Gavin A. D’SouzaSchool of Dynamic Systems,

Mechanical Engineering Program,

University of Cincinnati,

Cincinnati, OH 45221

Srikara V. PeelukhanaSchool of Dynamic Systems,

Mechanical Engineering Program,

University of Cincinnati,

Cincinnati, OH 45221

Rupak K. Banerjee1

School of Dynamic Systems,

Mechanical Engineering Program,

University of Cincinnati,

Cincinnati, OH 45221

e-mail: rupak.banerjee@uc.edu

Diagnostic Uncertainties DuringAssessment of Serial CoronaryStenoses: An In Vitro StudyCurrently, the diagnosis of coronary stenosis is primarily based on the well-establishedfunctional diagnostic parameter, fractional flow reserve (FFR: ratio of pressures distaland proximal to a stenosis). The threshold of FFR has a “gray” zone of 0.75–0.80, belowwhich further clinical intervention is recommended. An alternate diagnostic parameter,pressure drop coefficient (CDP: ratio of trans-stenotic pressure drop to the proximaldynamic pressure), developed based on fundamental fluid dynamics principles, has beensuggested by our group. Additional serial stenosis, present downstream in a single vessel,reduces the hyperemic flow, ~Qh, and pressure drop, D~p, across an upstream stenosis.Such hemodynamic variations may alter the values of FFR and CDP of the upstream ste-nosis. Thus, in the presence of serial stenoses, there is a need to evaluate the possibilityof misinterpretation of FFR and test the efficacy of CDP of individual stenoses. In-vitroexperiments simulating physiologic conditions, along with human data, were used toevaluate nine combinations of serial stenoses. Different cases of upstream stenosis (mild:64% area stenosis (AS) or 40% diameter stenosis (DS); intermediate: 80% AS or 55%DS; and severe: 90% AS or 68% DS) were tested under varying degrees of downstreamstenosis (mild, intermediate, and severe). The pressure drop-flow rate characteristics ofthe serial stenoses combinations were evaluated for determining the effect of the down-stream stenosis on the upstream stenosis. In general, ~Qh and D~p across the upstream ste-nosis decreased when the downstream stenosis severity was increased. The FFR of theupstream mild, intermediate, and severe stenosis increased by a maximum of 3%, 13%,and 19%, respectively, when the downstream stenosis severity increased from mild tosevere. The FFR of a stand-alone intermediate stenosis under a clinical setting isreported to be �0.72. In the presence of a downstream stenosis, the FFR values of theupstream intermediate stenosis were either within (0.77 for 80%–64% AS and 0.79 for80%–80% AS) or above (0.88 for 80%–90% AS) the “gray” zone (0.75–0.80). This artifi-cial increase in the FFR value within or above the “gray” zone for an upstream interme-diate stenosis when in series with a clinically relevant downstream stenosis could lead tomisinterpretation of functional stenosis severity. In contrast, a distinct range of CDP val-ues was observed for each case of upstream stenosis (mild: 8–10; intermediate: 47–54;and severe: 130–155). The nonoverlapping range of CDP could better delineate the effectof the downstream stenosis from the upstream stenosis and allow for the accurate diagno-sis of the functional severity of the upstream stenosis. [DOI: 10.1115/1.4026317]

Keywords: serial stenoses, coronary diagnostic parameters, fractional flow reserve, pres-sure drop coefficient, in vitro experiments

1 Introduction

Coronary artery disease is known to be a common cause ofdeath among the U.S. population. It may be initiated by a singlefocal stenosis or multiple stenoses in series or a diffuse athero-sclerotic narrowing, either present in a single epicardial vessel ormultiple vessels [1,2]. A disease in the downstream microvascula-ture could also be present in addition to an epicardial stenosis.Quantitative coronary angiography has been a common standard,extensively used to visually evaluate the severity of a stenosis.However, the method of visual interpretation from an angiogramfails to assess the functional (hemodynamic) severity of a stenosis[3]. Therefore, current decisions for the treatment of coronary ste-nosis are based on well-established functional diagnosticparameters: coronary flow reserve (CFR) and fractional flowreserve (FFR) [4–6].

FFR is defined as the ratio of the pressures distal andproximal to a stenotic region [4]. FFR is the most widelyused functional parameter and is considered by many to bethe gold standard for the evaluation of functional significanceof coronary stenosis [7–9]. Under a clinical setting, FFR isinvasively measured with a pressure wire at maximal arterialvasodilation (hyperemia) induced using a vasodilatory drug.Previous clinical studies have reported an FFR cut-off of 0.75for a stenosis present in a single vessel [4,7,10] and 0.80 forstenoses present in multiple vessels [11–13]. Cases with anFFR below 0.75 are recommended for further clinical inter-vention while those with a value above 0.80 are deferred fur-ther intervention. The region between 0.75 and 0.80 is knownto be the “gray” zone for which diagnosis remains uncertain.The other diagnostic parameter, CFR, invasively measuredwith a pulsed Doppler catheter, is defined as the ratio of theflow at hyperemia to the flow at resting (basal) condition[14,15]. A CFR value of <2.0 indicates a condition of eitherepicardial dysfunction or microvascular impairment [5]. How-ever, during in vitro testing, CFR and FFR can be evaluatedusing non-invasive measurements of flow and pressure,

1Corresponding author.Contributed by the Bioengineering Division of ASME for publication in the

JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received September 22, 2013;final manuscript received December 16, 2013; accepted manuscript postedDecember 23, 2013; published online February 5, 2014. Editor: Victor H. Barocas.

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obtained using a flow sensor and pressure scanner,respectively.

