Where ΔP = pressure gradient across the constricted area (or stenotic valve), νmax and νprox are the velocity in and proximal to the stenosis, respectively, ρ = mass density of blood, prox ∫ max (dv/dt)/ds is the varying velocity vector of the fluid element at each distance along the flow stream path, and R (v) is a constant describing the viscous losses.
Accordingly, the ΔP occurs due to energy loss as a result of:
Convective acceleration: Conversion of pressure or potential energy to kinetic energy occurs with convection of fluid with normal flow velocity from one point in space to another point in space at the stenosis with high velocity flow. This is the most energy-dissipating portion and distal to the narrowed orifice, kinetic energy is reconverted back to pressure or potential energy. However, some of the pressure energy is lost, in part because of dissipation of kinetic energy as heat, flow separation, as well as conversion of flow distal to the stenosis into turbulent non-laminar flow with vortex formation. These flow vortices develop circumferentially around the ejected jet distal to the AV and constrict the flow current at the vena contracta, thus constricting the EOA.
Flow acceleration: additional acceleration occurs through changes in the blood flow velocity during systole to overcome inertial forces especially at the time of valve opening and closing. Flow acceleration occurs proportionately to the square of the distance. However, it is negligible at peak velocity and can be omitted.
Viscous friction: This occurs between the laminar layers of fluid (viscous losses), specifically from friction between the fluid element and the neighboring fluid and depends on maximum velocity (v max) and the whole velocity profile. However, the viscous losses are negligible for the fluid element with the v max and can be omitted. Moreover, with turbulent flow as seen with aortic stenosis, the contribution of the viscous forces is minimal.
The Reynolds number describes the ratio of inertial or acceleration forces to viscous forces [9]:
Where ρ = mass density of blood, V is velocity of flow, L is length, and v is viscosity.
Acceleration or inertial forces are more prevalent with turbulent flow (at high Reynolds number), while viscous forces are prevalent at laminar flow (at low Reynolds number) and become negligible. As such, with increase turbulent flow with severe AS, viscous forces are omitted in the gradient calculation.
Accordingly, the acceleration losses increase exponentially with flow, while viscous losses are negligible and are linearly related to flow [9].
Additionally, the flow vortices generated are highly dependent on flow. In the presence of high or normal flow, more kinetic energy develops that leads to destruction of these vortices, thus causing a larger EOA. In conditions of low flow across the aortic valve, whether the EF is preserved or not, there is a decrease in kinetic energy that leads to lesser destruction of flow vortices that develop on the sides of the aorta beyond the AV resulting in more “squeeze” on the ejection jet by the flow vortices and constricting the EOA [6] (Fig. 3.1).
Fig. 3.1
(a, b) Illustrates the GOA, EOA by both catheter and Doppler, as well as pressure and area recovery. (c) Illustrates: (1) The initial pressure, kinetic, lost, and final pressure energy. (2) The various types of gradients (∆Pmax, ∆Pnet, ∆Pmean, ∆PMIG, ∆PPPG, and Prec) generated across the AV in the presence of a stenosis. (3) The pressure gradient determinants (perivalvular, aortic, and vascular). (4) The methods of gradient detection (Doppler and Catheterization). (5) The different types of area assessment (GOA, EOAcath, and EOADop). (LV left ventricle, Valve aortic valve, A aorta, VC vena contracta, remaining abbreviations as text) (From Garcia et al. [10] with permission)
The resultant ΔP generated is exponentially proportionate to baseline stenosis and trans-lesion flow in a curvilinear fashion. The ∆P is thus directly proportionate to the square of Q and inversely proportionate to the square of AVA.
As such, higher relative gradients are generated with a delta reduction in aortic valve area in the severe range as well as delta increase in flow in the higher range than with reduction in aortic valve area in the mild to moderate range and increase in flow in the mild to moderate range.
The pressure gradient at the vena contracta is measured by Doppler and is the highest gradient measured across the AV. Upstream from the vena contracta the vortices eventually break up and flow decelerates and diverges with reconversion of kinetic energy to potential energy. A portion of pressure loss is gradually recovered until a plateau is reached, a phenomenon known as pressure recovery (Prec) [10] (Figs. 3.1 and 3.2). This leads to a lower ∆P at catheterization, than that determined at the vena contracta by Doppler. Since the catheter–obtained EOA (EOAcath) is derived from the invasively obtained gradients, it is larger that the EOADop, and closer in value to the GOA, a phenomenon known as area recovery (Arec) [11, 12] (Figs. 3.1 and 3.2).
