Pressure- and 3D-Derived Coronary Flow Reserve with Hydrostatic Pressure Correction: Comparison with Intracoronary Doppler Measurements

Purpose: To develop a method of coronary flow reserve (CFR) calculation derived from three-dimensional (3D) coronary angiographic parameters and intracoronary pressure data during fractional flow reserve (FFR) measurement. Methods: Altogether 19 coronary arteries of 16 native and 3 stented vessels were reconstructed in 3D. The measured distal intracoronary pressures were corrected to the hydrostatic pressure based on the height differences between the levels of the vessel orifice and the sensor position. Classical fluid dynamic equations were applied to calculate the flow during the resting state and vasodilatation based on morphological data and intracoronary pressure values. 3D-derived coronary flow reserve (CFRp-3D) was defined as the ratio between the calculated hyperemic and the resting flow and was compared to the CFR values simultaneously measured by the Doppler sensor (CFRDoppler). Results: Haemodynamic calculations using the distal coronary pressures corrected for hydrostatic pressures showed a strong correlation between the individual CFRp-3D values and the CFRDoppler measurements (r = 0.89, p < 0.0001). Hydrostatic pressure correction increased the specificity of the method from 46.1% to 92.3% for predicting an abnormal CFRDoppler < 2. Conclusions: CFRp-3D calculation with hydrostatic pressure correction during FFR measurement facilitates a comprehensive hemodynamic assessment, supporting the complex evaluation of macro-and microvascular coronary artery disease.


Introduction
According to the current European guideline on coronary revascularization, pressure wire-derived fractional flow reserve (FFR) measurement is recommended for the functional assessment of lesion severity in patients with 40-90% diameter stenosis and without prior evidence of ischemia [1]. A more recent guideline suggests the consideration of a guidewire-based coronary flow reserve CFR measurement in patients with persistent symptoms but with preserved FFR [2] based on earlier publications [3][4][5]. The combination of FFR and CFR evaluation may identify the potential components of ischemia originating from the decreased conductance of the epicardial vessels and the increased resistance of the microvasculature [6][7][8][9]. 2

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As a temperature sensor, the pressure-wire sensor makes it possible to calculate thermodilution; however, the bolus method comes with several limitations, as already detailed in early validation studies [10][11][12]. On the other hand, the direct measurement of coronary flow velocity by a Doppler sensor is considered technically difficult to perform; consequently, it is not routinely used in clinical practice.
The resistance of the microvasculature (MR) is defined as the ratio of the distal coronary pressure divided by the distal coronary flow rate. The resistive reserve ratio (RRR) is the index expressing the ratio between basal and hyperemic microcirculation resistance (bMR divided by hMR) [13,14].
Lately, the term microvascular resistance reserve (MRR) was suggested for specific characterization of the microvasculature [15]: MRR = (CFR/FFR) × (Pa rest/Pa hyp) (1) where Pa rest and Pa hyp are the aortic pressures during resting and hyperemic state. The concept was proposed in connection with the continuous thermodilution technique (requiring a special infusion catheter) and was validated by intracoronary Doppler measurements [16].
In our study, we aimed at developing a clinically applicable method for calculating specific CFR and RRR values (CFR p-3D and RRR p-3D ) during FFR measurement, using simple hemodynamic calculations that combine intracoronary pressure data and 3D anatomical parameters ( Figure 1). The results of our calculations were compared to data obtained using invasive Doppler wire measurement, as a gold standard of flow assessment. As a temperature sensor, the pressure-wire sensor makes it possible to calculate thermodilution; however, the bolus method comes with several limitations, as already detailed in early validation studies [10][11][12]. On the other hand, the direct measurement of coronary flow velocity by a Doppler sensor is considered technically difficult to perform; consequently, it is not routinely used in clinical practice.
The resistance of the microvasculature (MR) is defined as the ratio of the distal coronary pressure divided by the distal coronary flow rate. The resistive reserve ratio (RRR) is the index expressing the ratio between basal and hyperemic microcirculation resistance (bMR divided by hMR) [13,14].
Lately, the term microvascular resistance reserve (MRR) was suggested for specific characterization of the microvasculature [15]: where Pa rest and Pa hyp are the aortic pressures during resting and hyperemic state. The concept was proposed in connection with the continuous thermodilution technique (requiring a special infusion catheter) and was validated by intracoronary Doppler measurements [16].
In our study, we aimed at developing a clinically applicable method for calculating specific CFR and RRR values (CFRp-3D and RRRp-3D) during FFR measurement, using simple hemodynamic calculations that combine intracoronary pressure data and 3D anatomical parameters ( Figure 1). The results of our calculations were compared to data obtained using invasive Doppler wire measurement, as a gold standard of flow assessment.  It has recently been underlined that pressure differences are systematically detectable between the different segments of the coronary arteries in the supine position [17][18][19]. We also investigated how the correction of distal pressure for hydrostatic pressure offset affects the pressure-derived flow determinations. Calculation of CFR and RRR values during FFR measurement. The method for calculating CFR p-3D and RRR p-3D uses hemodynamic calculations combining intracoronary pressure data (top left panel) and 3D anatomical parameters (bottom left panel). Based on the hyperemic and resting pressure data, as well as 3D anatomical parameters, simple hemodynamic equations were used to calculate resting and hyperemic flow, CFR, and RRR. The detailed description of the flow calculations is described in the patent of the method: https://patents.google.com/patent/WO2019175612A2/en (accessed on 5 March 2022).
It has recently been underlined that pressure differences are systematically detectable between the different segments of the coronary arteries in the supine position [17][18][19]. We also investigated how the correction of distal pressure for hydrostatic pressure offset affects the pressure-derived flow determinations.

