In this model study, we demonstrate the dependence of subendocardial layer perfusion on DTF. Since perfusion of the myocardial layers depends on DTF, clinical measurements that are performed by artificial hyperemia by infusing adenosine may overestimate subendocardial layer perfusion at exercise when DTF is reduced as compared during clinical measurement.
This model study demonstrates the importance of standardization of conditions of cardiac function in testing the physiological state of the coronary circulation. More specifically, cardiac function assessment by using a hyperemia stress test is dependent on myocardial testing conditions. This is especially important for these factors that dominate subendocardial perfusion: DTF and perfusion pressure. The absolute values of the perfusion predictions depend on parameterization of the model for which animal data were used. Therefore, extrapolation of distribution of perfusion in the human has to be performed with care. However, the model behavior is rather general and can be interpreted in the following way. There is a reference condition, DTF1, defined by coronary perfusion pressure and DTF for which perfusion of the myocardial layers is evenly distributed. Increasing DTF from this reference value will increase hyperemic subendocardial perfusion while decreasing DTF will do the opposite. It further may be concluded that a clinical test applying, e.g., adenosine to obtain maximal vasodilatation may deviate from perfusion distribution during real exercise induced hyperemia.
4.1 Microsphere data
The literature contains numerous studies in which microspheres have been applied to study blood flow distribution over the myocardium in hyperemic conditions. The general conclusion is that the subendocardium is the location where blood flow is most sensitive to contraction-related flow-impeding mechanisms [
22]. In contrast, perfusion of the subepicardium is hardly or oppositely affected by cardiac contraction [
8]. Therefore, the Endo/Epi flow ratio has been used as an index to define the perfusion state of the subendocardium with the subepicardium as reference.
In experiments where coronary perfusion pressure is maintained, but the heart arrested the endo/epi ratio is about 1.5 [
6], which indicates that intrinsic subendocardial vascular resistance (no effect of contraction) is lower than that in the epicardium [
23]. This agrees with the observation that luminal volume percentage of resistance arteries in the subendocardium is higher than that at the subepicardium [
23]. At very high HR, around 180 beats/min, the endo/epi ratio is about 0.5. Hence, with rather constant epicardial resistance the contraction of the heart may vary the subendocardial resistance by a factor of three.
For model purposes however, a data set is needed under normal controlled conditions and with sufficient variation in the parameter values for parameter estimations. Few studies do deliver this information. The classical dataset from Bache [
1] provides the effect of DTF on hyperemic flow distribution but only at Pc = 100 mm Hg. However, it also provides information on flow distribution at rest and hence allows for the estimation of
R
hyp and
R
auto at this value of Pc. The more recent dataset of Fokkema et al. [
8] provides the information on how the relation between
R
hyp and DTF is modulated by Pc, essential for prediction of the effects of a stenosis.
4.2 Sensitivity analysis
In order to validate the dependency of the model outcomes on the starting parameters a sensitivity analysis was performed. Setting the normal flows for the subendocardium and the subepicardium to the flow level of the midmyocardium did not alter the model outcomes significantly. Setting subepicardial conductance independent of Pc [
8], results in the percent flow of the epicardial layer decreasing linear with decreasing Pc. Subepicardial steal in case of a severe coronary stenosis however remained.
Changes in the myocardial layer conductances affect the model outcomes to a larger extent. Increasing the influence of DTF on myocardial layer conductance of midmyocardial and subendocardial layers by 25%, produces comparable outcomes albeit with increased effect of subepicardial steal when DTF is low. Instead, reducing the influence of DTF by 25% decreases subepicardial steal for low DTF; however, this mechanism remains present. Increasing the influence of myocardial layer perfusion pressure on layer conductance by 25% leads to lower perfusion when coronary pressure is reduced. In contrast, decreasing the influence of layer perfusion pressure leads to slightly lower pressures when subendocardial perfusion is decreased.