Fig. 3.2
The relationship between transvalvular ∆P and AVA in normal and AVprosthesis. ∆P starts to increase at an AVA <1.5 cm2, with a steeper increase <1 cm2, and even a more marked increase with an AVA <0.8 cm2 (From Deneshvar and Rahimtoola [30] with permission)
Assessing the Severity of Aortic Stenosis
This section will include an overview of the physiological principles of invasive and echocardiographic measures that evaluate the severity of aortic stenosis:
1.
Measures of trans-aortic pressure gradient
2.
Measures of aortic valve area
3.
Other measures to assess severity of aortic valve stenosis
4.
Measures of left ventricular hemodynamic burden
Aortic Valve Gradient Calculations
As noted, the principle of conservation of energy states that the total amount of energy in a closed system remains constant. Energy can change its location and form but can be neither created nor destroyed.
∆P is mainly measured invasively or via Doppler echocardiography (and more recently MRI, Chap. 4). Depending on the level of ∆P determination, a different measure of gradient is obtained as outlined below.
Maximum Achievable Pressure Gradient (∆P max )
At the vena contracta, the ∆P generated is the maximum achievable gradient (∆Pmax) (Fig. 3.1). ∆Pmax is estimated by Doppler, which assumes that pressure is irretrievably lost across the AV and measures the gradient between the peak LV systolic pressure and the aortic pressure at a single and the same point in time [1] (Fig. 3.3).
Fig. 3.3
Eccentric (a) and centric (b) jets across the aortic valve as viewed above the valve from the aorta as demonstrated on 3D color in two different patients with bicuspid (left) and tricuspid (right) severe aortic stenosis
Noninvasively, ∆Pmax is determined by Doppler on the principles of the Bernoulli equation as described above. The equation is further modified in clinical cardiology as:
V2 represents the Doppler derived blood flow velocity distal to the valve and V1 the proximal blood flow velocity. In the presence of severe AS, V2 is usually significantly greater than V1 and thus V1 is omitted and the equation is further simplified into
When either V1 > 1.5 and/or V2 < 3 m/s, the modified Bernoulli equation, but not the simplified one, should be used, as the difference between V1 and V2 becomes non substantial and the proximal velocity (V1) has to be included in the equation. However, because it is not possible to match each point on the ejection curve between the proximal and distal velocity profiles, it is not possible to “correct” the mean gradient when V1 is significant, and in these circumstances, the measure of mean gradient should not be used to grade stenosis severity [1, 2]. Utilization of a derivative of the Bernoulli equation to non-invasively estimate transvalvular ∆P was initially proposed by Hatle et al. for mitral stenosis [7] and then further extrapolated to aortic stenosis in another study [8].
Doppler provides a maximum instantaneous gradient (∆PMIG), which is the highest achievable instantaneous gradient across the AV (Fig. 3.3), and a mean gradient (∆Pmean) that is generated as an average of instantaneous gradients over ejection time and is the highest achievable ∆Pmean.
Net Pressure Gradient (∆Pnet)
As noted above, the pressure lost is not irretrievable and the final resulting ∆P following complete Prec is known as the net pressure gradient (∆Pnet) and is an overall lower ∆P than initially generated at the vena contracta [10] (Figs. 3.1 and 3.2).
Cardiac catheterization measures an invasive ∆P that progressively decreases as the site of the catheter placement in the aorta moves downstream from the vena contracta, where the pressure measured is partially recovered, until the extent of Prec has reached its plateau, at which ∆Pnet is achieved.
Invasively, ∆Pnet is obtained via a double lumen single catheter, dual catheters, or pull back of a single catheter across the AV. Utilizing a catheter placed in the LV and another placed in the femoral artery will lead to an overestimation of the true ∆Pnet due to the delay that occurs in pressure transmission from the proximal aorta to the femoral artery and should not be used. Conversely, the practice of “aligning” the LV and peripheral tracing will lead to an underestimation of the true ∆Pnet and should also not be used.