Patient Inclusion and Exclusion Criteria
Patients, who underwent clinically indicated invasive physiological investigations, were selected for this study, with single stenosis of intermediate severity (40-80% based on a visual assessment) in a main branch of the epicardial coronary artery system. Cases with good quality hyperemic and resting pressure and Doppler traces were included for the evaluations. Only traces without pressure drift (<1 mmHg) confirmed by the pullback of the pressure sensor at the end of the procedure were considered. Patients with an acute coronary syndrome, left main stenosis, ostial stenosis, earlier bypass surgery, or diffuse coronary artery disease were excluded. The study has been approved by the local ethics committee of the University of Debrecen and has therefore been performed in concordance with the Declaration of Helsinki.

Invasive Coronary Angiography and Simultaneous Pressure and Flow Measurement by ComboWire
After administering 5000 international units (IU) of intravenous, unfractionated heparin (UFH) and intracoronary glyceryl trinitrate (GTN), diagnostic angiographic cinerecordings were acquired from standard projections, using digital X-ray equipment (Axiom Artis, Siemens, Erlangen, Germany). Diagnostic angiographic images were recorded at 15 frames per second. Low-or iso-osmolar contrast material (CM) (iopamidol (Scanlux) or iodixanol (Visipaque)) was injected in 5 mL fractions with a speed of 3 mL/sec using a dedicated contrast pump (ACIST CVi™, ACIST Medical Systems, Eden Prairie, MN, USA). If the operator detected a 40-80% diameter stenosis by visual assessment, complete physiological measurements were performed via a 6F guiding catheter, using a ComboWire equipped with both pressure and Doppler sensors (Philips Volcano, San Diego, CA, USA).
After the pressures were equalized with the sensor positioned at the level of the catheter tip, it was advanced through the coronary artery stenosis, and measurements were performed approximately 2 cm distal to the lesion. Following the basal pressure and flow measurements, 150-200 µg intracoronary adenosine was administered, and the pressure and Doppler traces were recorded. One representative measurement is presented in Figure 2.

