-elasticity significantly reduced the average relative root-mean-square errors between numerical and experimental waveforms over the 70 locations measured in the in vitro model: from 3.0% to 2.5% (p<0.012) for pressure and from 15.7% to 10.8% (p<0.002) for the flow rate. In the frequency domain, average relative errors between numerical and experimental amplitudes from the 5th to the 20th harmonic decreased from 0.7% to 0.5% (p<0.107) for pressure and from 7.0% to 3.3% (p<10(-6)) for the flow rate. These results provide additional support for the use of 1-D reduced modelling to accurately simulate clinically relevant problems at a reasonable computational cost.

Distance measurements for the assessment of carotid to femoral pulse wave velocity.

BACKGROUND: Carotid-femoral pulse wave velocity can be determined using different distances - either direct carotid-femoral distance or subtracted [(sternal-femoral) - (carotid-sternal)] distance - resulting in pulse wave velocity differences of up to 30%. The present study aims to present and validate a population-based model for the conversion between distances. METHOD: Three thousand one hundred and sixteen participants from the Asklepios study (n = 2510) and Hôpital Européen Georges Pompidou (n = 606) databases, in which all distance measurements were available, were randomly distributed in a model (n = 311) and validation (n = 2805) population. Model parameters for the conversion equations were selected and evaluated using multiple linear regression with stepwise selection of covariates (age, sex, weight, height, BMI and waist circumference). The proposed model was evaluated on the validation population. RESULTS: The difference between direct and subtracted distances was found to be partially dependent on body height, and its inclusion in the multivariate model improved model performance by over 20%. Other combinations of adjustments did not improve model prediction. Conversion equations derived in the model population were: Estimated Direct_distance = 0.45*Subtracted_distance + 0.21*height + 0.08 and Estimated Subtracted_distance = 1.04*Direct_distance - 0.11*height - 0.02, respectively. Applying these equations for estimation of direct and subtracted distances in the validation population yielded good correspondence to measured results (r = 0.73 and 0.57, respectively), with nonsignificant mean differences between estimated and measured values. Increasing the size of the model population did not significantly change the model validity. CONCLUSION: In cases in which not all distance measurements are available for exact conversion, the presented equations can be used to convert between distance definitions.

Long-term pressure monitoring with arterial applanation tonometry: a non-invasive alternative during clinical intervention?

Arterial tonometry is a non-invasive technique for continuous registration of arterial pressure waveforms. This study aims to assess tonometric blood pressure recording (TBP) as an alternative for invasive long-term bedside monitoring. A prospective study was set up where patients undergoing neurosurgical intervention were subjected to both invasive (IBP) and non-invasive (TBP) blood pressure monitoring during the entire procedure. A single-element tonometric pressure transducer was used to better investigate different inherent error sources of TBP measurement. A total of 5.7 hours of combined IBP and TBP were recorded from three patients. Although TBP performed fairly well as an alternative for IBP in steady state scenarios and some short-term variations, it could not detect relevant long-term pressure variations at all times. These findings are discussed in comparison to existing work. Physiological alterations at the site of TBP measurement are highlighted as a potentially important source of artifacts. It is concluded that at this point arterial tonometry remains not enough understood for long-term use during a delicate operative procedure. Physiological changes at the TBP measurement site deserve further investigation before tonometry technology is to be considered as an non-invasive alternative for long-term clinical monitoring.

Age and gender related patterns in carotid-femoral PWV and carotid and femoral stiffness in a large healthy, middle-aged population.

BACKGROUND: The relationship between aortic (carotid-femoral) pulse wave velocity and stiffness measures based on local diameter and pressure readings is not yet fully understood. METHODS: We compared the relationship with age and gender of aortic pulse wave velocity to stiffness indices (compliance and distensibility coefficient) evaluated at the common carotid and femoral arteries in 2195 (1131 women) apparently healthy subjects, aged 35-55 years participating in the Asklepios study. Aortic pulse wave velocity was further compared with previously reported central arterial stiffness parameters on the same population. Subjects were divided into four age groups for analysis. RESULTS: Femoral arterial stiffness was higher in men than in women (P < 0.001) but did not change with age and no age-gender interaction was evident. Carotid arterial stiffness increased with age (P < 0.001) and showed a significant (P < 0.001) age-gender interaction, with carotid stiffness increasing more rapidly in women than in men, crossing over around the age of 45. Aortic pulse wave velocity did not differ between men and women, but did increase with age (P < 0.001). No age-gender interaction was evident. CONCLUSION: The relation with age and gender of local and central stiffness measures is not the same over the age range 35-55 in apparently healthy men and women. Depending on the central stiffness parameter used, age-gender effects evident at the carotid artery are or are not found centrally. Though the relevance of these differences requires further evaluation in a longitudinal study with outcome data, they need to be kept in mind when designing or interpreting results from arterial stiffness evaluation studies.

