A Novel Hydrodynamic Approach for the Evaluation of Microvascular Resistance during Provocative Spasm Testing

Abstract

Introduction

Intracoronary acetylcholine provocative testing is the gold standard method for the assessment of epicardial and/or microvascular spasm, with the latter diagnosed when there are acetylcholine (ACh)-induced chest pain and ischaemic electrocardiogram changes in the absence of epicardial spasm. While epicardial spasm can be visualised, microvascular spasm cannot and remains a presumed diagnosis.

Methods

This article describes a hydrodynamic model developed to calculate the epicardial and microvascular resistances for both pre- and post-ACh administration. The model is based on the concept of two resistances (epicardial and microvascular) located in a series arrangement. The epicardial resistance is obtained as a hydraulic resistance, accounting for the friction resistance between the coronary blood flow and the arterial walls. The microvascular resistance is calculated by subtracting the epicardial resistance from the ratio of the pressure and flow measured using coronary guidewire-based techniques.

Conclusion

This novel methodology provides key insights into the physiological characteristics of epicardial and microvascular spasm during ACh provocation testing. Further clinical validation is required to explore the clinical utility of this methodology.

Introduction

Approximately 1 in three patients undergoing invasive coronary angiography for the investigation of chest pain have angina and non-obstructive coronary arteries [1]. With obstructive atherosclerotic coronary artery disease excluded as a cause of their chest pain, coronary vasomotor disorders must be considered (i.e., coronary artery spasm and/or coronary microvascular disorders). Functional coronary angiography incorporating provocative spasm testing with acetylcholine (ACh) is the gold standard approach for the assessment of coronary artery spasm [2]. Thus, ACh provocation may identify (a) epicardial coronary artery spasm, defined as a ≥90% coronary artery constriction associated with reproducible chest pain symptoms and ischaemic electrocardiogram (ECG) changes [3], (b) microvascular spasm, defined as ACh-induced reproducible chest pain and ischaemic ECG changes in the absence of epicardial spasm [4], or (c) no inducible coronary artery or microvascular spasm [3, 5]. By this definition, a diagnosis of both epicardial and microvascular spasm is not possible. Microvascular spasm is a presumed diagnosis in the absence of significant epicardial constriction as the microscopic vessels are not visible via standard medical imaging techniques. However, conceptually the two may coexist.

Developing a novel engineering model to simulate changes in epicardial and microvascular resistances during ACh provocation can improve the pathophysiological understanding of coronary artery spasm and provide insights to address current diagnostic limitations. The objective of this article was to detail a novel hydrodynamic model that enables independent assessment of epicardial and microvascular resistances during ACh provocation utilising measurements of blood flow velocity and coronary pressure derived from an intracoronary pressure-Doppler flow wire.

Method

Study Cohort

De-identified angiographic images and physiologic data from patients with angina and non-obstructive coronary artery undergoing a standardised functional coronary angiography protocol [6] were used in this study, with institutional ethics approval. Indices of coronary haemodynamics were measured utilising an intracoronary dual sensor-tipped pressure-Doppler flow wire (ComboWire, Phillips, CA) deployed in the mid-left anterior descending artery (mid-LAD) during ACh provocation testing, thereby enabling real-time recording of coronary pressure and blood flow velocity [6].

Hydrodynamic Rationale

From a haemodynamic perspective, the intra-arterial pressure declines due to increased intra-arterial resistance, influenced by several factors including (1) friction between the arterial wall and blood (explained through Poiseuille’s law [7]), (2) arterial obstruction – i.e., the presence of stenosis or temporal arterial narrowing such as arterial spasm, and (3) arterial tortuosity. The blood flow resistance (R), can be defined analogously to electrical resistance in Ohm’s law, where the pressure drop (∆P) is analogous to voltage, and flow rate (Q) is analogous to current, thus expressed as:

$$∆P=QR,$$ (1)

The pressure drops throughout the coronary circulation to its distal terminus (i.e., coronary venous system) due to both epicardial (R_epicardial) and microvascular (R_mv) resistances. The proposed model considers these as two resistances connected in a series configuration.

Figure 1 schematically illustrates the model, with the ComboWire situated in the mid-LAD to assess blood flow velocity and coronary pressure, alongside coronary artery diameter measurements facilitating the calculation of epicardial and microvascular resistances. The epicardial resistance within the LAD (as discussed by Freidoonimehr et al. [8]), is calculated based on the Darcy-Weisbach equation; an empirical equation that relates the pressure drop due to the friction along a given length of pipe to the average velocity of the fluid flow. This equation is calculated as follows:

$${∆P}_{LAD}=\frac{128\mu L{Q}_m}{\pi D_{ave}^4},$$ (2)

where ∆P_LAD is the pressure drop along the LAD (difference between the pressure value at the wire tip and the distal pressure at the distal end of LAD), μ is the blood viscosity, L is the length of LAD from a reference point (typically starting from the left coronary artery bifurcation) to the very end of the artery captured on angiography, and D_ave is the average diameter of the LAD. The blood viscosity is assumed to be constant and equal to 3 centipoise. Based on this equation, the epicardial resistance inside the LAD is calculated as:

$$R_{epicardial}=\frac{128\mu L}{\pi D_{ave}^4},$$ (3)

Fig. 1.