Patient Inclusion and Exclusion Criteria
Patients, who underwent clinically indicated invasive physiological investigations, were selected for this study, with single stenosis of intermediate severity (40-80% based on a visual assessment) in a main branch of the epicardial coronary artery system. Cases with good quality hyperemic and resting pressure and Doppler traces were included for the evaluations. Only traces without pressure drift (<1 mmHg) confirmed by the pullback of the pressure sensor at the end of the procedure were considered. Patients with an acute coronary syndrome, left main stenosis, ostial stenosis, earlier bypass surgery, or diffuse coronary artery disease were excluded. The study has been approved by the local ethics committee of the University of Debrecen and has therefore been performed in concordance with the Declaration of Helsinki.

Invasive Coronary Angiography and Simultaneous Pressure and Flow Measurement by ComboWire
After administering 5000 international units (IU) of intravenous, unfractionated heparin (UFH) and intracoronary glyceryl trinitrate (GTN), diagnostic angiographic cinerecordings were acquired from standard projections, using digital X-ray equipment (Axiom Artis, Siemens, Erlangen, Germany). Diagnostic angiographic images were recorded at 15 frames per second. Low-or iso-osmolar contrast material (CM) (iopamidol (Scanlux) or iodixanol (Visipaque)) was injected in 5 mL fractions with a speed of 3 mL/sec using a dedicated contrast pump (ACIST CVi™, ACIST Medical Systems, Eden Prairie, MN, US). If the operator detected a 40-80% diameter stenosis by visual assessment, complete physiological measurements were performed via a 6F guiding catheter, using a ComboWire equipped with both pressure and Doppler sensors (Philips Volcano, San Diego, CA, USA).
After the pressures were equalized with the sensor positioned at the level of the catheter tip, it was advanced through the coronary artery stenosis, and measurements were performed approximately 2 cm distal to the lesion. Following the basal pressure and flow measurements, 150-200 µg intracoronary adenosine was administered, and the pressure and Doppler traces were recorded. One representative measurement is presented in Figure 2.  Results of simultaneous pressure and flow measurements by the ComboWire. In this case, the average proximal (aortic) and distal pressures were detected to be 95 mmHg and 88 mmHg, respectively. At maximal hyperemia (P), the average peak velocity (APV-P) increased to 29 cm/s from the basal (B) velocity of 10 cm/s (APV-B) parallel with the increase in the pressure drop (the proximal and distal pressures were 89 mmHg and 79 mmHg, respectively). The measured FFR was 0.89, while the CFR was 2.9 (Case 10).

Three-Dimensional Quantitative Coronary Artery Reconstruction and Hemodynamic Calculations
Offline 3D angiographic reconstruction was performed from two selected angiograms of good quality, with at least 25 • difference in angle, using dedicated software (QAngio XA ® Research Edition 1.0, Medis Specials bv, Leiden, The Netherlands). The reconstructed vessel segment was marked from the coronary orifice to the location of the wire sensors. Numerous geometric measures describing the lesion (average cross-sectional diameters and vessel segment lengths), as well as the proximally and distally connecting vessel segments, were automatically obtained by the software. These values with intracoronary pressure at the proximal and distal positions during the resting and vasodilation states were combined for hemodynamic calculations. The method and its validation are described in our previous papers in detail [20,21], and an online calculation tool (http://coronart. unideb.hu/) (accessed on 5 March 2022) is available.

Calculation of the Doppler-Derived Indices
The resistance of the microvasculature (MR) was defined as the ratio of the distal coronary pressure divided by the distal coronary flow rate both in the basal state and during hyperemia: where bMR: basal microvascular resistance, hMR: hyperemic microvascular resistance and APV-B: basal average peak velocity, APV-P: peak average velocity measured by the ComboWire during basal and hyperemic flow (see Figure 2). The resistive reserve ratio (RRR) as the index of the ratio between basal and hyperemic microcirculation resistance [13,14] was calculated as follows:

Calculation of the RRR p-3D
The RRR was also defined analogously from the calculated flows defined by simple flow equations using the pressure and 3D anatomy data (Q p-3D ):

Correction of the Distal Coronary Pressure for Hydrostatic Pressure
In the supine position, the measured pressure difference between the catheter tip and the pressure sensor distal to the lesion originates from two components, namely the pressure loss caused by the flow through the stenosis, the difference between the hydrostatic pressure at the catheter tip at the coronary orifice, and the level of the distal intracoronary sensor (Figure 3).
The latter component can be referred to as hydrostatic offset (∆P hydrostatic pressure) and can modify the detected pressure ratio values through the "altered" distal pressure value [18,19].
The correction of distal pressure for hydrostatic pressure (Pd corr) was based on the height differences between the orifice and other coronary artery segments in supine positions. The distal pressure values were corrected, using a correction factor of 0.77 mmHg hydrostatic pressure per 1 cm height difference, where blood density was taken as 1050 kg/m 3 ( Figure 3): Pd corr = Pd − ∆P hydrostatic pressure (6) Figure 3. The height difference between the LAD orifice and the sensor position. After 3D reconstruction, the height difference between the orifice and the pressure wire sensor was transformed to mmHg getting hydrostatic pressure (red) (Case 10). This value (5.58 mmHg) influences the gradient between the aortic pressure at the tip of the catheter and the pressure detected by the sensor of the pressure wire, and it has a great impact on the results of the CFR calculation.
The latter component can be referred to as hydrostatic offset (∆Phydrostatic pressure) and can modify the detected pressure ratio values through the "altered" distal pressure value [18,19].
The correction of distal pressure for hydrostatic pressure (Pd corr) was based on the height differences between the orifice and other coronary artery segments in supine positions. The distal pressure values were corrected, using a correction factor of 0.77 mmHg hydrostatic pressure per 1 cm height difference, where blood density was taken as 1050 kg/m 3 ( Figure 3):

Statistical Analysis
Statistical evaluations were performed in MedCalc Statistical Software, Version 14.8.1 (MedCalc Software bvba, Ostend, Belgium). Following a normality test, Spearman's correlation analysis was carried out. The correlation between CFRp-3D and the CFRDoppler was examined both without and with hydrostatic pressure correction of the distal pressure. The agreement between CFRDoppler and CFRp-3D was assessed using the Bland-Altman analysis. The area under the curve (AUC) calculated by receiver operating characteristic analysis was applied to determine the diagnostic power of CFRp-3D without and with hydrostatic pressure correction. The sensitivity and specificity of CFRp-3D without and with hydrostatic pressure correction were calculated using the standard method.

Results
We performed simultaneous intracoronary pressure and Doppler measurement by ComboWire in 20 patients screened in the study. In 3 cases the Doppler signal quality was insufficient for the calculation, in 1 further case more than 2 mmHg drift was detected at the end of the investigation and the attempt for repeat measurement also failed. Therefore, sixteen 16 patients (14 males, 2 females) with single, intermediate epicardial coronary stenosis were involved in the study. In 3 cases, measurements were performed both before and after stent implantation. Patient characteristics are presented in Table 1. The results of 3D reconstruction and the measured physiological data are summarized for each interrogated vessel in Table 2. The height difference between the LAD orifice and the sensor position. After 3D reconstruction, the height difference between the orifice and the pressure wire sensor was transformed to mmHg getting hydrostatic pressure (red) (Case 10). This value (5.58 mmHg) influences the gradient between the aortic pressure at the tip of the catheter and the pressure detected by the sensor of the pressure wire, and it has a great impact on the results of the CFR calculation.