Effect of an abdominal aortic aneurysm on wave reflection in the aorta.

Despite extensive attention to abdominal aortic aneurysm (AAA) in the biomedical engineering community, its effect on aortic hemodynamics and arterial wave reflection has not been addressed before. We used experimental and numerical methods, relying on a realistic AAA geometry constructed from patient computer tomography scans (CT-scans), to study this issue. Pressure and flow waves were measured and simulated before and after AAA repair, and wave reflections were analyzed using linear wave separation and wave intensity analysis. With AAA, pronounced reflections were present in the pressure and flow waveforms. The reflection coefficient measured experimentally in the upper aorta was negative with AAA (-0.10) versus 0.47 without AAA. Wave intensity analysis confirmed the presence of a backward expansion wave caused by sudden expansion of the aorta; this was absent without AAA. These results were confirmed using a 1-D numerical model. A parameter study using this model demonstrated that dominant factors are diameter and compliance of the aneurysm, with larger diameters and more compliant AAA generating more negative reflections. Finally, a preliminary noninvasive study in three patients before and after AAA repair demonstrated that AAA-repair increased the reflection coefficient. In conclusion, the presence of AAA significantly alters wave reflection and hemodynamics in the aorta, with apparently measurable effects in humans.

Enhanced oxygen availability improves liver-specific functions of the AMC bioartificial liver.

Long-term culturing of primary porcine hepatocytes (PPH) inside the Academic Medical Center (AMC)-bioartificial liver is characterized by increased anaerobic glycolysis. Recommendations to increase oxygen availability were proposed in a previous numerical study and were experimentally evaluated in this study. Original bioreactors as well as new configuration bioreactors with 2.2-fold thinner nonwoven matrix and 2-fold more capillaries were loaded with PPHs and oxygenated with different gas oxygen pressures resulting in medium pO(2) (pO(2-med)) of either 135-150 mm Hg or 235-250 mm Hg. After 6 days culturing, new configuration bioreactors with pO(2-med )of 250 mm Hg showed significantly reduced anaerobic glycolysis, 60% higher liver-specific functions, and increased transcript levels of five liver-specific genes compared to the standard bioreactor cultures. Changed bioreactor configuration and increasing pO(2-med) contributed equally to these improvements. Histological examination demonstrated small differences in cell organization. In conclusion, higher metabolic stability and liver-specific functionality was achieved by enhanced oxygen availability based on a prior modeling concept.

Assessment of pressure wave reflection: getting the timing right!

Assessment of timing and magnitude of wave reflection is ideally based on wave separation analysis (WSA). In clinical practice, however, waveform analysis (WFA) is often used to study wave reflection, with different coexisting approaches to assess 'landmarks' on the waveform which are indicative for return of the reflected wave. The aim of this work was to compare WSA and WFA. Data were obtained from 2132 subjects (1093 women) aged between 35 and 56 and free from overt cardiovascular disease. Carotid pressure and aortic flow waveforms, and carotid-femoral pulse wave velocity were measured non-invasively. WSA yielded the timing of return of reflected wave (T(f-b)), the ratio of forward and backward pressure wave (P(b)/P(f)), and the effective length of the arterial tree (L(eff)). WFA resulted in identification of the shoulder (T(sho)) or inflection point (T(inf)) as landmark points, with subsequently derived augmentation index and L(eff) (AIx(sho) and L(eff,sho), AIx(inf) and L(eff,inf), respectively). (i) Neither T(inf) nor T(sho) corresponded with the timing obtained from WSA. (ii) Measurements of L(eff) were found to decrease with age (conforming with current physiological insights) whilst L(eff,inf) was found to increase with age in women, and mixed results were obtained for L(eff,sho). (iii) Both AIx(inf) and AIx(sho) showed a persistent gender difference which was not present in P(b)/P(f). Using the pressure at T(f-b) to calculate AIx, the systematic gender difference in AIx(f-b) was greatly reduced. Analysis of pressure wave reflection is optimally based on measurement of pressure and flow, rather than on waveform analysis alone.

Particle image velocimetry-validated, computational fluid dynamics-based design to reduce shear stress and residence time in central venous hemodialysis catheters.

