Introduction

Cardiac Diffusion Tensor imaging (cDTI) is a powerful non-contrast technique that probes the displacement of water molecules and from it infers the cellular structure in vivo. Advanced motion-compensated gradient designs have been proposed for cDTI^1,2_, such as first and second order nulled designs. These designs rely upon the assumption of linear velocity or linear acceleration of cardiac motion during the encoding of diffusion. These waveforms successfully compensate cardiac motion during most of systole, but generally not during diastole. No designs have been proposed to compensate cardiac motion in diastole, principally due to the lack of knowledge on the interaction between motion compensated designs and real cardiac displacements.

Spatiotemporally resolved maps of cardiac displacements can be measured with DENSE³ MRI Although, from the acquired displacements, it is theoretically possible to estimate if the cardiac motion respects the assumption of linear velocity or acceleration, the complete interaction between cardiac motion, diffusion motion, and motion compensated waveforms is still unknown.

The objective of this work was to provide a new simulation framework to study the interaction between cardiac motion and motion-compensated diffusion encoding waveforms. This framework uses realistic cellular structure and a real cardiac displacement field measured in vivo using DENSE MRI to simulate motion-altered diffusion signal.

Methods

The simulation framework shown in the animated Figure 1 is composed of 4 steps:

1) Cell structure generation: The cardiac structure was generated by inserting and connecting cardiomyocytes in a 0.5x0.5x0.5 mm³ voxel until a given ECV was reached. Cardiomyocytes are represented using cylinders 100µm long and 10-20µm in diameter. Subsequently, a look-up table (mask) for intra- and extra cellular compartments with resolution 1mm was generated.
2) Diffusion Displacement Simulation: The displacement of water molecules was simulated using a particle-based random-walk method with a native coefficient of diffusion D₀ equal to 3x10^-3mm²/s and 2.2x10^-3mm²/s in the extra- and intra-cellular compartments⁴, respectively. These compartments were kept impermeable. A time step Dt=10µs was adopted and diffusion motion was linearly interpolated to 1µs in the MR simulations.
3) Cardiac Displacement Simulation: A 3D displacement field was applied to the voxel boundary (corners) and then linearly interpolated to the water molecules within the voxel to simulate the effect of cardiac deformation on the diffusion displacement distribution.
4) MR Simulation: Diffusion MR phase distribution were generated by numerically integrating the water molecules’ displacements and the diffusion encoding gradients with Dt=1ms.


First, nine cellular structures with ECV ranging from 0.15 to 1.0 and 25 repetitions using 10,000 water molecules each were simulated to validate the framework presented in Steps 1 & 2.

Subsequently, a single model using mean ECV=0.25 with N=1,000 particles (Steps 1-2) was used in each voxel of the mid short axis DENSE slice to simulate Steps 3 & 4. The cardiac displacement field was extracted from cine DENSE images acquired in a healthy volunteer on a 3T scanner (Prisma, Siemens). Six cine DENSE slices were acquired in short axis (SA) and long axis (LA) views during breath holds using 2D displacement encoding (ke=0.1 cycle/mm, balanced 3-point encoding, TE=1ms, TR=15ms, 2.5x2.5x8mm³). Unfiltered SA and LA 2D displacements were combined to generate a 3D displacement field. Monopolar (M₀), first order (M₀M₁), and second order motion compensated (M₀M₁M₂) waveforms were generated for a b-value of 350s/mm² resulting in a TE of 38, 54, 61ms and for twelve encoding directions.

For each step, the Mean Diffusivity (MD) and Fractional Anisotropy (FA) were extracted based on a tensor model and using only the water molecules in the extra-cellular compartment. MD_water, FA_water, first (E1_water) and second (E2_water) eigenvalues were calculated directly from the water displacement distribution. MD_MR was calculated from the MR signal attenuation generated from the phase distribution. The deviations from the linear velocity (D_LinVel) and linear acceleration (D_LinAcc) hypotheses were computed for the acquired DENSE displacement field

Results

Figure 2 shows MD_water, FA_water, E1_water and E2_water reported as function of ECV. MD_water, E1_water and E2_water increase and FA_water decreases as ECV increases. All values converge to an isotropic water distribution for ECV=1. As E2_water corresponds to water molecules that are originally more restricted, E2_water increases more than E1_water as ECV increases.

Maps of MD_water generated after applying the cardiac motion on top of diffusion are shown in Figure 3. Due to motion corruption, MD_water significantly increases in all cardiac phases above the value without motion.

Mean diffusivity (MD_MR) maps obtained after simulating the three (M_0, M₀M_1, and M₀M₁M₂) encoding diffusion waveforms are shown in Figure 4. M₀M₁ and M₀M₁M₂ waveforms reduce the phase disruption due to cardiac deformation. Motion-compensated waveforms reduce MD_MR across cardiac phases compared to M₀ waveforms, but MD_MR remains above the case without motion (Figure 5). D_LinVel and D_LinAcc are the smallest in mid-systole (200ms) and in diastasis (700ms), which are also local minima for MD_MR.

Discussion and conclusion

In this work a new simulation framework enables studying the effect of real cardiac motion on the diffusion signal. Results indicate that cardiac motion contains high-order components that affect cardiac diffusion signal even when M0-M1-M2 motion-compensated gradients are adopted. This framework paves the way to design in silico new motion compensated waveforms to optimize cardiac diffusion imaging throughout the cardiac cycle.

Acknowledgements

No acknowledgement found.