Schematics of the LAD and the coronary microcirculation and how they are modelled as two resistances in a series configuration, including the epicardial resistance, R_epicardial, and microvascular resistance, R_mv. Pressure and velocity at the tip of the ComboWire are P_a and VA, respectively, and P_v indicates venous pressure.

The microvascular resistance (R_mv) is then calculated by subtracting the epicardial resistance from the ratio of the pressure and the velocity within the LAD as:

$$\frac{P_a-P_v}{Q_a}=R_{epicardial}+R_{mv},$$ (4)

$$R_{mv}=\frac{P_a-P_v}{Q_a}-R_{epicardial},$$ (5)

where P_a is the pressure at the proximal artery, Q_a is the blood flow rate (calculated by multiplying the blood velocity by the cross-sectional area of the artery at the wire tip), and P_v is the venous pressure, assumed to be equal to 5 mm Hg [9].

Figure 2 demonstrates the expected schematic profile of the LAD and microcirculation resistances with and without the presence of microvascular spasm. As shown in Eq. 3, the resistance is inversely proportional to the power of 4 of the diameters. As the microvascular diameter is much smaller than the LAD, the microvascular resistance is then much larger than the LAD resistance. Microvascular spasm is attributed to severe constriction of the microvessels and, thus, manifests as an increased microvascular resistance. Hence, the microvascular resistance is higher when there is microvascular spasm.

Fig. 2.

The coronary arterial resistance of the LAD comprises the epicardial vessel and microcirculation. The resistance inside the LAD is shown from the location of ComboWire. The epicardial LAD resistance was less compared to the microcirculation resistance. It is assumed upon the presence of microvascular spasm, the microcirculation resistance increases considerably. LAD refers to the left anterior descending coronary artery, R_a is the proximal resistance, R_epicardial and R_mv are the epicardial and microvascular resistances, respectively.

Proposed Haemodynamic Analysis

To calculate the epicardial and microvascular resistances, the following steps are required.

• 1.Pressure and Flow Recordings. The ComboWire recordings are evaluated to calculate the pressure and blood flow velocity values at baseline (pre-ACh) and maximum dosage of ACh (post-ACh) (i.e., dose at which epicardial spasm is induced, or at 100 μg if there is no inducible spasm). A 20-s window of continuous recordings is extracted for the pre-ACh and post-ACh from the ComboMap software (Fig. 3), and the corresponding average values and standard deviations are calculated. These values are used as P_a and Q_a in Eq. 5.
• 2.Coronary Artery Diameter Measurement. The angiogram images are processed to calculate the length (L) of the LAD segment using standard reference points (i.e., from the artery origin to the distal tip of the LAD), and the diameter (D) of the distal LAD at different sites.

Fig. 3.

a ComboWire continuous pressure and flow velocity recordings with a 20-s window extracted for pre-ACh (b) and post-ACh (c).

The Choice of Reference Point Location

The reference point to calculate the epicardial resistance and, consequently, microvascular resistance was selected at a standard reference point, i.e., the origin of LAD. This location was selected to ensure that the ComboWire is located within the selected region for both pre-ACh and post-ACh measurements. The choice of this location does not impact the model result. An example of varying the selected starting reference location by the intervals of 10 mm from the standard LAD origin reference point is shown in Figure 4, with the reference point chosen up to 30 mm distal to the LAD origin. Any further downstream shift in the reference point would result in the ComboWire being located outside the selected domain. This comparison demonstrates that although the epicardial and microvascular resistance absolute values change based on different reference points (due to average diameter and length changes in Eq. 3), the proportional resistance change does not vary significantly since any changes in the starting point would affect them concurrently.

Fig. 4.

Variation in the selected starting reference location to calculate the epicardial resistance for both pre-ACh (a) and post-ACh (b). The starting location shifts downstream by intervals of 10 mm compared to the chosen reference point. Table c tabulates the epicardial and microvascular resistances calculated based on different selected reference points.