Removal of the Bernoulli component of the SR, in Eq. 1, leads to a decreased luminal diameter, i.e., 67 and 77% diameter occlusion, necessary for an FFR of 0.75 and 0.5, respectively. Although in this case, the nonlinear pressure loss for severe stenosis was included in the model, it is not essential for interpretation of the model outcomes. Here, different values of DTF, lead to different myocardial layer conductances, so that myocardial flow is altered and as a consequence pressure loss across the stenosis is affected. Finally, the normal flow and conductance of the midmyocardial and subendocardial layers was set equal, and the influence of DTF on layer conductance was reduced. In spite of these changes in model parameters, the model outcomes essentially remain unchanged; i.e., subepicardial hyperemic steal develops for low DTF with adenosine administration and FFR is dependent on DTF.
4.3 Limitations
The model we used is empirical and the dependence of the
R
hyp on DTF is not based on physical principles of compressed intramural vessels. Several of these models relate the dynamic changes of diameter of intramural vessels to changes in their resistances and predict in that way the effect of DTF and Pc [
17]. This latter approach is certainly useful in order to arrive at a more detailed understanding of how contracting myocardium affects its perfusion [
22]. However, the present model allows extrapolation from relationships obtained in animal studies to the clinical situation without assumptions related to the actual perfusion contraction interaction.
The experimental data used to parameterize the model were obtained in controlled conditions applying anesthesia [
1] and an extra corporeal perfusion system [
8]. Most likely the parameters of
R
hyp(DTF, Pc) may differ between man and animals. Therefore, human studies are needed to arrive at reliable parameters. However, it is unlikely that the general trends of the model behavior will drastically change and likely that a reference condition under which flow distribution over endocardial and epicardial layers is even will hold. For DTF values lower than the DTF value at this reference condition the subendocardium is at risk but it is relatively safe for higher DTF values.
In this study we kept aortic pressure constant and at 90 mm Hg as to stay close to the range of experimental data on flow distribution. It will be especially interesting to see what happens during more pathophysiological conditions as hypertension and hyperthrophy.
The distinction between hyperemic and autoregulatory resistance is very practical for the model design but rather artificial. Autoregulation is caused by changing the smooth muscle tone in small arteries with diameters varying between 10 and 400 μm. Hyperemic conditions occur when this tone is reduced to 0 and the vessels obtain their maximal diameter determined by the connective tissue in the wall. Hence, in this condition where R
auto = 0 these vessels still have resistance which contributes to our hyperemic resistance parameter R
hyp. Hence, the distinction between R
auto and R
hyp does not relate to anatomical location, but is to be considered as a functional model characteristic that describes the experimental data.
4.4 Clinical implications
Currently, MRI-based methods for routine measurements of myocardial perfusion distribution are being developed. It is therefore of paramount importance that the clinician is able to interpret the data resulting from such a new functional imaging techniques. An important benefit is that the spatial resolution of these novel image-based flow distribution modalities, approach that of the earlier microsphere studies in animals. Therefore, a model able to describe quantitatively the earlier findings on perfusion distribution obtained by that technique could be of great help. The present model demonstrates how important it is to standardize the conditions of measurement with respect to DTF and coronary perfusion pressure.
In general it is recognized that the subendocardium is most vulnerable to ischemia and this has been related to the increased subendocardial resistance as a result of heart contraction. This model study demonstrates that this paradigm needs modification since the vulnerability, expressed as reduced hyperemic subendocardial flow depends on DTF and perfusion pressure.
Patients with signs of cardiac ischemia are in general medicated with Beta-blockers in order to reduce their heart rate and systemic blood pressure. Two important beneficial effects then result; myocardial oxygen demand is reduced, and the DTF-related hyperemic flow potential at the subendocardium is increased. The positive effect of reduction in oxygen demand is better recognized than the effect of increased hyperemic flow potential. However, it can be shown that the sensitivity of hyperemic flow potential to a change in HR is larger than the sensitivity to a change in oxygen demand [
17].