CFR, which is based on flow alone, fails to delineate betweenan epicardial and microvascular disease and is affected by fluctua-tions in hemodynamic factors such as heart rate, blood pressure,and myocardial contractility [16,17]. FFR, on the contrary, isknown to remain unaffected by these hemodynamic factors [18].However, it is known to be affected by changes in hemodynamicconditions brought about by the presence of either downstream se-rial stenoses or concomitant microvascular disease or downstreamcollaterals [19–21]. Therefore, we have proposed an alternatediagnostic parameter, pressure drop coefficient (CDP), derivedfrom fundamental fluid dynamics principles. CDP is defined asthe ratio of the trans-stenotic pressure drop to the dynamic pres-sure proximal to a stenosis [22]. Simultaneous measurements offunctional parameters (pressure drop and proximal velocity), nec-essary for the evaluation of CDP, can be readily obtained duringroutine cardiac catheterization procedures using a dual-sensortipped guidewire, also known as a combowire [23–27]. CDP hasbeen validated in pre-clinical trials [21,23,24,26,27] and under aclinical setting [25], in order to delineate epicardial stenoses. Fur-thermore, it has been shown to be independent of heart rate[24,26] and contractility [27,28] in recently conducted in vivo ani-mal studies. CDP is known to have a large range of values com-prising a lower and upper limit of 0 and 1000. A specificdiagnostic cut-off value is currently under clinical investigation.

Evidence of additional stenoses present in a single vessel is of-ten observed in many clinical scenarios [29–34]. In the presenceof serial stenoses, the additive nature of the resistances of the indi-vidual stenoses would lead to an increase in the pressure drop, D~p,coupled with a reduction in hyperemic flow, ~Qh, in the coronaryvessel [35,36]. Conventional angiographic assessment of serialstenoses severity is based only on the degree of area reduction,ignoring the hemodynamic complexities and changes caused bymultiple stenoses in a single vessel [1]. Conclusions from severalin vitro and in vivo tests indicate that serial stenoses have agreater effect on the hyperemic flow response than a single steno-sis of equivalent length and severity [1,35,37–41]. Such observa-tions emphasize the need for better assessment of serial coronarystenoses.

The evidence of the complex fluid dynamic interaction betweenserial stenoses has been reported in literature [1,32,33,35,36,42].Therefore, the need to evaluate these interactions while assessingthe severity of the individual stenosis is of clinical importance tothe cardiovascular intervention community. In the presence of se-rial stenoses, the clinical diagnosis and treatment of disease isfocused on conducting angioplasty on the more significant steno-sis [2,32,33]. Therefore, the hemodynamic significance of con-comitant serial stenoses is often overlooked. While assessing thecombined effect of serial stenoses, it is important to consider theseverity of the individual stenosis since one stenosis may affectthe hemodynamic significance of the other. A second stenosis,present downstream, increases the resistance of the coronaryvessel, thereby reducing ~Qh and, consequently, D~p across anupstream stenosis and vice versa. More importantly, a stenosislocated downstream is shown to have a greater hemodynamiceffect on the one located upstream [32,33]. The true severityof an upstream stenosis may thus be masked by the presenceof a downstream stenosis, particularly if the severity of thedownstream stenosis is comparable to or greater than that ofthe upstream stenosis.

CFR is restricted to assessing the combined functional severityof serial stenoses, thus failing to evaluate the individual stenosisseverity. On the contrary, pressure-based FFR could be used toassess the functional severity of the individual stenosis, but it maybe overestimated in the presence of serial stenoses because of thedecrease in ~Qh and D~p. Thus, FFR may fail to accurately interpretthe true functional severity of individual stenoses in series, lead-ing to the misinterpretation and misdiagnosis of a clinically rele-vant stenosis.

In order to address the effect of serial stenoses, De Bruyne et al.[29] revised the formulation of FFR to include the coronary wedgepressure in addition to the proximal and distal pressures. The re-vised FFR provided a better estimate of the true functional sever-ity of individual stenoses located in series [33]. However, since itscalculation involves the use of coronary wedge pressure that couldbe recorded only during coronary balloon angioplasty, the use ofthe revised FFR is merely limited to theory.

Furthermore, previous studies have failed to account for thereduction in ~Qh, an effect of serial stenoses on coronary autoregu-lation. Here, in order to delineate the effect of the downstream ste-nosis from the upstream stenosis, we assessed the D~p� ~Qcharacteristics of serial stenoses using in vitro experiments whileapplying physiologic hemodynamic conditions. The extent of mis-interpretation of the FFR values for the upstream stenosis wasevaluated in the presence of a varying degree of downstream ste-nosis. In addition, the alternate diagnostic parameter, CDP, wasevaluated to determine the functional severity of the individualstenosis in the presence of serial stenoses.

2 Methodology

The following section describes the in vitro experimental setupalong with the detailed protocol used for assessing the effect ofserial stenoses under physiologic conditions of flow and pressure.

