1 The Need of Non-invasive Physiological Assessment

Despite highly advanced technologies and devices in invasive physiological modalities, there is still enormous clinical need of non-invasive physiological assessment as follows. First, indirect assessment of physiological parameters is based on the profound understanding of coronary pathophysiology and exact modeling of coronary physiology. For example, computational modeling of fractional flow reserve highly depends on the exact modeling of coronary circulation. Second, non-invasive assessment enables a large-scale or population-scale study of coronary physiology which might be limited by invasive physiological assessment. Third, non-invasive physiological assessment before sending the patients to catheterization procedure might find out patients who would not benefit from invasive angiography or physiological study and reduce unnecessary procedure. Finally, replacing invasive physiological assessment with non-invasive technology might greatly reduce the burden of medical cost.

Coronary computed tomography angiography (CCTA) is the best non-invasive modality that depicts anatomy of coronary artery. However, anatomical stenosis is a poor predictor of physiological severity and frequently underestimates or overestimates physiological severity of stenosis. Fractional flow reserve (FFR) < 0.80, a widely accepted gold standard of vessel-specific physiologically significant stenosis which may evoke myocardial ischemia, is identified in less than a half of vessel with significant stenosis defined by diameter stenosis (DS) ≥ 50%, and the discordance between anatomical stenosis and physiological severity is found as high as 40% [1, 2]. The key role of coronary artery is supplying sufficient blood flow that contains vital materials such as oxygen or glucose required by myocardium. Therefore, the insufficiency of blood supply can be defined by decreased myocardial perfusion, decreased pressure gradient or arterial flow across stenosis, or relative ratio of minimal luminal area which represents the maximal blood supply to the subtended myocardial mass. These concepts constitute the principles of non-invasive assessment of myocardial ischemia (Fig. 31.1).

Fig. 31.1
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Concepts for non-invasive assessment of myocardial ischemia

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2 Perfusion CT

The strength of perfusion imaging is visualizing the myocardial blood flow on which myocardial metabolism depends. Perfusion MR uses similar concept used in nuclear perfusion imaging or perfusion cardiac magnetic resonance imaging (CMR). From the myocardial and left ventricular cavity arterial input function or time-attenuation curves, the extent of regional myocardial perfusion is calculated or compared with the other regional myocardial perfusion. Perfusion is imaged in a complete cardiac cycle (dynamic perfusion imaging) or as a snapshot (static perfusion imaging). Scanners equipped with dual energy source can be used for perfusion imaging and mostly used for static perfusion imaging (Fig. 31.2). The performance of perfusion CT for predicting functionally significant stenosis is considered to be similar to nuclear perfusion imaging, stress CMR, or stress echocardiography, and is being validated against FFR [3,4,5]. Standard coronary angiography can be done along with perfusion imaging, which enables simultaneous anatomic evaluation of coronary arteries with functional evaluation of heart. Therefore, perfusion CT combined with coronary CT angiography can be a one-stop shop modality that assesses both anatomical and functional stenosis within a single session [6].

Fig. 31.2
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Principle of myocardial perfusion CT . The difference between myocardial blood flow correlates with the myocardial up-slope normalized by arterial input function (AIF) up-slope, area under curve (AUC) of myocardial signal intensity up to AIF peak, or myocardial peak signal intensity. The difference between normal tissue and ischemic tissue is imaged as perfusion defect (line with red arrows)

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2.1 Technical Aspect of Perfusion CT Imaging

Hyperemia is induced by pharmacological stress agents . Intravenous adenosine is widely used in a continuous dose of 140 μg/kg/min for 2 or 3 min. Regadenoson has longer plasma half time than adenosine and is administered in a single agent. Also it is a selective adenosine 2A receptor agonist and can be used in patients with asthma or airway disease. Dobutamine, a myocardial beta-1 agonist, or dipyridamole, adenosine receptor blocker, is not commonly used (Table 31.1).