As crucial factors in blood clot formation, shear stress distribution and low flow zones are assessed in different central venous catheter tip designs by using a combined numeric and experimental approach. Computational Fluid Dynamics was validated with Particle Image Velocimetry by comparing simulated and measured velocities and shear strains in three designs of the blood withdrawing arterial lumen: cylindrical and with tip (1) cut straight, (2) cut at an angle, or (3) cut straight with a sleeve entrance. After validation, four additional designs were studied: (4) with two side holes and tip cut straight or (5) at an angle, (6) concentric lumens, and (7) Ash Split-based. In these seven designs, shear stress (SS), blood residence time (RT), and Platelet Lysis Index, which combines the influence of shear stress magnitude and exposure time, were simulated. Concentric catheter was discarded due to highly elevated SS. Ash Split-based design had elevated RT values in the distal tip zone as major inflow occurs through the most proximal side holes, but this is compensated by low average SS. A straight-cut tip and possibly two side holes are preferred when aiming at minimal SS and RT. These data may lead to more patent catheters.

Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements.

A numerical model based on the nonlinear, one-dimensional (1-D) equations of pressure and flow wave propagation in conduit arteries is tested against a well-defined experimental 1:1 replica of the human arterial tree. The tree consists of 37 silicone branches representing the largest central systemic arteries in the human, including the aorta, carotid arteries and arteries that perfuse the upper and lower limbs and the main abdominal organs. The set-up is mounted horizontally and connected to a pulsatile pump delivering a periodic output similar to the aortic flow. Terminal branches end in simple resistance models, consisting of stiff capillary tubes leading to an overflow reservoir that reflects a constant venous pressure. The parameters required by the numerical algorithm are directly measured in the in vitro set-up and no data fitting is involved. Comparison of experimental and numerical pressure and flow waveforms shows the ability of the 1-D time-domain formulation to capture the main features of pulse wave propagation measured throughout the system test. As a consequence of the simple resistive boundary conditions used to reduce the uncertainty of the parameters involved in the simulation, the experimental set-up generates waveforms at terminal branches with additional non-physiological oscillations. The frequencies of these oscillations are well captured by the 1-D model, even though amplitudes are overestimated. Adding energy losses in bifurcations and including fluid inertia and compliance to the purely resistive terminal models does not reduce the underdamped effect, suggesting that wall visco-elasticity might play an important role in the experimental results. Nevertheless, average relative root-mean-square errors between simulations and experimental waveforms are smaller than 4% for pressure and 19% for the flow at all 70 locations studied.

Noninvasive (input) impedance, pulse wave velocity, and wave reflection in healthy middle-aged men and women.

The relation between arterial function indices, such as pulse wave velocity and augmentation index with parameters derived from input impedance analysis, is still incompletely understood. Carotid pressure, central flow waveforms, and pulse wave velocity were noninvasively acquired in 2026 apparently healthy, middle-aged subjects (1052 women and 974 men) 35 to 55 years old at inclusion. Input and characteristic impedance, reflection coefficient, the ratio of backward-to-forward pressure amplitude (reflection magnitude), and augmentation index were derived. Pulse wave velocity increased by 15% (from 6.1 to 7.0 m/s) both in men and women. In qualitative terms, input impedance evolved from a pattern indicative of wave transmission and reflection to a pattern more compatible with a windkessel-like system. In women, a decrease in total arterial compliance led to an increased input impedance in the low frequency range, whereas few changes were observed in men. Characteristic impedance did not change with age in women and even decreased in men (P<0.001) and could not be identified as the primary determinant of central pulse pressure. Augmentation index increased with age, as was expected, and was systematically higher in women (P<0.001). Reflection coefficient and reflection magnitude increased with age (P<0.001) without gender differences. We conclude that, in healthy middle-aged subjects, the age-related increase in arterial stiffness (pulse wave velocity) is not fully paralleled by an increase in arterial impedance, suggesting a role for age-dependent modulation of aortic cross-sectional area. Wave reflection increases with age and is not higher in women than in men.

New echocardiographic applications for assessing global left ventricular diastolic function.