2.1 Stenosis Geometry and Test Section. Angiographic evi-dence from an in vivo data set of 32 patients [43] was used to con-struct rigid models of arterial stenosis representing a mild (�64%area stenosis (AS) or a 40% diameter stenosis (DS)) and severe(�90% AS or 68% DS) condition [44–46]. A third stenosis of in-termediate severity (�80% AS or 55% DS) was constructed usingclinical data reported by Roy et al. [46] and Back and Denton[47]. The stenosis models, fabricated from Lexan material, wereassumed to have a concentric shape with smooth walls. The geo-metric dimensions of the three stenoses are tabulated in Table 1.Each stenosis was composed of a converging and diverging sec-tion separated by a throat region. The three individual stenoseswere paired in series in various combinations to form serialstenoses. A typical test section with the two serial stenoses (seeFig. 1(a)) consisted of an upstream and downstream stenosis con-nected with a Plexiglas connector. Nine combinations of serialstenoses were obtained by varying the severity (mild, intermedi-ate, and severe) of both the upstream and downstream stenosis.The proximal and distal regions represented the inlet and outlet ofeach stenosis (see Fig. 1(a)). A constant distance was maintainedbetween the two stenoses for all of the combinations in order toassess only the primary effect of area reduction on the diagnosticparameters, thus neglecting the secondary effect of length.

2.2 Experimental Setup. The flow loop, shown in Fig. 1(b),was used to perform benchtop tests on serial stenoses under physi-ologic conditions of flow and pressure. The blood analog fluid(BAF), circulated through the loop, was composed of 80% water,20% glycerin, and 0.02% xanthum gum by weight, in order toclosely mimic the non-Newtonian behavior of blood. The viscos-ity of the BAF fluid was measured using a concentric cylinderviscometer (Brookfield Engineering Laboratories Inc.), and thenmatched with the standard Carreau model, similar to our previousstudies [48,49]. A pulsatile blood pump (Harvard Apparatus) was

Table 1 Dimensions of stenotic geometries used

Case lc (mm) lm (mm) lr (mm) dm (mm) de (mm) % ASa

Severe 6.28 0.39 1.59 0.98 3.0 89Intermediate 6.35 0.95 1.62 1.32 3.0 81Mild 6.96 3.15 1.79 1.75 3.0 66

aHere, AS denotes area stenosis.

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used to generate ventricular flow. The flow at the outlet of thepump was split into two branches, one representing aortic flowand the other representing flow through the coronary circulation,which contained the serial stenoses test-sections. A physiologicdiastolic-dominant coronary flow pulse was then obtained byadjusting the flow-level in the compliance chambers, Comp1 andComp2, and regulating the flow rate using the flow valves, R1 andR2 (see Fig. 1(b)). An ultrasound Doppler flow sensor connectedto a digital flow meter console (Transonic Systems Inc.) measuredthe flow rate at the inlet of the test section. The variation in pres-sure across the test sections was recorded using eight pressureports spread over the length of each of the individual stenosesplaced in series. A total of 16 ports were connected to a pressuresensor array module (Scanivalve Corp.), calibrated up to an accu-racy of 60.20%. The simultaneous recording of instantaneousflow and pressure was achieved through a data acquisition systemfitted with an analog input module (National Instruments). Post-processing of the pressure and flow data was done using user-defined macros in Microsoft Excel.

2.3 Pressure and Flow Measurements. An example of theflow pulse and pressure pulses proximal to the upstream anddownstream stenosis obtained during the experiment is shown inFig. 2. These pulses are consistent with previous studies[45,49–51]. Apart from the mean pressure values, no significantdifference was observed between the shapes of the two pressurepulses. The time period of the flow pulse in all cases was approxi-mately 0.8 s; thus representing a typical cardiac cycle. The ratioof the average to peak flow rate varied in the range of 0.5–0.7[45,51]. Based on clinical evidence, mean aortic pressures ð~paÞ

were maintained at 89 mm Hg, 86 mmHg, and 84 mm Hg for anupstream stenosis with severe, intermediate, and mild area block-age, respectively [43,47].

A 0.014 in. (0.35 mm) guidewire was inserted across the serialstenoses with its tip located in the distal region of the downstreamstenosis in order to replicate a clinical setting. This configurationis referred to as condition C1. Pressure recordings were made atfour different flow rates for each serial stenoses combination. Theguidewire was then pulled back across the downstream stenosissuch that the tip was then located in the distal region of theupstream stenosis. This configuration is referred to as conditionC2. Similar pressure-flow recordings were repeated under thisconfiguration for all of the nine combinations of serial stenoses.

Fig. 1 (a) The schematic of the stenotic geometry used. The subscripts e, c, m, and r denote proximal, con-vergent, throat, and distal, respectively for diameter (d) and length (l). (b) A schematic of the experimentalflow loop.

Fig. 2 Pressure and flow pulses obtained during theexperiments

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Three sets (n¼ 3) of experiments were carried out and the threepressure-flow data sets were averaged to obtain the pressure drop-flow rate ðD~p� ~QÞ curves for each of the nine combinations ofserial stenoses.

2.4 Diagnostic Parameters. The diagnostic parameters, frac-tional flow reserve (FFR) and pressure drop coefficient (CDP)were evaluated at hyperemia for assessing the severity of the indi-vidual stenosis. In the following sections, the functional stenosisseverity assessed using FFR and CDP is referred to as stenosis se-verity. A brief overview of these parameters is given in Secs.2.4.1 and 2.4.2.

2.4.1 Fractional Flow Reserve. FFR is defined as the ratio ofmaximum myocardial blood flow in the presence of a stenosis tothe theoretical maximum flow in a normal artery. Under physio-logic condition, at hyperemia, the resistance offered by the distalmicrovasculature is considered minimal and the blood flow is pro-portional to the driving pressure. Therefore, the FFR can be calcu-lated as the ratio of the pressures distal and proximal to a stenosis[4]

FFR ¼ ~prh � ~pv

~pah � ~pv

where ~pah (mm Hg) and ~prh (mm Hg) are the mean hyperemicpressures recorded in the proximal and distal regions of a stenosis,respectively. Here, ~pv (mm Hg) is the mean venous pressurewhich has a value of �0 mm Hg, signifying negligible microvas-cular impairment.