Exercise-induced hyperemia is difficult to realize during catheterization or MRI measurement. Therefore, adenosine is administered to induce maximal vasodilation and thereby hyperemic conditions. However, the present model clearly demonstrates that in the presence of a stenosis pharmacological vasodilation has different effects on the heart than exercise-induced vasodilation. Pharmacological vasodilation augments ‘steal’ of perfusion from one layer to another and depending on DTF can favor perfusion of the subendoardium or subepicardium.
During catheterization the physiological severity of a stenosis is often indicated by the FFR. Assuming that the venous pressure is 0, FFR simply is the ratio between pressure distal of the stenosis and aortic pressure but measured at hyperemic conditions where all autoregulatory resistances are 0. In terms of resistance circuit analysis such as depicted in Fig.
1b, this ratio equals
R
m/(
R
s +
R
m) where
R
m is the replacement of all distal resistances in parallel and
R
s is the SR. Consequently, FFR only reflects
R
s when
R
m is well-defined. In the clinical literature it is often assumed that
R
m is constant but this model study indicates clearly that
R
m, and therefore FFR, depends on DTF and not uniquely reflects the SR. This dependency is not unimportant since in clinical practice a threshold of FFR = 0.75 is applied below which a stent is placed. Hence, a change in HR during the measurement of FFR may result in a change of treatment decision [
16].
Although FFR and CFVR depend on DTF, the changes in these epicardial-determined indices reflect only the changes in subendocardial perfusion in a rather attenuated manner as indicated by Figs.
9a and b. Obviously, this is the result of the subepicardial layer which resistance is rather independent of DTF and blunts the response of the subendocardium on epicardial measurements. Using a SPECT stress test, threshold values for FFR = 0.75 and CFVR = 2 have been reported in the literature [
9,
11,
13] below which ischemia is induced. Figure
9b demonstrates that these values correspond to the reference value chosen for this study where the endocardial epicardial flow ratio is 1 at a DTF = 0.5. Based on this figure one might conclude that at FFR = 0.75 a flow reserve is left of about 2. However, this flow reserve will be lost with an increase in oxygen consumption that most likely is the result of an increased HR inducing a downward shift in the subendocardial hyperemic flow pressure relationship. As a consequence, pharmacologically determined flow reserve, without simultaneously increased oxygen demand, may prove an overestimation of the actual increase in oxygen demand that the coronary circulation may facilitate.
An important clinical implication of this study is the finding of epicardial hyperemic steal [
2,
4,
7], where flow is increased in the epicardium at the expense of a decrease in the subendocardium. Figure
7 illustrates that upon administration of adenosine the autoregulatory resistances are set to 0, after which flow distribution to the myocardium may change significantly. These changes in flow distribution may especially be significant when due to a coronary stenosis the endocardial autoregulation resistance prior to adenosine administration was absent or reduced [
10]. In that case endocardial flow may significantly decrease due to decreased coronary pressure, which is reduced as a consequence of increased flow to the entire myocardium through the stenosis after adenosine administration. This effect is illustrated in Fig.
7c.
In the case that microvascular dysfunction might have significantly increased the hyperemic resistance [
5], an increased myocardial flow by lowering of autoregulatory resistances, may cause abnormal distribution of flow and result in endocardial ischemia [
12]. This type of flow redistribution in hyperemia, has been suggested with the use of MRI [
12,
19]. However, the reduction in endocardial perfusion was not confirmed in a recent study [
19], but instead the ratio of endocardial and epicardial flow was reduced. The second effect here, precluding an accurate assessment of endocardial flow is the influence of DTF. As established previously, changes in DTF may change hyperemic resistance significantly; causing either adequate endocardial perfusion or significant underperfusion as is illustrated by Figs.
9a and b.
This study also confirms the beneficial action of drugs that prolong DTF, e.g., dobutamine [
3,
8] without affecting HR, or propranolol, a beta-blocker which increases DTF and reduces HR [
3], or isoproterenol which is a beta adrenergic agonist similar to dobutamine and increases DTF by shortening systole while increasing HR [
3].