Catheterization provides the peak-to-peak gradient (∆PPPG), which is the difference between peak LV pressure and the peak aortic pressure, (which occur at two different points in time) and the mean gradient (∆Pmean) (average peak to peak gradients over time) [1] (Fig. 3.3), both of which occur during or following Prec. The ∆PPPG has little physiological meaning as the two peaks of pressure gradient do not occur at the same time of the cardiac cycle as described above thus no “real” actually ∆PPPG exists. Clinically, the “recovered pressure gradient or ∆Pnet” obtained invasively is more representative of the actual hemodynamic burden placed on the left ventricle than the instantaneous gradient obtained by Doppler [13].
Pressure Recovery (Prec)
The absolute degree of Prec is the absolute difference between ∆Pmax and ∆Pnet (Prec = ∆Pmax −∆Pnet), while the relative degree or extent of pressure recovery is the ratio between both (Prec/Pmax) and is more clinically relevant. A Prec/Pmax >20 % is considered clinically significant and manifests as discordance between Doppler and catheter-derived ∆Pmean [14].
Determinants of Transvalvular Gradients (∆P) and Prec
The generated trans aortic valve ∆P and degree of Prec are dependent on perivalvular determinants (factors around the AV including the presence and type of a prosthesis); vascular determinants: including measures of afterload; and aortic determinants (aortic diameter and area). These determinants are illustrated in Table 3.1.
Table 3.1
Factors determining the trans aortic valve gradient
Variable | ΔPmax | ΔPnet | Absolute Prec (Pmax– Pnet) | Relative Prec (Prec/Pmax) |
|---|---|---|---|---|
Peri-valvular determinants | ||||
Aortic valve area (AVA) | The smaller the AVA, the more severe the AS, the higher the ΔPmax | The smaller the AVA, the more severe the AS, the higher the ΔPnet | The smaller the AVA, the more severe the AS, the higher the absolute Prec | The higher the AVA, the less severe the AS, the higher the relative Prec (more with moderate AS) |
Left ventricular outflow tract (LVOTD) diameter | Increased LVOTD increases the ΔPmax for the same AVA | Increased LVOTD increases ΔPnet | Increased LVOTD decreases the absolute Prec | Increased LVOTD decreases the relative Prec |
Jet eccentricity | Increased jet eccentricity, increases ΔPmax | Increased jet eccentricity, increases ΔPnet | Increased jet eccentricity decreases absolute Prec | Increased jet eccentricity decreases relative Prec |
Flow | Increased flow increases ΔPmax | Increased flow increases ΔPnet | Increased flow increases absolute Prec | No effect |
Bileaflet mechanical prosthetic valve | Increases ΔPmax | Decreases ΔPnet | Increases absolute Prec | Increases relative Prec |
Aortic valve morphology | Variable | Variable | Variable | Variable |
Aortic determinants | ||||
Ascending aorta diameter (AoD)/ratio of AVA/AoD | No effect | Increased AoD increases ΔPnet | Increased AoD decreases absolute Prec | Increased AoD decreases relative Prec |
Vascular determinants | ||||
Systolic blood pressure (SBP) | Increased afterload via increased SBP, Ea, and SVRI, and/or decrease in Ca causes a decrease in trans AV flow leading to a decreases in ΔPmax | Increased afterload decreases ΔPnet due to decrease flow | Increased afterload decreases absolute Prec due to decrease flow | Changes in flow do not affect the relative Prec |
Systemic vascular compliance (Ca) | ||||
Effective arterial elastance (Ea) | ||||
Systemic vascular resistance index (SVRI) | ||||
Para Valvular Determinants
The relationship between the AVA and the generated ∆P is highlighted in Fig. 3.2, with a steep increase in ∆P when the AVA <1 cm2. Similarly, as transvalvular flow increases, the ∆P is increased in an exponential manner and the delta change of ∆P for the amount of Q is higher with severely stenotic valves (<1 cm2) (Fig. 3.4).