A number of promising and highly technological echocardiographic imaging tools have recently been introduced to assess left ventricular diastolic function (i.e., the capacity of the ventricle to relax and fill). They permit quantification of distinct features of intraventricular blood flow velocity and pressure fields and myocardial tissue velocities. However, accurate interpretation of the new images and clinical indices is still cumbersome, as basic knowledge about intraventricular hemodynamics and ventricular wall mechanics is often insufficient. This review article provides a comprehensive and original overview of the hemodynamical and mechanical events that occur during diastole and discusses how this new information can be used in the clinical and research setting to evaluate diastolic function in the healthy and the diseased heart. It furthermore aims to explain the underpinnings of the techniques in such a way that the underlying biomechanical concepts (fluid dynamics and wall mechanics) become less obscure to cardiologists and echocardiographers and such that the biomedical engineers are given some insights into the avalanche of diastolic performance indices that currently exist.

Three-dimensional numerical modeling and computational fluid dynamics simulations to analyze and improve oxygen availability in the AMC bioartificial liver.

A numerical model to investigate fluid flow and oxygen (O(2)) transport and consumption in the AMC-Bioartificial Liver (AMC-BAL) was developed and applied to two representative micro models of the AMC-BAL with two different gas capillary patterns, each combined with two proposed hepatocyte distributions. Parameter studies were performed on each configuration to gain insight in fluid flow, shear stress distribution and oxygen availability in the AMC-BAL. We assessed the function of the internal oxygenator, the effect of changes in hepatocyte oxygen consumption parameters in time and the effect of the change from an experimental to a clinical setting. In addition, different methodologies were studied to improve cellular oxygen availability, i.e. external oxygenation of culture medium, culture medium flow rate, culture gas oxygen content (pO(2)) and the number of oxygenation capillaries. Standard operating conditions did not adequately provide all hepatocytes in the AMC-BAL with sufficient oxygen to maintain O(2) consumption at minimally 90% of maximal uptake rate. Cellular oxygen availability was optimized by increasing the number of gas capillaries and pO(2) of the oxygenation gas by a factor two. Pressure drop over the AMC-BAL and maximal shear stresses were low and not considered to be harmful. This information can be used to increase cellular efficiency and may ultimately lead to a more productive AMC-BAL.

Hemodynamic modes of ventricular assist with a rotary blood pump: continuous, pulsatile, and failure.

Pulsatile operation of rotary blood pumps (RBPs) has received interest due to potential concern with nonphysiological hemodynamics. This study aimed to gain insight to the effects of various RBP modes on the heart-device interaction. A Deltastream diagonal pump (Medos Medizintechnik GmbH) was inserted in a cardiovascular simulator with apical-to-ascending aorta cannulation. The pump was run in continuous mode with incrementally increasing rotating speed (0-5000 rpm). This was repeated for three heart rates (50-100-150 bpm) and three levels of left ventricular (LV) contractility. Subsequently, the Deltastream was run in pulsatile mode to elucidate the effect of (de)synchronization between heart and pump. LV volume and pressure, arterial pressure, flows, and energetic parameters were used to evaluate the interaction. Pump failure (0 rpm) resulted in aortic pressure drops (17-46 mm Hg) from baseline. In continuous mode, pump flow compensated by diminished aortic flow, thus yielding constant total flow. High continuous rotating speed resulted in acute hypertension (mean aortic pressure up to 178 mm Hg). In pulsatile mode, unmatched heart and pulsatile pump rates yielded unphysiologic pressure and flow patterns and LV unloading was found to be highly dependent on synchronization phase. Optimal unloading was achieved when the minimum rotating speed occurred at end-systole. We conclude that, in continuous mode, a perfusion benefit can only be achieved if the continuous pump flow exceeds the preimplant (baseline) cardiac output. Pulsatile mode of support results in complex pressure and volume variations and requires accurate triggering to achieve optimal unloading.

Predicting ATS Open Pivot heart valve performance with computational fluid dynamics.

BACKGROUND AND AIM OF THE STUDY: In-vitro studies on the ATS heart valve have indicated that valve opening is less in an expanding conduit than in a straight conduit. METHODS: Bileaflet valve behavior was studied using a new computational fluid-structure interaction model. A three-dimensional model of the ATS valve was studied in two geometries, simulating the valve in a geometry with sudden expansion downstream of the valve, and in a straight conduit. Mitral and aortic flow patterns were simulated. RESULTS: The ATS valve in the expanding geometry showed opening to a maximum angle of 77.5 degrees; this was confirmed in previous clinical and in-vitro studies. The mean and maximum transvalvular Doppler pressure gradients were 1.1 and 4.3 mmHg, respectively. The maximum shear stress calculated on the leaflet was 25 Pa. Maximum opening of the valve was achieved in the straight conduit; with mean and maximum pressure gradients of 2.1 and 4.6 mmHg, respectively. The maximum shear stress calculated on the leaflet was 35 Pa. CONCLUSION: The results of this numerical study confirmed that valve hemodynamics and leaflet motion were dependent on the geometrical conditions of the valve: the presence of a diverging flow influenced the maximum opening angle of the valve leaflets. This model could be used to predict pressure gradients, effective orifice area, performance index and shear stress loading of mechanical heart valves, and in future will serve as a major research tool to characterize the hemodynamics of existing and new mechanical heart valves.