2.4.2 Pressure Drop Coefficient. CDP is defined as the ratioof the trans-stenotic pressure drop to the dynamic pressure proxi-mal to a stenosis [22]. CDP has been derived based on the funda-mental principles of fluid dynamics and signifies thedimensionless pressure drop across a stenosis [52,53]

CDP ¼ D~p

0:5q ~U2e

where D~p (dyne/cm2) represents the mean hyperemic pressuredrop across a stenosis. Here, ~Ue (cm/s) is the mean hyperemic ve-locity recorded in the proximal region of a stenosis and q (g/cm3)is the fluid density.

3 Results

The pressure drop-flow rate ðD~p� ~QÞ characteristics, derivedfrom the in vitro experiments, were used in conjunction with thecoronary flow reserve-distal perfusion pressure (CFR-~prh) plot inorder to obtain physiologic hyperemic flow rates for differentcombinations of serial stenoses. Subsequently, the effect of avarying degree of downstream stenosis on the hyperemic flow,~Qh, and D~p across an upstream stenosis was evaluated. In addi-tion, the severity of the upstream stenosis was assessed usingdiagnostic parameters; FFR and CDP. Data sets for all of the serialstenoses’ combinations obtained for condition C1, where theguidewire is placed across both stenoses (i.e., the sensor tip islocated in the distal region of the downstream stenosis), are pre-sented in this section. The values obtained under condition C2,where the guidewire was placed across the upstream stenosis only(i.e., the sensor tip is located in the distal region of the upstreamstenosis) showed similar trends and produced similar outcomeswhen compared to those obtained under condition C1. Hence, abrief analysis of the results obtained under condition C2 has beenincluded in the Appendix section.

3.1 Pressure Drop-Flow Rate ðD~p� ~QÞ CharacteristicCurves. The D~p� ~Q characteristics of serial stenoses can beexpressed by a quadratic relation D~p ¼ a ~Qþ b ~Q2 obtained after a

polynomial curve-fit to the D~p� ~Q data points [37,42,51–54]. Theeffects of viscous loss and loss due to the change in momentum,contributing to the pressure drop across serial stenoses, are repre-

sented by the terms a ~Q and b ~Q2, respectively. The correspondingcontribution of each effect can be weighed through the viscousloss coefficient ‘a’ and the loss coefficient ‘b’ due to the change inmomentum.

Figure 3 shows the D~p� ~Q curves of the nine combinations ofserial stenoses obtained from in vitro experiments under condi-tions C1 and C2. For both conditions, each D~p� ~Q curve wasplotted using the total D~p, which was obtained using the pressureports and by summing the pressure drops across the individualstenoses placed in series [1,5,35,42,55]. A physiologic limiting D~pof 35 mm Hg was imposed in order to account for the Brown–Bol-son–Dodge criteria for subendocardial ischemia [56]. Figure 3(a)represents the D~p� ~Q curves obtained when the guidewire wasplaced across both stenoses (condition C1). The D~p� ~Q curvesobtained when the guidewire was placed across the upstream ste-nosis only (condition C2) are shown in Fig. 3(b). In general, withthe increase in severity of serial stenoses (upstream or down-stream or both) from mild to severe, the nonlinearity of theD~p� ~Q curve increased, as indicated by higher values of the ‘b’coefficient (see Fig. 3). The method to obtain physiologically rele-vant D~p and ~Q values at hyperemia using the experimentalD~p� ~Q curves is explained in Sec. 3.2.

Fig. 3 Pressure drop – flow rate (D~p� ~Q) characteristics of se-rial coronary stenoses combinations with varying degrees ofseverities: (a) condition C1: 0.014 in. guidewire across bothstenoses, and (b) condition C2: 0.014 in. guidewire across theupstream stenosis

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3.2 Determination of Hyperemia Using Coronary FlowReserve-Distal Perfusion Pressure and D~p� ~Q Plots. The hy-peremic flow rates, ~Qh, for all of the serial stenoses combinationswere obtained using the intersection of the coronary flow reserve-distal perfusion pressure (CFR-~prh) line and the experimental

D~p� ~Q curve (see Fig. 4) [46,48,51]. The linear curve in Fig. 4represents the relationship between the CFR and the correspond-ing ~prh of 32 patients [43] having a focal lesion and undergoingpercutaneous transluminal coronary angioplasty (PTCA). Evi-dence of any microvascular dysfunction was not reported in thesepatients. The left ventricular ejection fraction remained normalwith no left ventricular hypertrophy or valvular heart disease. Inaddition, no signs of myocardial infarction or stenosis in the par-ent branch or angiographically evident collateral flow wereobserved. As seen in Fig. 4, the CFR-~prh line has an x-intercept of20 mm Hg. At this zero-flow pressure ~pzf flow to the subendocar-dium ceases. Van Herck et al. [57] observed a ~pzf of 14.6 6 8.0mm Hg in patients with stable angina pectoris whereas Bache andSchwartz [58] reported a ~pzf of 18 mm Hg for a dog. Thedistal perfusion pressure at hyperemia ~prh (the x-axis of Fig. 4) ofserial stenoses was obtained using the experimentally obtained

D~p� ~Q relation (see Fig. 3) and the known mean aortic pressure,

i.e., ~prh ¼ ~pa � D~p ¼ ~pa � ða ~Qþ b ~Q2Þ. In other words, the

intersection of the experimentally obtained nonlinear D~p� ~Q

characteristic curve of the serial stenoses in combination with thephysiologically reported linear CFR-~prh plot provides the ~prh at

the downstream stenosis and the CFR (¼ ~Qh= ~Qb (the y-axis

in Fig. 4); where ~Qh, is the hyperemic flow and ~Qb is the

known value of basal flow) [46,54,59]. In this study, a ~Qb value of50 ml/min was considered for the calculation of the CFR [43].