Fig. 3.4
The relationship between transvalvular ∆P and flow at variable EOA (a). Based on the Gorlin equation (b), at a flow of 125 ml/s, mild (AVA 1.5 cm2), moderate (AVA 1.0 cm2), and severe AS (AVA 0.7 cm2) all have a ΔP <20 mmHg. However, at a flow of 250 ml/s, we are able to distinguish the severity based on ΔP and severe AS has a ΔP >40 mmHg (a data from Tandon and Grayburn [48] with permission)
High flow may occur with fever, severe anemia, pregnancy, thyrotoxicosis, arterio-venous fistulas, and thiamine deficiency [12]. In addition, aortic regurgitation may also increase transaortic flow leading to an increase in the AVvel and thus the ∆P, particularly in the presence of combined valve stenosis and regurgitation.
Conversely, for gradients to remain low, the EOA must be proportionate to Q requirements that under resting conditions are related to BSA. As such, in patients with an AV prosthesis that has a fixed and too small of an area relative to patients’ BSA (and hence cardiac output, CO), a disproportionately higher ∆P is generated across the prosthesis, a condition that is referred to as prosthesis-patient mismatch (PPM).
Q is usually assessed by stroke volume indexed to BSA (SVI) via Doppler, where a low flow is considered at a SVI ≤35 ml/m2 and a high flow at a SVI ≥58 ml/m2. Invasively, CO and cardiac index (CI) are usually used to determine flow status. Q is dependent on preload, LV contractility, and afterload but not on ejection fraction (EF).
∆Pmax is also directly related to the LVOT diameter and eccentricity of the flow jet through the AV [10, 15] (Fig. 3.3). Increased LVOT diameter will lead to more initial drop of pressure as blood flow converges towards the AV. Thus, with larger LVOT diameters, there is an elevation in both Doppler ∆Pmax and invasive ∆Pnet that is disproportionate to the degree of area stenosis. However, Doppler and invasive gradients are close to each other [15–17] (Doppler-Catheter Concordance). Thus for a given AVA, a larger LVOT diameter yields a higher gradient, higher AVVel, and a smaller dimensionless index (LVOTvel/AVvel, DI). Moreover, the larger the LVOT size compared to that of the GOA, the lower the EOA [15]. Stated differently, with a more abrupt narrowing at the AV from a large LVOT to a stenotic AV, there is a sudden expansion in the lumen beyond the AS. This causes more energy loss and less energy is recovered as pressure distally. These effects cause an increase in both Doppler and catheter-derived gradients with less pressure recovery.
The impact of LVOT diameter on Doppler-derived Pmean was further elucidated in a recent Doppler study of about 10,000 patients. In this study, an AVA of 1 cm2 corresponded to a Pmean of 42 mmHg, AVVel of 4.1 m/s, and a DI of 0.22 in patients with a large LVOTD (>2.3 cm). While it corresponded to a Pmean of 35 mmHg, AVVel 3.8 m/s, and a DI of 0.29 in patients with an average LVOTD (2–2.2 cm). Finally, it corresponded to a Pmean of 29 mmHg, AVVel 3.5 m/s, and a DI of 0.36 in patients was with a small LVOTD (1.7–1.9 cm) [17].
Similarly, in the presence an eccentric jet across the AV (as in cases of a bicuspid AV, non uniform calcification of cusps, and uneven restriction of AV leaflets), there is an increase in pressure loss as the eccentric jet collides with the ascending aortic wall with resultant energy loss due to heat, flow separation, and vortex formation. In addition to increased pressure loss, there is a decrease in Prec, and the ∆P derived from either Doppler or catheterization, will be disproportionately higher relative to the GOA (Doppler-Catheter Concordance). Similarly, the EOA is constricted between the vortices on one side and the aortic wall on the other, and being derived from gradients, will be disproportionately lower compared to the GOA. Based on computational models, this effect occurs to a higher degree in the presence of more severe AS [15, 18, 19]. However, no further significant effect on either Doppler or catheter-derived gradients or EOA is noted beyond an eccentricity angle of 30–35°.
Finally, ∆Pmax also becomes higher in the presence of a bileaflet mechanical AV prosthesis . This occurs due to localized high velocity and pressure drop within the central orifice, causing an overestimation of ∆Pmax by Doppler [13] and published reference values for expected gradients across mechanical valves are available.