Statistical Analysis
Statistical evaluations were performed in MedCalc Statistical Software, Version 14.8.1 (MedCalc Software bvba, Ostend, Belgium). Following a normality test, Spearman's correlation analysis was carried out. The correlation between CFR p-3D and the CFR Doppler was examined both without and with hydrostatic pressure correction of the distal pressure. The agreement between CFR Doppler and CFR p-3D was assessed using the Bland-Altman analysis. The area under the curve (AUC) calculated by receiver operating characteristic analysis was applied to determine the diagnostic power of CFR p-3D without and with hydrostatic pressure correction. The sensitivity and specificity of CFR p-3D without and with hydrostatic pressure correction were calculated using the standard method.

Results
We performed simultaneous intracoronary pressure and Doppler measurement by ComboWire in 20 patients screened in the study. In 3 cases the Doppler signal quality was insufficient for the calculation, in 1 further case more than 2 mmHg drift was detected at the end of the investigation and the attempt for repeat measurement also failed. Therefore, sixteen 16 patients (14 males, 2 females) with single, intermediate epicardial coronary stenosis were involved in the study. In 3 cases, measurements were performed both before and after stent implantation. Patient characteristics are presented in Table 1. The results of 3D reconstruction and the measured physiological data are summarized for each interrogated vessel in Table 2.

Correlation and Agreement between the Results of the CFR Doppler Measurements and Calculated CFR p-3D Values without and with the Correction for Hydrostatic Offset
When including morphological data from 3D coronary angiography in the hemodynamic calculation and correcting the values for hydrostatic pressure, a strong correlation was found between the individual CFR p-3D values and the CFR Doppler measurements (r = 0.89, p < 0.0001). A weak but still significant correlation was demonstrated even without the correction of hydrostatic error (r = 0.57, p = 0.01) ( Figure 4A,B). The difference between the two correlations was found to be significant (p = 0.02).   : coronary flow reserve calculated from intracoronary pressure data and 3D anatomical parameters; APV-B: average peak velocity at rest, APV-P average peak velocity during vasodilatation measured by Doppler wire; CFR Doppler : coronary flow reserve measured by Combowire; RRR p-3D : resistive reserve ratio calculated from intracoronary pressure data and 3D anatomical parameters; RRR Doppler : resistive reserve ratio measured by Combowire.
When including morphological data from 3D coronary angiography in the hemodynamic calculation and correcting the values for hydrostatic pressure, a strong correlation was found between the individual CFRp-3D values and the CFRDoppler measurements (r = 0.89, p < 0.0001). A weak but still significant correlation was demonstrated even without the correction of hydrostatic error (r = 0.57, p = 0.01) ( Figure  4A,B). The difference between the two correlations was found to be significant (p = 0.02).

Correlation and Agreement between the Results of the ComboWire Based RRR Measurements (RRRDoppler) and the Calculated RRRp-3D Values with the Correction for Hydrostatic Offset
The calculated microvascular resistance reserve (RRRp-3D) also demonstrated a good correlation with the measured RRRDoppler values (r = 0.83, p < 0.0001) Figure 5A. The Bland-Altman analysis showed the mean differences between the Doppler-measured and the calculated RRRp-3D values with hydrostatic offset correction to be -0.03 (±1.96 SD: 0.63, -0.68) Figure 5B.

Correlation and Agreement between the Results of the ComboWire Based RRR Measurements (RRR Doppler ) and the Calculated RRR p-3D Values with the Correction for Hydrostatic Offset
The calculated microvascular resistance reserve (RRR p-3D ) also demonstrated a good correlation with the measured RRR Doppler values (r = 0.83, p < 0.0001) Figure 5A. The Bland-Altman analysis showed the mean differences between the Doppler-measured and the calculated RRR p-3D values with hydrostatic offset correction to be −0.03 (±1.96 SD: 0.63, −0.68) Figure 5B. Figure 6 shows the clustered multiple variable graphs of resting Pd/Pa (A), FFR (B), and the CFR p-3D (C) without and with hydrostatic pressure correction. In line with the findings of our previous work [18], the correction of the hydrostatic offset resulted in specific concordant differences between the uncorrected and corrected values in the main coronary branches in both resting and hyperemic (FFR) states ( Figure 6A,B). The correction definitively increased the values in the LAD, while in the LCx and the RCA, the values decreased. We observed much higher differences in CFRs, especially in the range of higher CFR values ( Figure 6C).  Figure 6 shows the clustered multiple variable graphs of resting Pd/Pa (A), FFR (B), and the CFRp-3D (C) without and with hydrostatic pressure correction. In line with the findings of our previous work [18], the correction of the hydrostatic offset resulted in specific concordant differences between the uncorrected and corrected values in the main coronary branches in both resting and hyperemic (FFR) states ( Figure 6A,B). The correction definitively increased the values in the LAD, while in the LCx and the RCA, the values decreased. We observed much higher differences in CFRs, especially in the range of higher CFR values ( Figure 6C).