The labelled LAD section length and spatial diameter distribution are calculated using MATLAB (MathWorks, CA, USA). To achieve this, a series of steps are utilised to analyse arterial structure systematically. First, the centreline of the artery is extracted to establish a central path for further calculations. Subsequently, the boundary of the artery is computed to define its edge accurately. The shortest distance from each point on the centreline to the corresponding edge is calculated to assess the diameter distribution along the centreline. Through this approach, a comprehensive profile of arterial diameter variation along the length of the LAD is established. A calibration factor is then applied to convert the values in pixels obtained from angiogram images to unit length (mm). This procedure is repeated for both pre-ACh and post-ACh. The manual mapping process of the LAD was conducted on 10 cases by two independent, blinded observers to avoid bias and assess technique reproducibility. In addition, each observer completed the mapping process twice, with the second measure conducted independently and blinded, without reference to their initial mapping. The coefficients of variation for both inter-observer and intra-observer reproducibility were 7% and 3.3%, respectively.

The process of LAD mapping for two cases with and without epicardial spasm for the pre-ACh and post-ACh is shown in Figure 5. The spatial diameter of the artery and the percentage changes in the LAD for the post-ACh compared to the pre-ACh are illustrated in Figure 6. Figure 6b illustrates the utility of this precise methodology in measuring changes in vessel diameter post-ACh across the length of the artery. A significant narrowing can be observed in several locations for the case with epicardial spasm upon administration of the maximum ACh dose (post-ACh), which is consistent with the clinical diagnosis of this patient.

• 3.Calculation of Resistances. The values obtained from the previous two steps are substituted into equations 3 and 5 to calculate the epicardial and microvascular resistances, respectively. The calculations assume a constant viscosity of 3 centipoise and a coronary venous pressure of 5 mm Hg. The justification for these assumptions is detailed in the Supplementary Data (for all online suppl. material, see https://doi.org/10.1159/000547197).

Fig. 5.

Image mapping protocol applied to calculate the diameter and the length of LAD for two cases without (left column) and with (right column) epicardial spasm for both pre-ACh (top row) and post-ACh (bottom row).

Fig. 6.

The profiles of artery diameter for two cases without and with epicardial spasm at different locations from proximal to the ComboWire to the very distal aspect of the LAD for both pre-ACh (solid blue line) and post-ACh (dashed blue line). The right-hand-side vertical axis shows the changes in the diameter of the LAD at post-ACh compared to the pre-ACh (solid orange line).

Discussion

Current diagnostic methods do not allow the concurrent diagnosis of epicardial and microvascular spasm as the latter can only be diagnosed with the demonstration of ACh-induced myocardial ischaemia in the absence of epicardial coronary artery spasm. Thus, microvascular spasm is a presumptive diagnosis without any physiological evidence of abnormal coronary microvascular function. For the first time, the detailed hydrodynamic model provides an independent assessment of epicardial and microvascular resistance, thereby enabling the evaluation of abnormal coronary microvascular function with concurrent assessment of potentially contributing epicardial coronary artery spasm. Future clinical studies utilising this novel model will enable the diagnosis of concurrent epicardial and microvascular spasm.

Figure 7 shows a flowchart example of how the hydrodynamic model may be applied to improve understanding of physiological changes occurring during provocative spasm testing and categorise potential pathophysiological subtypes. The presence of epicardial spasm may be identified based on an increase in the epicardial resistance post-ACh compared to pre-ACh. The presence of microvascular spasm could similarly be identified by quantification of changes in the microvascular resistance. Importantly, the proposed hydrodynamic model has been tailored for microvascular spasm and other coronary microvascular disorders [10] (such as the coronary slow flow phenomenon and impaired coronary vasodilatory response) will require additional pathophysiological studies.

Fig. 7.

A proposed flowchart to identify the presence of epicardial and/or microvascular spasms based on the levels of epicardial and microvascular resistances pre- and post-ACh.

The hydrodynamic model utilises a unique approach for identifying epicardial spasm, which is based on an increase in epicardial resistance post-ACh compared to pre-ACh. Since the epicardial resistance is calculated using the Darcy-Weisbach formulation, where the resistance is inversely proportional to the power of 4 of the average diameter (Eq. 3), any induced vessel constriction would affect the average diameter and, hence, the epicardial resistance. This method for the calculation of epicardial resistance relies on the average vessel diameter; hence, it covers the whole artery constriction and provides a more accurate representation of the degree of the epicardial spasm.

The current clinical utility of this novel hydrodynamic model is primarily for proof-of-principle research studies. For example, intracoronary ACh may induce 70% constriction of a large coronary artery, chest pain and ischaemic ECG changes – should this be diagnosed as epicardial spasm, microvascular spasm or both? The contemporary definition would suggest that this should be diagnosed as microvascular spasm but is the epicardial artery constriction haemodynamically significant? By quantitating the contribution of both epicardial and microvascular resistance the model provides key insights into the appropriate diagnosis. Thus, further clinical research studies using the model are required to improve our pathophysiological understanding in the diagnosis of vasospastic coronary vasomotor disorders. These additional clinical research studies may demonstrate the necessity to incorporate the model into routine clinical provocative ACh spasm testing; however, the model would need to be further customised to streamline measurement for routine practice.