Table 31.1 Stress agents for perfusion imaging
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Static or snap-shot perfusion CT assesses myocardial contrast distribution in a single time and doable in most CT scanners with lesser radiation exposure to dynamic perfusion CT. With sophisticated mathematical modeling, dynamic perfusion CT enables direct quantification of myocardial blood flow (MBF), myocardial blood volume, and myocardial flow reserve (Table 31.2). Regarding the diagnostic performance, static perfusion CT showed sensitivity = 0.85 (95% confidence interval = 0.70–0.93), specificity = 0.81 (0.59–0.93), area under curve = 0.90 (0.87–0.92) [7]. A recent dynamic perfusion CT showed comparable performance compared to CMR (Table 31.3) [8,9,10,11,12,13,14,15,16,17,18,19,20]. Also perfusion CT is better suited for quantification of myocardial blood flow than perfusion MR. Based on the nuclear perfusion studies, the nominal value of resting myocardial blood flow is known to be 0.9 ml/μg/min. The cut-off value of hemodynamically significant stenosis in perfusion CT was reportedly 0.75–0.78 ml/μg/min [16].

Table 31.2 Techniques for myocardial perfusion CT
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Table 31.3 Diagnostic performance of perfusion CT
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3 Computational Simulation of Fractional Flow Reserve

Increase of myocardial blood flow by 2 to 3-fold is required to match the increased need of cardiac output in most activities. Coronary microvessel accounts for most resistance or pressure drop in coronary circulation. The increase of myocardial blood flow is mainly controlled by decrease in microvascular resistance. Therefore functionally significant epicardial coronary artery stenosis can be defined by failure to increase blood flow during hyperemia which induces maximal dilatation of resistance vessel. Fractional flow reserve (FFR) is defined by the ratio of hyperemic coronary flow through stenotic vessel to the hypothetical normal vessel. Because flow is proportional to pressure in fixed stenosis, FFR can be measured by average pressure gradient. Pressure drop of more than 20% or FFR ≤ 0.80 is widely advocated as a gold standard of vessel-specific physiologically significant stenosis which may evoke myocardial ischemia.

FFR is measured during invasive cardiac catheterization and requires insertion of a pressure wire inserted through the stenosis. There may be and instability of measurement and signal shift. Placement of a pressure wire near the stenosis or pressure recovery zone may lead to overestimation of FFR. A non-invasive simulation of FFR would be very valuable to avoid these procedural shortcomings and the expense of pressure wire and invasive cardiac catheterization.

3.1 Computation of Simulated FFR

Like the other fluid systems, blood flow in the cardiovascular system is ruled by the physical laws of mass conservation, momentum conservation, and energy conservation. Therefore it can be calculated by mathematical models. For patient-specific coronary circulation, 3-dimensional numerical models based on computational flow dynamics which can compute complex flow patterns are preferred to zero dimensional models or lumped parameter model which is employed in large systemic vessels. Computational FFR is derived based on the regional physical geometry, the boundary condition which is the behavior and properties at the boundaries of the region, and the physical laws of fluid in the region.

FFR can be described as a pressure gradient across stenotic segment during maximal hyperemia. Anatomical stenosis, myocardial mass, and microvascular resistance constitute FFR value and can be calculated from patient-specific sophisticated coronary arterial anatomical model, vessel-specific myocardial mass, and microvascular resistance which determine the outlet boundary condition [21, 22]. CT images provide patient-specific anatomy model of local geometry, individual coronary artery morphology, volume, and myocardial mass. From these data, cardiac output and baseline coronary blood flow can be calculated by using allometric scaling laws [23,24,25]. This computational approach was derived from a general model that describes the transport of essential materials through space-filling fractal branched networks, and is based on a form-function relationship [26]. The diameter-flow rate relation is determined according to Murray’s law [27] and Poiseuille’s equation, which considers shear stress on the endothelial surface and remodeling to maintain homeostasis [28]. Morphometry laws are also adapted to obtain the physiological resistance to flow aroused by coronary artery branches [29]. Microvascular resistance at baseline and during maximal hyperemia, which is fundamental for FFR measurement, can be approximated using population-based data on the effect of adenosine on coronary flow [30] (Fig. 31.3).

Fig. 31.3
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Concept of computational FFR

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3.2 Clinical Results of Computational FFR

Landmark trials including DISCOVER-FLOW [31], DeFACTO [32], and NXT [33] showed that FFR-CT, a proprietary computational FFR, showed high diagnostic performance in discriminating ischemia in patients who had intermediate coronary artery stenosis. The NXT trial reported sensitivity and negative predictive value of FFR-CT in diagnosis of ischemia (defined as invasive FFR < 0.80) in patients with intermediate stenosis severity were 80% and 92%, respectively [33]. In a recent meta-analysis of FFR-CT based on 833 patients and 1377 vessels, FFR-CT showed a moderate diagnostic performance for identification of ischemic vessel with pooled sensitivity = 84% and specificity = 76% at a per-vessel basis [34] (Table 31.4). The PLATFORM study showed that a decision-making strategy using CCTA with FFR-CT was associated with clinical outcomes comparable to using invasive FFR and a 33% cost reduction [35]. Therefore, FFR-CT can effectively rule out intermediate lesions that cause ischemia and could also reduce the unnecessary ICA and invasive FFR.