Figure 4(a) indicates the estimation of ~Qh under condition C1.For example, in case of the 90%–64% AS combination, the inter-

section of the D~p� ~Q characteristic curve and the CFR-~prh lineprovides a CFR value of 2.1 and a ~prh of 52.5 mm Hg (the dottedhorizontal and vertical lines in Fig. 4(a)). Keeping the upstream %AS to be severe (90% AS or 68% DS), the CFR decreased from1.9 to 1.5 when the downstream stenosis severity was increasedfrom intermediate (80% AS or 55% DS) to severe (90% AS) (seearrow number 1 in Fig. 4(a)). Consequently, the corresponding ~prh

decreased from 50.1 mm Hg to 43.6 mm Hg. For the case with anupstream stenosis of intermediate severity (80% AS), the CFRdecreased from 2.7 to 2.5 and, subsequently, to 1.8 when theseverity of the downstream stenosis was increased from mild tointermediate and, subsequently, to severe, respectively. Conse-quently, the ~prh for the corresponding cases decreased from 62.3mm Hg to 59.1 mm Hg and, subsequently, to 48.1 mm Hg.Similarly, when the upstream stenosis severity was mild (64%AS or 40% DS), the CFR decreased from 3.3 to 2.6 and furtherto 1.9 when the severity of the downstream stenosis was increasedfrom mild to intermediate and, further, to a severe % AS, respec-tively. A subsequent decrease in ~prh from 71.5 mm Hg to 60.0 mm

Fig. 4 CFR – ~prh curves of serial coronary stenoses combina-tions with varying degrees of severities: (a) condition C1: 0.014in. guidewire across both stenoses, and (b) condition C2: 0.014in. guidewire across the upstream stenosis

Fig. 5 Bar graphs indicating the effect of serial coronary sten-oses on hemodynamic parameters under condition C1: (a) hy-peremic flow, and (b) upstream stenosis pressure drop

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Hg and further to 49.7 mm Hg was observed for the respectivecases.

In general, for each case of upstream stenosis, the CFR and ~prh

values of the combination decreased with an increase in down-stream severity. An overlap of CFR and ~prh values was observedbetween each case of upstream stenosis as the downstreamseverity was varied. Similar trends were observed in the CFR-~prh

values evaluated under condition C2 (see Fig. 4(b)).

3.3 Guidewire Across Both the Stenoses (Condition C1)

3.3.1 Effect of Serial Stenoses on Flow and Pressure. The bargraphs plotted in Figs. 5(a) and 5(b) indicate the effect of the pres-ence of a downstream stenosis on the hyperemic coronary flow,~Qh, and pressure drop across the upstream stenosis, D~pu, (the sub-script ‘u’ denotes an upstream stenosis), respectively, when eval-uated under condition C1 (see Table 2).

Upstream severe stenosis. The ~Qh decreased from 104.8 ml/min to 97.1 ml/min when the downstream severity increased frommild to intermediate. As the downstream stenosis increasedfurther to a severe condition, ~Qh decreased to 76.1 ml/min; thusindicating an overall reduction of nearly 27% (percentage varia-tion¼ (maximum value – minimum value)� 100/maximumvalue) in maximum flow across the upstream severe stenosis (seeTable 2). A D~pu of 33.5 mm Hg was observed across the upstreamsevere stenosis in the presence of a downstream mild stenosis.The D~pu decreased to 27.7 mm Hg and further to 20.4 mm Hg inthe presence of a downstream intermediate and severe stenosis,respectively. Due to the reduction in ~Qh, a significant overallreduction (�39%) in D~pu was observed when the downstream ste-nosis severity increased from mild to severe.

Upstream intermediate stenosis. The ~Qh decreased from 136.4ml/min to 126.4 ml/min for cases with a downstream mild and in-termediate stenosis, respectively (see Table 2). The value of ~Qh

corresponding to the case with a downstream severe stenosis was90.7 ml/min. Thus, a greater overall reduction (�34%) in ~Qh wasobserved for this case in comparison to the case with an upstreamsevere stenosis. Subsequently, D~pu across the intermediate steno-sis decreased from 19.7 mm Hg to 17.8 mm Hg and, further, to10.1 mm Hg for the cases with a downstream mild, intermediate,and severe stenosis, respectively, resulting in a reduction of D~pu

of nearly 49%, considering the entire range.

Upstream mild stenosis. By varying the severity of the down-stream stenosis, a significant effect was observed on ~Qh and D~pu

for an upstream mild stenosis (see Table 2). The ~Qh decreased bynearly 42% (166.1 ml/min for 64%–64% AS, 130.8 ml/min for64%–80% AS, and 95.9 ml/min for 64%–90% AS) while the D~pu

decreased by nearly 57% (4.8 mm Hg for 64%–64% AS, 3.7 mmHg for 64%–80% AS, and 2.1 mm Hg for 64%–90% AS).

In general, ~Qh through a coronary vessel decreased when the se-verity of the downstream stenosis was increased. Consequently,D~pu also reduced with an increase in the downstream % AS.