Assumptions and Limitations

This method calculates the resistance inside the LAD, as a hydraulic resistance inside a straight pipe, based on the Darcy-Weisbach formulation. This formulation does not consider the effect of arterial curvature and tortuosity on the pressure drop and, hence, resistance. Although the LAD is not a straight artery and has unique curvatures that differ between patients, these anatomical features remain unchanged during the administration of ACh compared to baseline. Since the hydrodynamic model is based on comparing the level of resistances pre-ACh and post-ACh, any potential increase in LAD epicardial resistance due to the arterial curvature and tortuosity would not change the results obtained from this method for epicardial and microvascular resistances (Freidoonimehr [11]).

The blood flow rate used to calculate the total resistance, and hence the microvascular resistance, was obtained from the ComboWire recording, located in the mid-LAD. It is assumed that the blood flow inside the LAD is laminar and remains the same throughout the artery until it arrives at the microvasculature; hence, the flow within the LAD branches (e.g., diagonal and septal branches) is considered negligible. This is particularly valid when these branches are small in diameter and according to Murray’s law [12]; the flow is maintained primarily in the parent artery. This law expresses that flow within bifurcated arteries is proportional to the diameter of the branches to the power of three. Therefore, if the diameter of the LAD is three-fold larger than the diagonal branch, then the flow rate within the LAD after the diagonal would be almost 27 times higher than within the diagonal branch. Thus, the hydrodynamic model can be accurately applied even in the presence of subsidiary small branches. However, if the branches have a similar diameter to the LAD, an adjustment in the flow rate term, Q_a in Eqs. 4 and 5, based on Murray’s law, is required to account for the changes in the flow rate following the branch, and its consequent change in the total and microvascular resistances.

The proposed method calculates resistance in both the epicardial and microvascular regions of the same artery using vessel-specific coronary blood flow and pressure derived from invasive intracoronary pressure-Doppler flow wire measurements. However, it is unable to calculate resistances in other branches in the absence of these invasively measured values. In addition, as the method calculates the epicardial resistance based on the average diameter of the artery of interest, it cannot differentiate between diffuse and focal spasm. Moreover, this model assumes that the guide-wire Doppler signal is not dampened due to probe impingement on the vessel wall, and that blood viscosity and coronary venous pressure are constant (see online supplementary Data). Furthermore, microvascular resistance is assumed to be uniformly distributed within the myocardium.

Conclusion

This article introduces a novel hydrodynamic model to evaluate the physiological changes occurring during ACh provocative spasm testing based on the calculation of resistances obtained from the Darcy-Weisbach equation, the LAD pressure and flow velocity recordings (as the artery of interest), and the LAD diameter measurements from angiogram images. Future work is required to identify the impact of the type of induced spasm (i.e., focal or diffuse) and to validate this model and its utility in clinical practice.

Statement of Ethics

The Central Adelaide Local Health Network Ethics Committee approved the study (Reference No.: 8192), and written informed consent was obtained from all patients.

Conflict of Interest Statement

The authors have no conflicts of interest to declare.

Funding Sources

This work was supported by a 2022 Vanguard Grant (107010-2022) from the National Heart Foundation of Australia. In addition, the first author was supported by a 2023 Postdoctoral Fellowship (107146-2023) from the National Heart Foundation of Australia. O Girolamo is supported by the University of Adelaide Research Training Program Stipend Scholarship, and T Atkins is supported by the Australian Government Research Training Program Scholars. J Beltrame is supported by a named personal chair from the Michell Bequest. The remaining authors received no additional funding.

Author Contributions

Navid Freidoonimehr: conceptualisation, methodology, analysis, visualisation, and manuscript drafting. Olivia Girolamo: data curation, methodology, analysis, validation, and manuscript review. Tam Atkins: data curation, analysis, and investigation. Bo Yang: analysis and investigation. Rosanna Tavella: methodology, analysis, data curation, and manuscript review. Christopher Zeitz: methodology, analysis, and data curation. Maziar Arjomandi: methodology, analysis, supervision, and manuscript review. John Beltrame: conceptualisation, methodology, analysis, supervision, funding acquisition, and manuscript review.

Funding Statement

This work was supported by a 2022 Vanguard Grant (107010-2022) from the National Heart Foundation of Australia. In addition, the first author was supported by a 2023 Postdoctoral Fellowship (107146-2023) from the National Heart Foundation of Australia. O Girolamo is supported by the University of Adelaide Research Training Program Stipend Scholarship, and T Atkins is supported by the Australian Government Research Training Program Scholars. J Beltrame is supported by a named personal chair from the Michell Bequest. The remaining authors received no additional funding.

Data Availability Statement

All data generated or analysed during this study are included in this article and its online supplementary material. Further enquiries can be directed to the corresponding author.