Diagnostic Powers of CFRp-3D Calculated from the Distal Pressure without and with Hydrostatic Offset Correction for Identifying CFRDoppler < 2
The diagnostic power of different computations of the CFRp-3D for predicting the abnormal CFRDoppler was assessed using the computed CFRp-3D (cut-off value = 2). The AUCs of the values calculated without and with hydrostatic error correction was 0.73 (CI: 0.48-0.90) and 0.96 (CI: 0.78-1.00), respectively. Correcting for hydrostatic pressure offset   Figure 6 shows the clustered multiple variable graphs of resting Pd/Pa (A), FFR (B), and the CFRp-3D (C) without and with hydrostatic pressure correction. In line with the findings of our previous work [18], the correction of the hydrostatic offset resulted in specific concordant differences between the uncorrected and corrected values in the main coronary branches in both resting and hyperemic (FFR) states ( Figure 6A,B). The correction definitively increased the values in the LAD, while in the LCx and the RCA, the values decreased. We observed much higher differences in CFRs, especially in the range of higher CFR values ( Figure 6C).

Diagnostic Powers of CFRp-3D Calculated from the Distal Pressure without and with Hydrostatic Offset Correction for Identifying CFRDoppler < 2
The diagnostic power of different computations of the CFRp-3D for predicting the abnormal CFRDoppler was assessed using the computed CFRp-3D (cut-off value = 2). The AUCs of the values calculated without and with hydrostatic error correction was 0.73 (CI: 0.48-0.90) and 0.96 (CI: 0.78-1.00), respectively. Correcting for hydrostatic pressure offset

Diagnostic
Powers of CFR p-3D Calculated from the Distal Pressure without and with Hydrostatic Offset Correction for Identifying CFR Doppler < 2 The diagnostic power of different computations of the CFR p-3D for predicting the abnormal CFR Doppler was assessed using the computed CFR p-3D (cut-off value = 2). The AUCs of the values calculated without and with hydrostatic error correction was 0.73 (CI: 0.48-0.90) and 0.96 (CI: 0.78-1.00), respectively. Correcting for hydrostatic pressure offset increased the specificity of the method from 46.1% to 92.3%, while the sensitivity of both calculations was 100%.