3.3.2 Effect of Serial Stenoses on Diagnostic Parameters. Thediagnostic parameters, FFR and CDP (see Table 3), were calcu-lated for the upstream stenosis using the hyperemic values of thepreviously discussed pressure and flow. The effect of serial sten-oses, evaluated under condition C1 on the FFR and CDP is shownin Figs. 6(a) and 6(b), respectively. The shaded region of FFRfrom 0.75 to 0.80 in Fig. 6(a) corresponds to the “gray” zone ofFFR for which diagnostic uncertainties are well documented.Clinical intervention is generally recommended for FFR valuesbelow 0.75.

Fractional Flow Reserve (FFR)

Upstream severe stenosis. FFR of the upstream severe stenosiswas 0.62 when a mild stenosis was placed downstream (see Table3). Similarly, an FFR value of 0.69 was recorded for the case witha downstream intermediate stenosis. This value increased to 0.77,which was within the “gray” zone, when a severe stenosis wasplaced downstream.

Upstream intermediate stenosis. The FFR values for a singleintermediate stenosis were previously reported to be 0.72 [60] and0.73 [51], based on clinical and in vitro studies, respectively. Inthe presence of a downstream mild and intermediate stenosis, theFFR values of the upstream intermediate stenosis increased to0.77 and 0.79, respectively, and were within the “gray” zone (seeFig. 6(a)). Hence, the severity of the upstream intermediate steno-sis may be misdiagnosed when placed in series with a downstreammild or intermediate stenosis. When the downstream severityincreased further to a severe stenosis, the FFR value increased to0.88. This value is well above the upper threshold limit for clinicalintervention and could lead to the incorrect diagnosis, leading to

Table 2 Effect of serial stenoses on flow and pressure

Hyperemic flow, ~Qh (ml/min) Upstream stenosis pressure drop, D~pu (mm Hg)

Downstream stenosis 64% 80% 90% 64% 80% 90%

Upstream stenosis C1 C2 C1 C2 C1 C2 C1 C2 C1 C2 C1 C2

90% 104.8 106.1 97.1 98.4 76.1 82.7 33.5 33.5 27.7 28.5 20.4 24.180% 136.4 134.6 126.4 130.1 90.7 102.9 19.7 20.9 17.8 17.9 10.1 12.464% 166.1 170.7 130.8 138.8 95.9 111.0 4.8 4.8 3.7 4.8 2.1 3.6

Table 3 Effect of serial stenoses on diagnostic parameters

FFR CDP

Downstream stenosis 64% 80% 90% 64% 80% 90%

Upstream stenosis C1 C2 C1 C2 C1 C2 C1 C2 C1 C2 C1 C2

90% 0.62 0.62 0.69 0.68 0.77 0.73 134 131 129 130 155 15580% 0.77 0.76 0.79 0.79 0.88 0.86 47 51 49 47 54 5264% 0.94 0.94 0.96 0.94 0.98 0.96 8 7 9 11 10 13

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deferral of intervention for the clinically relevant intermediatestenosis.

Upstream mild stenosis. An overestimation in the FFR of theupstream mild stenosis was observed when the downstream steno-sis severity increased from mild to intermediate and, further, to asevere area blockage (see Table 3). However, as observed in Fig.6(a), all FFR values of the mild stenosis were above the “gray”zone [0.94 for 64%–64% AS, 0.96 for 64%–80% AS, and 0.98 for64%–90% AS]. Under such a scenario, the functional diagnosis ofserial stenoses remains unaffected.

Overall, with an increase in the severity of the downstream ste-nosis from mild to severe, causing reduced hyperemic flow andpressure drop, the FFR of the upstream mild, intermediate, andsevere stenosis increased by a maximum of 3%, 13%, and 19%,respectively. For the clinically relevant upstream intermediate ste-nosis, while in the presence of a downstream severe stenosis, theFFR value increased above the threshold range. This may lead tomisinterpretation and misdiagnosis of stenosis severity. Addition-ally, as previously discussed, for upstream severe and intermedi-ate stenoses, uncertainties in the FFR values (the “gray” zone)could be observed when the severity of the downstream stenosesincreased. However, in standard clinical practice, a visually severestenosis would be treated based on angiographic evidence aloneand irrespective of the FFR value. Under such a scenario, for the

case with an upstream intermediate stenosis present in series witha downstream severe stenosis, the lesion will be re-assessed usingthe FFR under increased hyperemic flow conditions to determinethe true severity of the upstream intermediate stenosis. Further-more, the overestimation in the FFR of the upstream severe steno-sis would not affect clinical decision making when present inseries with another downstream severe stenosis.

Pressure Drop Coefficient (CDP)

Upstream severe stenosis. The CDP values of the severe steno-sis corresponding to the cases with a downstream mild and inter-mediate stenosis were 134 and 129. However, the CDP valuesomewhat increased to 155 when a severe stenosis was placeddownstream. Thus, the CDP showed no specific trend with theincrease in the downstream stenosis severity (see Fig. 6(b)).

Upstream intermediate stenosis. The CDP of the intermediatestenosis was 47 when combined with a downstream mild stenosis,which then increased to a value of 49 when placed in series with adownstream intermediate stenosis. When the % AS of the down-stream stenosis increased to severe, the CDP of the upstream ste-nosis further increased to 54 (see Table 3).

Upstream mild stenosis. An insignificant increase in the CDPvalues of the upstream mild stenosis was observed when thedownstream severity was increased (8 for 64%–64% AS, 9 for64%–80% AS, and 10 for 64%–90% AS).

Hence, minimal changes were observed in the CDP values ofthe upstream stenosis when the downstream severity wasincreased. More importantly, a distinct range of CDP values wasobserved for each case of upstream stenosis (mild: 8-10; interme-diate: 47-54; and severe: 130-155).