Operator dependence of 3-D ultrasound-based computational fluid dynamics for the carotid bifurcation.

The association between vascular wall shear stress (WSS) and the local development of atherosclerotic plaque makes estimation of in vivo WSS of considerable interest. Three-dimensional ultrasound (3DUS) combined with computational fluid dynamics (CFD) provides a potentially valuable tool for acquiring subject-specific WSS, but the interoperator and intraoperator variability associated with WSS calculations using this method is not known. Here, the accuracy, reproducibility and operator dependence of 3DUS-based computational fluid dynamics were examined through a phantom and in vivo studies. A carotid phantom was scanned and reconstructed by two operators. In the in vivo study, four operators scanned a healthy subject a total of 11 times, and their scan data were processed by three individuals. The study showed that with some basic training, operators could acquire accurate carotid geometry for flow reconstructions. The variability of measured cross-sectional area and predicted shear stress was 8.17% and 0.193 N/m2 respectively for the in vivo study. It was shown that the variability of the examined parameters was more dependent on the scan operators than the image processing operator. The range of variability of geometrical and flow parameters reported here can be used as a reference for future in vivo studies using the 3DUS-based CFD approach.

Echocardiographic assessment of aortic elastic properties with automated border detection in an ICU: in vivo application of the arctangent Langewouters model.

We studied whether combined pressure and transesophageal ultrasound monitoring is feasible in the intensive care unit (ICU) setting for global cardiovascular hemodynamic monitoring [systemic vascular resistance (SVR) and total arterial compliance (C(PPM))] and direct estimation of local ascending and descending aortic mechanical properties, i.e., distensibility and compliance coefficients (DC and CC). Pressure-area data were fitted to the arctangent Langewouters model, with aortic cross-sectional area obtained via automated border detection. Data were measured in 19 subjects at baseline, during infusion of sodium nitroprusside (SNP), and after washout. SNP infusion lowered SVR from 1.15 +/- 0.40 to 0.80 +/- 0.32 mmHg.ml(-1).s (P < 0.05), whereas C(PPM) increased from 0.87 +/- 0.46 to 1.02 +/- 0.42 ml/mmHg (P < 0.05). DC and CC increased from 0.0018 +/- 0.0007 to 0.0025 +/- 0.0009 l/mmHg (P < 0.05) and from 0.0066 +/- 0.0028 to 0.0083 +/- 0.0026 cm2/mmHg (P < 0.05), respectively, at the descending, but not ascending, aorta. The Langewouters model fitted the descending aorta data reasonably well. Assessment of local mechanical properties of the human ascending aorta in a clinical setting by automated border detection remains technically challenging.

Influence of zero flow pressure on fractional flow reserve.

Fractional flow reserve (FFR) is a commonly used index to assess the functional severity of a coronary artery stenosis. It is conventionally calculated as the ratio of the pressure distal (Pd) and proximal (Pa) to the stenosis (FFR= Pd/Pa). We hypothesize that the presence of a zero flow pressure (Pzf), requires a modification of this equation. Using a dynamic hydraulic bench model of the coronary circulation, which allows one to incorporate an adjustable Pzf, we studied the relation between pressure-derived FFR = Pdo/Pa, flow-derived true FFRQ = Qs/QN (= ratio of flow through a stenosed vessel to flow through a normal vessel), and the corrected pressure-derived FFRc = (Pd-Pzf)/(Pa-Pzf) under physiological aortic pressures (70 mmHg, 90 mmHg, and 110 mmHg). Imposed Pzf values varied between 0 mmHg and 30 mmHg. FFRc was in good agreement with FFRQ, whereas FFR consistently overestimated FFRQ. This overestimation increased when Pzf increased, or when Pa decreased, and could be as high as 56% (Pzf=30 mmHg and Pa =70 mmHg). According to our experimental study, calculating the corrected FFRC instead of FFR, if Pzf is known, provides a physiologically more accurate evaluation of the functional severity of a coronary artery stenosis.