Vascular Determinants
Afterload represents what will be referred to as the vascular determinants of ∆Pmax. In addition to systolic blood pressure (SBP), it includes:
Systemic vascular compliance (Ca), which reflects the pulsatile component of afterload.
Systemic vascular resistance index (SVRI), which reflects the static component of afterload.
Effective arterial elastance (Ea), which is a lumped measure of arterial load that combines the effects of static and pulsatile afterload.
Increase in afterload via an increase in SBP, SVRI, and Ea or a decline in Ca indirectly decreases ∆Pmax through decreasing Q rather than a direct effect on ∆P [20, 21], thus underestimating ∆Pmax for the degree of AS, regardless of the presence of normal or low EF [22–25].
Valvulo-arterial impedance (Zva) is a global load that has been suggested to account non-invasively for both perivalvular and vascular (Ea) loads. Its increase has been correlated with poor prognosis in several studies [22–24, 26].
Normalized LV stroke work (LV stroke work/stroke volume) is a newly introduced non-invasive variable obtained from echocardiography and cardiac MRI to also assess global load and account for both perivalvular and valvular loads [25].
Aortic Determinants
The energy loss across the aortic valve and thus both absolute and relative Prec are affected by the ratio of the AVA to the ascending aortic area (Aa) [10], which will be referred to as the aortic determinant of the ∆P. The smaller the aortic diameter/or the greater the ratio of the AVA/Aa, the less is the energy loss and the greater is the absolute and relative Prec leading to a lower ∆Pnet, and increased Doppler/catheter discordance [10, 27].
Conversely, with a progressive increase in aortic root diameter, the energy loss increases and the Prec decreases until the root becomes ≥3 cm where no significant Prec occurs.
Determinants of Pressure Recovery and Concordance Between Doppler and Catheter Measures of Gradient
Doppler-derived ∆PMIG is routinely higher than catheter-derived ∆PPPG irrespective of P rec due to the inherent difference in the timing of measured data points (Fig. 3.5) [1, 28]. These gradients are not primarily used for diagnostic purposes of AS severity. Conversely, the ∆Pmean obtained by either method generally compare well in the absence of significant Prec [1, 28] and are mostly used for diagnostic purposes. Accordingly, ∆Pmax and ∆Pnet will be used in this chapter to reflect ∆Pmean obtained by Doppler and catheterization, respectively.
Fig. 3.5
Catheter ∆PPPG versus Doppler ∆PMIG: Note that the ∆PMIG measures the gradient between the aortic and ventricular pressure at the same point in time (T1, peak LV pressure), while the ∆PPPG measures the gradient at two different points in time (T1 and T2, peak aortic pressure). As such, ∆PMIG is always higher than ∆PPPG regardless of Prec. However, the ∆Pmean by either technique are comparable except in the presence of significant Prec, where ∆Pmean by catheterization is less than that by Doppler
Peri-valvular and vascular determinants of ∆P mentioned above determine the absolute value of both Doppler-derived ∆Pmax and catheter-derived ∆Pnet, while the aortic determinant affects the Prec, and hence determines only the absolute value of catheter-derived ∆Pnet and thus the difference between Doppler-derived ∆Pmax and catheter-derived ∆Pnet.
As the extent of Prec increases, the discrepancy of Doppler and catheter derived measures of gradient increase (Doppler/catheter discordance) [27]. The greater and faster the pressure recovers, the greater the difference between Doppler- and catheter-derived gradients with the Doppler-derived gradients being higher.
The larger the aortic root and/or the LVOT diameter, the more is the energy loss and the less is the Prec with Doppler/catheter concordance. However, the ∆Pmax is not affected. Similarly, in the presence of eccentric flow jets, more energy is lost with less absolute and relative Prec and a higher ∆Pnet. However, due to the initial energy lost as explained above, the ∆Pmax is also increased with elevated but concordant Doppler and catheter gradients [10, 27].
In the presence of an AVprosthesis, localized high velocity and pressure drop within the central orifice leads to an increase in ∆Pmax with immediate realignment of the central jet with flow from the lateral orifices and rapid recovery of pressure, and hence ∆Pnet remains within normal levels [13]. There are published “expected” Doppler gradients for most prosthetic valves that account for this phenomenon.
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