4 Discussion

Variations in flow and pressure, caused by the presence of serialstenoses in a coronary artery, are observed to influence the diag-nostic parameters: FFR and CDP. For serial stenoses, theincreased values of the FFR for an upstream intermediate stenosiscould be within the cut-off range of 0.75–0.80. Such an increasein the FFR near the “gray” zone may lead to misinterpretation ofstenosis severity. Hence, in the present in vitro experiment, weassessed the variability of the FFR and CDP of upstream mild, in-termediate, and severe stenosis, when in series with a downstreamstenosis of different area obstruction. In the presence of a down-stream stenosis, the FFR of a clinically relevant upstream interme-diate and severe stenosis was overestimated above or near theclinical cut-off value, which may lead to misdiagnosis of stenosisseverity. The CDP, on the contrary, showed a distinct range ofvalues for each case of the upstream stenosis. This could allow foran accurate diagnosis of the upstream stenosis severity, irrespec-tive of the presence of downstream stenoses.

Additional resistance offered by a downstream stenosis reduceshyperemic flow, ~Qh through the coronary vessel. As a conse-quence, the pressure drop across an upstream stenosis, D~pu

decreases. Such flow-related changes in D~pu, observed in thisstudy, are comparable to previous studies on serial stenoses[32,33,35,36]. Since the FFR is based on the pressure ratio alone,the decrease in D~pu would lead to a subsequent increase in theFFR values of the upstream stenosis. In order to analyze thisincrease in the FFR, in the presence of an additional downstreamstenosis, a comparison of our results is conducted with data froma patient group having a single coronary stenosis [60]. The FFR ofthe single stenosis before intervention (78610% AS), measuredusing a 0.014 in. guidewire, was 0.7260.10, which then increasedto 0.8460.08 post-intervention (64611% AS). An in vitro studypreviously conducted in our lab has reported an FFR value of 0.73for a single intermediate stenosis, which is similar to the clinicallyobserved value [51]. In the presence of an additional downstreamstenosis, the FFR values of the upstream stenosis of intermediate

Fig. 6 Bar graphs indicating the effect of serial coronary sten-oses on diagnostic parameters under condition C1: (a) FFR,and (b) CDP

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(80% AS) and mild (64% AS) severities, evaluated under condi-tion C1, were overestimated by a maximum of 18% of the pre-intervention and 14% of the post-intervention clinical values.Considering the reduction in ~Qh, such a moderate increase in theFFR for the upstream intermediate and mild stenosis, recorded inthe presence of an additional downstream stenosis, is expected ina clinical setting.

Furthermore, in order to validate the results from our in vitroexperiments, a comparison of our data is conducted with a clinicalstudy that had patients having serial coronary stenoses within asingle vessel [33]. Among all of the serial stenoses of the patientgroup, percutaneous transluminal coronary angioplasty (PTCA)was recommended for individual stenoses having �75% AS. TheFFR of the upstream stenosis, measured with a 0.014 in. pressureguidewire, was 0.87 6 0.08 in the presence of a downstream ste-nosis before the PTCA of the downstream stenosis. After thePTCA of the downstream stenosis, the FFR of the upstream steno-sis decreased to 0.76 6 0.02. This amounts to an overestimation of14% in the FFR value of the upstream stenosis when its value iscompared for pre- and post-PTCA of a downstream stenosis. Thisclinical data closely matches with: (a) the FFR �0.88 calculated inthe present study under condition C1, for the case with 80%–90%AS, which represents a pre-PTCA condition of the downstreamstenosis, and (b) the FFR �0.76 for 80%–64% AS representing acondition of post-PTCA of the downstream stenosis. Such a closecomparison with clinical data provides confidence to the results ofthis study. More importantly, the elevated FFR observed for theupstream stenosis, before the PTCA of the downstream stenosis,indicates the possibility of misinterpretation and misdiagnosis ofstenosis severity in the presence of serial stenoses.

In order to overcome the limitations of FFR for accurately diag-nosing the severity of serial coronary stenoses, an alternate diag-nostic parameter, CDP, is proposed [22]. CDP is unique since itincludes the nonlinear D~p� ~Q relationship developed from funda-mental fluid dynamics principles. In addition, under hyperemicflow, the higher significance paid to the mean proximal velocity(square of ~Ue), can provide an increased ability to accuratelyresolve the delineation of an individual epicardial stenosis whenplaced in series. In general, as the severity of a single stenosis wasvaried, CDP was shown to change by a few orders (range:0–1000) of magnitude [21,49,51,52]. Furthermore, CDP wasshown to delineate the severity of epicardial stenosis under a clini-cal setting [25]. In the presence of a serial downstream stenosis,CDP values showed no specific trend or relative variation for theupstream severe stenosis, while the values for the upstream mildand intermediate stenosis showed an insignificant increasing trendwith the increase in downstream severity, when evaluated underC1 condition. In contrast, considering a larger range of CDP, weobserved distinct ranges of CDP values calculated for eachupstream stenosis, irrespective of the variation in severity of thedownstream stenosis. Such trends and the distinct ranges of CDPvalues for each case of upstream stenosis may indicate that theCDP is a stenosis-specific parameter which will delineate theeffect of serial stenoses and better diagnose the severity of theindividual stenosis.

In the present study, in vitro measurements of pressure and flowfor the serial stenoses combinations were made under two condi-tions: one with the guidewire across both stenoses (condition C1)and the other with the guidewire across the upstream stenosis only(condition C2). The measurements made under condition C1 (incomparison to C2) provide a conservative estimate of D~p since thepresence of the guidewire across a stenosis causes a relativelyhigher reduction in flow, thus producing a somewhat decreasedD~p [46,61–63]. This limiting scenario would lead to the relativelyhigher overestimation in the FFR for serial stenoses. Furthermore,the results for the two conditions (C1 and C2 (see the Appendix))did not alter the outcome.

