High Shear Thrombus Formation under Pulsatile and Steady Flow

Abstract

Most previous studies have investigated in vitro thrombus formation under steady flow conditions at physiological shear rates, though occlusive thrombosis leading to myocardial infarction and stroke forms under elevated shear rates and pulsatile flow. Two reports of pulsatile flow on thrombosis have yielded conflicting results. In the present study, we quantify the effect of very high shear, reversing pulsatile flow relevant to coronary thrombosis on platelet deposition leading to occlusive thrombus formation. Whole porcine blood was perfused in a collagen-coated, tubular, stenotic test section under pulsatile or steady flow. Pulsatile flow was generated with a frequency of 60 beats per minute and large magnitude excursions similar to a coronary artery waveform. Alternatively, steady flow conditions from a pressure driven system created shear rates matched to the maximum (16000 s⁻¹), mean (3800 s⁻¹), and an intermediate (6500 s⁻¹) shear rates corresponding to the pulsatile system. Thrombus growth in thickness was recorded using a high-resolution CCD attached to a microscope. Steady flow recreated pulsatile flow thrombus formation in most cases. Lag time, t _lag, thrombus growth rate, dV/dt, and time to occlusion, t _occ, did not show statistically significant differences between pulsatile flow and steady flow with matched mean shear rate. Pulsatile flow conditions yielded t _occ = 5.5 ± 2.8 min, which was not significantly different compared to a steady mean shear rate condition with t _occ = 6.2 ± 1.7 min. Similarly, occlusion times for steady intermediate and steady maximum shear rate conditions were not significantly difference from pulsatile flow conditions yielding t _occ of 4.6 ± 2.9 and 4.6 ± 1.8 min, respectively. In contrast, lag time for steady flow at maximum shear rate of 16000 s⁻¹ was decreased to 26.1 s compared to pulsatile flow (t _lag = 42.7 s, p = 0.03), steady mean flow (t _lag = 60.9 s, p = 0.02), and steady intermediate flow (t _lag = 39.9 s, p = 0.01). Occlusive thrombus formation under high shear, pulsatile conditions may be modeled in vitro using steady flow with matched mean shear rate with respect to occlusion time, lag time, and growth rate. Our results indicate that the magnitude of shear rate more strongly affects thrombus growth characteristics than flow pulsatility for an arterial frequency.

Appendix

Reynolds Number

The Reynolds number (Re) is the non-dimensional ratio of inertial forces to viscous forces. For this study, Re was defined as

$$ Re = \frac{{\rho LU_{\text{mean}} }}{\mu } $$

(4)

where ρ is the fluid density, L is the diameter of the test section, U _mean is the mean velocity at the throat, and μ is the fluid viscosity. The density and viscosity of blood were taken as 1050 kg/m³ and 3.24 × 10⁻³ Pa s, respectively.22,30 Outside the stenosis, the diameter was 1.5 mm and the average velocity ranged from 0.0075 to 0.034 m/s across the three steady flow conditions, yielding a Reynolds number between 3.6 and 16.5. Inside the stenosis throat, an average diameter of 325 μm was used, and the average velocity ranged from 0.16 to 0.687 m/s, yielding a Reynolds number between 17 and 72.

Schmidt Number

The Schmidt number (Sc) is the non-dimensional ratio of momentum diffusivity to mass diffusivity, and is defined as

$$ Sc = \frac{\mu }{\rho D} $$

(5)

where D is the diffusivity of platelets. Platelet diffusivity may be considered either as the diffusivity of platelets in plasma, or as the effective diffusivity of platelets in blood under flow. Platelet diffusivity in plasma is 1 × 10⁻¹³ m²/s.21 However, since blood is a dense suspension of cells, effective platelet diffusivity increases with shear rate. Effective diffusivity (D _eff) cab be estimated by21,48

$$ D_{\text{eff}} = D_{\text{sf}} + 0.8a^{2} \gamma \varphi \left( {1 - \varphi } \right)^{0.15} $$

(6)

where D _sf is platelet diffusion in plasma (1 × 10⁻¹³ m²/s), a is the radius of the red blood cells (4.2 μm), γ is the shear rate, and Φ is the hematocrit (0.4). Using this equation, the maximum platelet diffusivity using the wall shear rates is 8.3 × 10⁻⁸ m²/s. Substituting the values for diffusivity into Eq. (5) gives a maximum Sc at the throat of the stenosis for the no-shear condition of 3.7 × 10⁶, and effective Sc between 154 for the mean shear condition and 37 for the maximum shear condition. This range of Sc reflects that platelet diffusion is slower than fluid momentum transfer.

Peclet Number

The Peclet number (Pe) is the non-dimensional ratio of advective transport rate to diffusive transport rate. Pe is defined as

$$ Pe = \frac{{LU_{\text{mean}} }}{D} = ReSc . $$

(7)

Multiplying the above values for Re and Sc for the various experimental conditions yields a Pe at the throat of the stenosis of between 6.2 × 10⁷ and 2.6 × 10⁸ for the minimum diffusivity, and between 2618 and 2664 using values for effective diffusivity. Such high Peclet numbers suggest that the platelet mass transport is dominated by the fluid flow and not simple diffusion.