Table 31.4 Results of non-invasive computational FFR technologies
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4 Intracoronary Transluminal Attenuation Gradient Analysis

4.1 Transluminal Attenuation Gradient (TAG) and Corrected Contrast Opacification (CCO)

Standard coronary CT image is a snapshot of dynamic transit of intravascular contrast driven by blood flow. Therefore, coronary CT is not only a simple static anatomical imaging but also contains information of coronary hemodynamics. Intracoronary contrast filling is governed by arterial input function from coronary ostium and the flow or velocity of intracoronary flow. Based on this intuitive concept, transluminal attenuation gradient (TAG ) was defined as the difference of intracoronary attenuation along vessel axis that reflects contrast kinetics and is readily available from conventional CCTA image without additional radiation or off-site long time computation [36]. TAG theoretically depends on the temporal uniformity of Z-axis coverage and adequate contrast enhancement curve (Fig. 31.4). TAG has been tested in both animal and human studies and showed consistently poor correlation with anatomical and functional stenosis [37,38,39,40,41,42]. Adjustment with descending aortic opacification (corrected contrast opacification, CCO ) or exclusion of nonlinear values caused by stented or calcified segment has been proposed but with mixed results [38, 42, 43]. Because coronary CT image is a snapshot of convection of intracoronary time-varying contrast bolus, TAG represents the spatial dispersion of contrast concentration along vessel axis. Therefore, the discordance among TAG and anatomical or functional stenosis is no wonder considering the well-known discordance among anatomical stenosis, fractional flow reserve (FFR), and coronary flow reserve (CFR).

Fig. 31.4
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Concept of transluminal attenuation gradient (TAG) and corrected contrast opacification (CCO)

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4.2 Transluminal Attenuation Flow Encoding (TAFE )

The principle of myocardial blood flow assessment in perfusion scan based on the comparison of enhancement dynamics between left ventricular cavity and myocardium can be applied with modification to standard CCTA data [44, 45]. This concept enables calculation of CBF from the time-dependent change of contrast density proximal to coronary artery as input function of contrast cohort, arterial volume to be filled by the contrast cohort, and the gradient of intraluminal contrast density which reflects blood flow velocity. All these input parameters are readily and rapidly available from current conventional CT suite [46]. Based on this concept, Lardo et al. reported an elegant engineering solution named transluminal attenuation flow encoding (TAFE) (Fig. 31.5) [47]. Coronary CT image is a snapshot of convection of intracoronary time-varying contrast bolus. Therefore TAG represents the spatial dispersion of contrast concentration along vessel axis. With additional temporal data from arterial input function, TAFE formula decodes the spatial dispersion of TAG into temporal dispersion of vessel-specific CBF. TAFE showed excellent correlation with myocardial blood flow (MBF) in animal microsphere model and warrants validation in human study.

Fig. 31.5
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Concept of transluminal arterial flow encoding (TAFE) . Addition of the arterial input function (AIF, yellow arrow) adds time domain to TAG (=ΔHU/arterial length) and enables calculation of vessel-specific coronary blood flow. Compared to normal artery, the flow of stenotic artery is slower and has lower flow rate. Numbers in circle represent time points

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5 Coronary Artery Stenosis and Subtended Myocardial Mass

FFR is a mean pressure gradient across stenosis with maximal myocardial blood flow. Anatomical stenosis, myocardial mass, and microvascular resistance are major constituents of FFR value [21]. The major unknowns in anatomical measurement are myocardial mass and microvascular resistance. Therefore the anatomic-physiological discordance can be reduced by addition of downstream myocardial mass to anatomical stenosis of supplying artery (Fig. 31.6). Based on the fluid continuity principle, functional severity of stenosis was shown to increase proportionally to the ratio of flow demand represented by subtended myocardial mass to flow supply represented by luminal area or diameter of supplying vessel [48, 49]. Principle of efficiency or minimum energy loss concept is considered in the structure of human vascular tree and myocardial territory based on the fact that energy-efficient provision of materials such as oxygen in hierarchical fractal-like network of branching tubes plays a key role in the mechanism of living organism [50].