4.1 Assumptions. The stenoses models were assumed to havea rigid wall based on clinical observations suggesting the loss of

compliance in a stenosed artery [64,65]. In addition, the rigid wallassumption provides a conservative estimate of D~p since a compli-ant artery produces a reduced D~p at similar flow rates [66]. Inaddition, for the present study, the hyperemic flow rates for serialstenoses were estimated using a CFR-~prh plot obtained for patientsundergoing PTCA of a single coronary stenosis. In the presence ofserial stenoses, the CFR-~prh line may have a somewhat reducedslope and this may cause some added reduction in ~Qh. However,we do not expect such a small reduction in ~Qh to alter the diagnos-tic parameters observed in this study. Additionally, the closematch of our results with the clinical data lends credibility to ourassumption.

4.2 Limitations and Future Work. The individual stenosesplaced in series were assumed to have a concentric shape withfixed geometric parameters such as the percentage of area block-age, converging and diverging angles, and length of stenosis [43].Although the heterogeneity in these geometric parameters,observed in a clinical scenario, could produce variations in theresults, it is the % AS that has the primary influence on the pres-sure drop data [67,68]. Thus, the length of an individual stenosis,compared to the % AS, has a lesser effect on ~Q and D~p due to thelesser change in viscous loss compared to the loss due to a changein momentum. Furthermore, all of the combinations of serial sten-oses were tested under a fixed connecting length, which allowedfor the reattachment of flow distal to the upstream stenosis. Thus,for the current study, the connecting length is sufficient for theflow to be fully developed in the downstream stenosis. However,the reduction in length separating the two stenoses may influencethe pressure drop across the stenoses’ combination. Therefore, theeffect of the variation in length between the two stenoses on thediagnostic parameters, the FFR and CDP, needs to be assessed inthe future. In addition, the stenosis length and % AS need to bestudied further in combination.

The experiments were conducted with an antegrade flow acrossthe stenoses; thus neglecting the effect of branched or collateralflow between the stenoses. Such flow may influence the pressuresdistal and proximal to the upstream and downstream stenosis,respectively, and hence affect the total pressure drop [21]. There-fore, future studies on serial stenoses that account for the presenceof collaterals and branched flow are needed.

5 Conclusion

In the presence of serial coronary stenoses, the hyperemic flow~Qh significantly reduced with an increasing severity of either theupstream stenosis or the downstream stenosis. Such a decrease in~Qh led to the decrease in the pressure drop D~p across either of theserial stenosis. Consequently, when the downstream stenosis se-verity increased from mild to severe, the FFR of the upstreammild, intermediate, and severe stenosis increased by a maximumof 3%, 13%, and 19%, respectively. For an upstream intermediatestenosis, the FFR increased and was either within or above the“gray” range of 0.75–0.80. Therefore, this increase in the FFRabove the clinical cut-off would lead to an incorrect deferral ofclinical intervention. This may cause misinterpretation of stenosisseverity. Considering the wide range of CDP, the CDP of theupstream stenosis varied insignificantly in the presence of a down-stream stenosis with a varying degree of severity. However, a dis-tinct range of CDP values for each case of upstream stenosis(mild: 8–10; intermediate: 47–54; and severe: 130–155) allowedfor better diagnosis of the upstream stenosis severity in the pres-ence of a downstream stenosis.

Thus, the complex hemodynamic interactions between serialstenoses may affect the hyperemic flow, pressure drop, and FFRacross the individual stenosis when placed in series. For the previ-ously discussed scenarios, the FFR may fail to account for the se-verity of the individual stenosis while assessing serial stenoses. Incontrast, CDP, which combines pressure and flow, may betterdelineate the effect of serial stenoses; thus, holding the promise

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for better functional assessment and clinical diagnosis of individ-ual stenosis severity.

Acknowledgment

The authors are thankful to Mr. Ishan Goswami for his helpwith the initial setup of the experiments and data analysis.

Appendix

The hyperemic flow, ~Qh, and upstream pressure drop, D~pu,evaluated under condition C2 (guidewire across the upstream ste-nosis only), decreased when the downstream stenosis severity wasincreased (see Fig. 7). These values are comparable to thoseobtained under condition C1 (guidewire across both stenoses) (seeTable 2). The FFR of the upstream mild, intermediate, and severestenosis, evaluated under condition C2, increased by a maximumof 3%, 12%, and 16%, respectively, when the downstream sever-ity increased from a mild to a severe condition (see Table 3). Withthe guidewire pull-back across the downstream stenosis, the FFRof the clinically relevant upstream intermediate stenosis was over-estimated (0.86; see Fig. 8(a)) above the clinical cut-off, thusleading to the possible misinterpretation of stenosis severity.Thus, similar trends in the FFR were observed under conditionsC1 and C2, except for the 90%–90% AS case, where the FFR ofthe severe upstream stenosis was below the “gray” zone whenevaluated under the C2 condition (see Fig. 8(a)). Thus, the diag-

nostic misinterpretation may not occur for this scenario. CDP,evaluated under condition C2 (see Fig. 8(b)), showed a distinctrange of values (mild: 7–13; intermediate: 47–52; and severe:130–155) for each case of upstream stenosis in the presence of avarying degree of downstream stenosis. Hence, the nonoverlap-ping range of the CDP may better delineate the effect of the down-stream stenosis from the upstream stenosis.

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