Discussion
In pioneering research, the pressure drop across arterial stenosis was estimated satisfactorily by simple flow equations [22]. Later the 3D anatomical characteristics of the coronary artery were also incorporated into computational fluid dynamics calculations leading to the virtual, image-based FFR assessment [23][24][25]. Recently, the possibility to determine coronary flow from invasively measured intracoronary pressure has arisen by "backward" calculations [26,27]. The so-called pressure-bounded coronary flow reserve (CFR pb ) assessment identified the possible range of CFR according to the resting and hyperemic pressures.
Wijntjens and colleagues compared the CFR pb to flow-derived CFR defined by thermodilution and Doppler measurements in 453 intermediate coronary lesions, but they found a poor diagnostic agreement between the two estimations [28]. It is important to emphasize, that in this publication, hydrostatic offset correction of the distal coronary pressure was not applied to CFR calculations.
Similar to the method presented in this article, an absolute flow calculation with fluid dynamic computation (CFD) using the Ansys software (QCFD) was recently published by Morris et al. [29]. In contrast with our method where the distal flow is rendered to the tapered vessel size [20], their in vitro and in vivo models did not account for flow to side branches, resulting in underestimation of the volumetric flow [30]. This underestimation could lead to unlikely low resting and hyperemic calculated flow values in major coronary branches, as was pointed out in the editorial responding to their paper [31]. It is very obvious that in their in vivo study, the hydrostatic pressure error had caused, at least partly, a very weak correlation to the Doppler results.
The direction of the effect of the hydrostatic offset depends on the orientation of the sensor in the distal position relative to the coronary orifice.
If one interrogates distal LAD with the sensor, the hydrostatic pressure is lower in the supine position, which results in higher pressure ratios after hydrostatic offset correction. In contrast, LCx takes a downward course, which leads to higher hydrostatic pressure at the level of the sensor, and consequently, the pressure values are lower compared to the one measured following correction. The height correction of RCA measurements can result in a slight increase of the distal pressure value, as the distal sensor in the distal RCA is at a lower level compared to the orifice ( Figure 6A,B) [18]. Thus, a slight increase in the corrected pressure ratios can be observed ( Figure 6A,B).
In our opinion, the correction of distal pressure for hydrostatic pressure is essential when determining pressure-derived CFR. A minor hydrostatic pressure may have a significant influence on the measured pressure gradient, especially in the resting state.
This phenomenon is demonstrated in Figure 6C, where the correction resulted in significant differences between the calculated CFR p-3D and the uncorrected values, most prominently in the range of higher CFR values.
The CFR p-3D values calculated after the correction for hydrostatic pressure and those derived from native pressure values were compared with the Doppler flow measurements. A strong correlation was demonstrated between the individual CFR p-3D and the CFR Doppler values when the correction for hydrostatic pressure was made, while the only weak correlation was found without hydrostatic pressure correction.
Importantly, the elimination of hydrostatic pressure offset increased the specificity of our method from 46.1% to 92.3%, while the sensitivity of both calculations remained 100% against the "gold standard" Doppler measurement.

Limitations of the Study
The main limitation of our pilot study of CFR p-3D calculations is represented by the small sample size; however, the archived and statistically highly significant results look promising.
We are aware that our simple model considers only Hagen-Poiseuille-type friction losses and highly simplified Borda-Carnot-type separation losses. For this reason, the calculation of the flow rate is also not expected to be always accurate, but because the CFR is by definition a ratio-type parameter, the CFR p-3D may be accurate enough for clinical applications [22]. The simplified hemodynamic model used for the calculation of the CFR p-3D can consider only one stenosis, with normal proximal and distal segments. Consequently, our flow calculation method in the present form may not be adequate for assessing the hemodynamic relevance of sequential stenoses.
In cases with a very low resting pressure gradient, any small error during the measurement could potentially cause a great deviation in the results, as these values are represented in the denominator during the calculations. However, most of the cases with intermediate coronary lesions showed not less than a 1-2 mmHg resting pressure gradient, which allowed the appropriate calculation of the CFR p-3D .

Conclusions
In this study, we proposed a method of combined determination of FFR and CFR/RRR without the need for a Doppler wire or thermodilution procedure. In our opinion, the CFR p-3D is applicable for most coronary angiography with the clinically indicated invasive measurement of the FFR, when the target vessel is suitable for 3D reconstruction. The flow calculation does not require significantly more time this way. As a result, the consequences of epicardial stenosis can be assessed simultaneously with the state of the microvasculature, thereby supporting the clinical decision for selecting the most appropriate therapy. In our opinion, large-scale studies are warranted to investigate the clinical relevance of the pressure-flow relation determined by our technique [32].

Patents
The patent of the method detailed in this paper has been issued by the European Patent Office (WO2019175612, applicant: University of Debrecen, inventor: Z.K.).