Fig. 31.6
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Concept of myocardial mass subtended by the vessel

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Two mathematical principles that have been used extensively in life science can be applied to calculate the relationship between vessel dimension and subtended myocardial mass (Table 31.5). Voronoi tessellation is based on the geometrical characteristics of vessel course and myocardial geometry. Allometric scaling law is a simple and universally observed logarithmic relationship among size, function, and energy expenditure in life science [26]. Stem-and-crown models describing scaling power between structures and functions were developed theoretically and validated experimentally in both animal and human studies [51, 52]. In clinical study, both Voronoi- and allometric scaling law-based study showed similar findings for the relation between vessel size and subtended myocardial mass (Table 31.6) [53, 54].

Table 31.5 Mathematical principles for the relationship between vessel dimension and subtended myocardial mass
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Table 31.6 Results of vessel dimension to subtended myocardial mass for detection of functionally significant stenosis
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The concept of myocardial mass subtended by specific coronary artery can be extended beyond vessel-specific ischemia and may lead to better diagnostic and therapeutic decision in cardiovascular medicine including the following clinical issues. It might be used for adjudicating myocardial infarction caused by supply and demand mismatch (type 2) [55]. It also may clarify the appropriateness and optimal threshold of revascularization. Direct assessment of the amount of ischemic myocardium as well as myocardium to be revascularized has been estimated semi-quantitatively by angiographic scoring systems. As the FFR could reclassify the need of revascularization based on the presence of ischemia, myocardial mass subtended by specific vessel might reclassify the strategy of revascularization based on the amount of ischemic myocardium to be saved [56,57,58,59]. The concept of vessel-specific myocardial mass explains the limited clinical benefit of bifurcation side branch and chronic total occlusion (CTO) revascularization [60], because both side branch of bifurcation and CTO vessel supply smaller or infarcted myocardial mass [61,62,63,64].

6 Limitations

The most important limitation of non-invasive physiological assessment is radiation exposure required by CT image, especially in perfusion CT imaging. A combined rest and stress myocardial perfusion CT may reach radiation dose of >15 mSv. Although the radiation exposure of CT is regarded as lower than those with nuclear imaging, appropriate radiation reducing strategy should be applied as reasonable as possible (Fig. 31.7).

Fig. 31.7
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Radiation exposure

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Insufficient spatial and temporal resolution is the major cause of inadequate results. Typical isotropic spatial resolution of CT image is 0.5 mm at best. Therefore even single voxel difference in 3.0 mm sized vessel results in 17% difference in diameter. Such vessel with 50% diameter stenosis would have just 7–9 voxels in the lumen. Addition or deletion of single voxel causes 33% difference in minimal luminal diameter or 11% difference in minimal luminal area (Fig. 31.8 ). Mathematical correction by subvoxel resolution technique and avoidance of partial volume effect is being developed.

Fig. 31.8
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Limitations in spatial resolution and motion artifact. (a) Less than 10 voxels consists lumen of typical coronary artery disease with 3.0 mm diameter and 50% stenosis. Omission or addition of single voxel affects significantly the result of computational FFR. (b) The limitation of spatial resolution may be worsen by the motion artifact

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Mismatch of perfusion defect and stenotic or non-stenotic coronary artery may occur as cardiac positron emission tomography (PET) and coronary CT. Concept of vessel-specific myocardial territory rather than traditional 17-segment model may reduce misregistration error [53, 54, 65].

Boundary conditions in computational flow dynamics are critical in the result of computational FFR but include several assumed parameters which cannot be determined from conventional coronary CT. The individual variation of blood pressure, heart rate, coronary flow reserve, extent of collateral flow may explain the discrepancy between computational FFR and invasively acquired FFR (correlation coefficient r = 0.72 in DISCOVER-FLOW study) [31]. The time to calculation and heavy computational resource is another limitation of computational FFR but may be overcome by big-data based machine learning [66].

Single measurement or modality may represent but cannot show every aspect of coronary artery disease and is not sufficient for decision of treatment strategy. Revascularization by percutaneous coronary intervention or bypass surgery relieves symptom but does not improve clinical outcome of all patients [67]. Non-invasive physiological assessment may vastly improve the predictive value of coronary artery disease evaluation and be additive to the current decision-making strategy (Fig. 31.9).

Fig. 31.9
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Multifactorial non-invasive evaluation of coronary artery disease

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