Mitral Valve Prosthesis Design Affects Hemodynamic Stasis and Shear In The Dilated Left Ventricle

Abstract

Dilated cardiomyopathy produces abnormal left ventricular (LV) blood flow patterns that are linked with thromboembolism (TE). We hypothesized that implantation of mechanical heart valves non-trivially influences TE risk in these patients, exacerbating abnormal LV flow dynamics. The goal of this study was to assess how mitral valve design impacts flow and hemodynamic factors associated with TE. The mid-plane velocity field of a silicone dilated LV model was measured in a mock cardiovascular loop for three different mitral prostheses, two with multiple orientations, and used to characterize LV vortex properties through the cardiac cycle. Blood residence time and a platelet shear activation potential index (SAP) based on the cumulative exposure to shear were also computed. The porcine bioprosthesis (BP) and the bileaflet valve in the anti-anatomical (BL-AA) position produced the most natural flow patterns. The bileaflet valves experienced large shear in the valve hinges and recirculating shear-activated flow, especially in the anatomical (BL-A) and 45-degree (BL-45) positions, thus exhibited high SAP. The tilting disk valve in the septal orientation (TD-S) produced a complete reversal of flow and vortex properties, impairing LV washout and retaining shear-activated fluid, leading to the highest residence time and SAP. In contrast, the tilting disk valve in the free-wall position (TD-F) exhibited mid-range values for residence time and SAP. Hence, the thrombogenic potential of different MHV models and configurations can be collectively ranked from lowest to highest as: BP, BL-AA, TD-F, BL-A, BL-45, and TD-S. These findings provide new insight about the effect of fluid dynamics on LV TE risk, and suggest that the bioprosthesis valve in the mitral position minimizes this risk by producing more physiological flow patterns in patients with dilated cardiomyopathy.

Appendices

Appendix A

Vortex identification was performed using the Q-criterion; and the instantaneous vortex circulation, KE density, position, and radius were computed at each time point. Circulation was defined as:

$$\varGamma = \mathop \smallint \limits_{A}^{ } \omega \left( {x,y} \right)dA,$$

(A1)

where ω(x,y) was the vorticity and A was the area enclosed within the vortex core⁵⁰. Vortices were identified as CW or CCW depending on the sign of their circulation. KE density was defined as:

$$KE = \frac{1}{2}\rho \mathop \smallint \limits_{A}^{ } \varvec{v}(x,y)^{2} dA,$$

(2)

where $\rho$ was the fluid density, and $\varvec{v}$ was the modulus of the 2-D velocity vector. The position of the vortex centroid was defined as:

$$\left( {\begin{array}{*{20}c} {x_{C} } \\ {y_{C} } \\ \end{array} } \right) = \frac{1}{\varGamma }\mathop \smallint \limits_{A}^{ } \omega \left( {x,y} \right)\left( {\begin{array}{*{20}c} x \\ y \\ \end{array} } \right)dA.$$

(3)

The vortex core was fit to an ellipse with axes given by the 2nd order moments of the vorticity distribution

$${\mathcal{O}} = \frac{1}{\varGamma }\mathop \smallint \limits_{A}^{ } \omega \left( {x,y} \right)\left[ {\begin{array}{*{20}c} {\left( {x - x_{C} } \right)^{2} } & {\left( {x - x_{C} } \right)^{ } \left( {y - y_{C} } \right)^{ } } \\ {\left( {x - x_{C} } \right)^{ } \left( {y - y_{C} } \right)^{ } } & {\left( {y - y_{C} } \right)^{2} } \\ \end{array} } \right]dA,$$

(4)

such that the eigenvalues and eigenvectors of the matrix ${\mathcal{O}}$ provided the major and minor axes of the ellipse, and , and their orientation. The characteristic radius of the vortex was defined as

$$R = \sqrt {ab} ,$$

(5)

as previously described.28 The results were made independent of the threshold applied to the Q criterion, Q_th, by recomputing the vortex properties over the area defined by an ellipse centered at (x_c, y_c) and with major and minor axes given by $2a$ and $2b$, and the aspect ratio calculated from a/b. This procedure was repeated iteratively until the vortex radius varied by less than 1% between iterations, which was usually achieved in 4-5 steps. Following previous studies,28 we defined an orthogonal anatomical reference system of the LV as the intersection of the long axis of the ventricle with the line that passes through the mitral annulus and the aortic tract. Vortex positions in this system were normalized by the long (range: 0 (mitral base) to 1 (apex)) and short (range: − 0.5 to +0.5) axes. The temporal waveforms for the radius, position, circulation, and KE were obtained and phase-averaged over the full CC for both main (CW) and secondary (CCW) vortices.

Appendix B: Shear Activation Potential Model and Fit to Experimental Data

Exposure of platelets to hemodynamic shear can trigger platelet activation. Although this process is not fully understood yet, it is recognized that both the intensity of the shear stresses and the cumulative time of exposure contribute to activation.15,32 To account for these two effects, one can model the activation and transport of platelets by blood flow using a forced advection equation

$$D_{t} {{\varSigma }} = \partial_{t} {{\varSigma }} + \nabla \cdot \left( {\varvec{v}{{\varSigma }}} \right) = \dot{\gamma }(x,y,t)^{\alpha } ,$$

(B1)

where $\dot{\gamma }$(x,y,t) is a measure of local instantaneous shear stress. This kind of models is common in the medical device literature.14 Using the scalar ${{\varSigma }}$ computed from Eq. (B1), we define a quantitative index that reflects the potential shear activation of platelets as $SAP = {{\varSigma }}^{{\frac{1}{\alpha - 1}}}$, which has dimensions of shear rate (i.e. inverse time). In this model, the value of the exponent α dictates the importance of shear intensity compared to that of cumulative exposure time. In the hypothetical limit scenario α = 0, one recovers the residence time equation (Eq. (2) in the main text) and platelet activation is exclusively determined by exposure time regardless of shear intensity. Likewise, as α increases, ${{\varSigma }}$ reflects the accumulation of increasingly stronger shear events along the flow pathlines, and platelet activation is preferentially determined by shear intensity rather than by exposure time.

The actual value of α results from cellular and molecular biomechanical phenomena that are very difficult to study in vivo. However, it can be estimated by fitting the model [B1] to experimental data. In this study, we fit the model to Hellums’ collection of data15 (Fig. B1), which represents the locus of platelet activation as a function of shear intensity and shear exposure time. These data are well described by the power law (a straight line in the log–log plot) $\dot{\gamma } \sim \sigma /\mu \approx 185 \frac{{dynes s^{1/2} }}{{cm^{2} }} t^{ - 1/2}$, where $\mu = 3.8 \frac{dynes s}{{cm^{2} }}$ is the viscosity of blood. This fit suggests that ${{\varSigma }}\sim \dot{\gamma }^{2} t$$\approx 3 \times 10^{4} s^{ - 1}$ represents a unified criterion for platelet activation that combines shear exposure time and shear intensity. Thus, we used $\alpha \approx 2$ to integrate Eq. (B1) and to calculate the SAP maps.

Figure B1

Power law least-squares fit to Hellums’ experimental compilation of data on shear-mediated activation of platelets.

Appendix C: List of Acronyms

$\dot{\gamma }$—shear rate

MHV—mechanical heart valve

TE—thromboembolic events

BL—bi-leaflet

LV—left ventricle

DCM—dilated cardiomyopathy

MV—mitral valve

AoV—aortic valve

$T_{R}$—residence time

EF—ejection fraction

LVP—left ventricle pressure

AoP—aortic root pressure

Q_AO—aortic flow rate

BP—Medtronic 305 Cinch bio-prosthesis valve

TD-S—Medtronic Hall tilting-disk valve oriented with the large orifice directing flow towards the septum wall

TD-F—Medtronic Hall tilting-disk valve oriented with the large orifice directing flow towards the free wall

BL-A—Carbomedics bi-leaflet valve oriented in the anatomical position

BL-AA—Carbomedics bi-leaflet valve oriented in the anti-anatomical position

BL-45—Carbomedics bi-leaflet valve oriented at a 45° angle

PIV—Particle image velocimetry

PI—Pulsatility index

SAP—shear activation potential

KE—kinetic energy

CW—clockwise

CCW—counter-clockwise

Appendix D: List of Symbols

$\dot{\gamma }$—shear rate

$T_{R}$—residence time

$Q_{AO} max$—maximum aortic flow rate

$Q_{AO} min$—minimum aortic flow rate

$Q_{AO} mean$—average aortic flow rate

$\vec{v}_{PIV}$—velocity field