Multi-frame biomechanical and relaxometry analysis during in vivo loading of the human knee by spiral dualMRI and compressed sensing

Abstract

Purpose: Knee cartilage experiences repetitive loading during physical activities, which is altered during the pathogenesis of diseases like osteoarthritis. Analyzing the biomechanics during motion provides a clear understanding of the dynamics of cartilage deformation and may establish essential imaging biomarkers of early-stage disease. However, in vivo biomechanical analysis of cartilage during rapid motion is not well established.

Methods: We used spiral displacement encoding with stimulated echoes (DENSE) MRI on in vivo human tibiofemoral cartilage during cyclic varus loading (0.5 Hz) and used compressed sensing on the k-space data. The applied compressive load was set for each participant at 0.5 times body weight on the medial condyle. Relaxometry methods were measured on the cartilage before (T_1ρ , T₂ ) and after (T_1ρ ) varus load.

Results: Displacement and strain maps showed a gradual shift of displacement and strain in time. Compressive strain was observed in the medial condyle cartilage and shear strain was roughly half of the compressive strain. Male participants had more displacement in the loading direction compared to females, and T_1ρ values did not change after cyclic varus load. Compressed sensing reduced the scanning time up to 25% to 40% when comparing the displacement maps and substantially lowered the noise levels.

Conclusion: These results demonstrated the ease of which spiral DENSE MRI could be applied to clinical studies because of the shortened imaging time, while quantifying realistic cartilage deformations that occur through daily activities and that could serve as biomarkers of early osteoarthritis.

Keywords: DENSE MRI; compressed sensing; knee cartilage; quantitative MRI; spiral acquisition.

Figure 1.. The experimental design for acquiring relaxometry measures (T1ρ,T2) and spiral DENSE MR images during rest and varus loading.

We implemented a pneumatic loading device which consists of thigh constraint, cylinder, and a boot section. Participants were positioned in a supine position inside the MRI bore while the knee coil collected MR images. The thigh constraint held the thigh while the pneumatic load from the cylinder pulled the boot to apply varus load on the knee. Varus load was applied in a cyclic fashion consisting of 1 s of load followed by 1 s of unload. On a static rest condition with no varus load, the experiment started with obtaining fast gradient echo MR images (scout) for localization then subsequentially 3D DESS acquisition to select a plane where there was a large tibiofemoral contact area in the medial condyle. After DESS acquisition, relaxometry measurements (${\mathrm{T}}_{1\mathrm{\rho }},{\mathrm{T}}_2$) were ran. Next, cyclic varus load was applied and after 8 minutes of preconditioning, spiral DENSE MR images were collected. The saved spiral DENSE MR phase images in $x$ and $y$ were converted to displacement fields in the selected ROI and smoothed prior to calculating Lagrange strain. To apply CS, k-space data was saved at the scanner and was inputted to BART which reconstructed CS phase images. On the reconstructed CS image, the equivalent process to calculate strain was applied. The displacement and strain calculation were conducted off-line. Lastly, ${\mathrm{T}}_{1\mathrm{\rho }}$ measures were collected after the varus loading was stopped. The images shown were collected on a 29-year-old male subject. Scale bar=25 mm.

Figure 2.. Spiral DENSE MRI during varus load showed time-course (40ms; 25 frames/s) displacement and strain maps in the articular cartilage on the medial condyle.

(A) The varus load applied on ankle was controlled to be equivalent to 0.5 times BW of compressive load on (B) the medial condyle shown in the representative image. (C) The displacement in both $x$ and $y$ showed a gradual increase where more displacement was observed in $x$ due to the translation occurring in the knee coil. Strain maps also displayed a gradual change in strain. ${\mathrm{E}}_{yy}$ showed a pronounced compression occurring while mild tension in ${\mathrm{E}}_{xx}$ and shear strain, ${\mathrm{E}}_{xy}$. The images were obtained on a 26-year-old female subject. Scale bar=15 mm.

Figure 3.. The SA displacement and strain within the ROI showed a gradual transition with time on all participants from the initially recruited group (n=8).

(A) All subjects from the former group, showed a gradual increase of SA displacement and strain with time where SA displacement $y$ was more than an order of magnitude higher than SA displacement $x$. Compressive strain in SA ${\mathrm{E}}_{yy}$ and tension in SA ${\mathrm{E}}_{xx}$ was observed on all subjects which validated the cartilage being compressed due do the varus load and spreading in the perpendicular direction to the loading direction. There was a significant difference in the loading status (loading, loaded) for displacement $x,y$, and ${\mathrm{E}}_{yy}$. (B) Male subjects had significantly more SA displacement in $x$ compared to females. There was no significant difference between gender in SA displacement $y$. The SA strain data in the male group showed a steady increase with time while the strain on females did not increase or decreased after t=560 ms in both normal and shear strain. This resulted in no significant difference in loading status for ${\mathrm{E}}_{xx}$ and ${\mathrm{E}}_{xy}$. Error bars are the standard error of the mean. *P<0.05, ***P<0.0001.

Figure 4.. T1ρ and T2 relaxometry measurements on the knee cartilage generated pixel-scale maps while no changes were observed after varus loading (T1ρ) or between gender (T1ρ,T2).

${\mathbf{T}}_{1\mathbf{\rho }}$ (A) ${\mathrm{T}}_{1\mathrm{\rho }}$ pixel values were overlayed on DESS images collected on a representative male (27-year-old) and female (29-year-old) subject. After cyclic loading, the average ${\mathrm{T}}_{1\mathrm{\rho }}$ values slightly increased on both male and female groups but were not statistically significant (P>0.05, effect size=0.373). Male and female ${\mathrm{T}}_{1\mathrm{\rho }}$ values were in a similar range (P>0.05, effect size=0.407). (B) ${\mathrm{T}}_2$ values showed an analogous trend with ${\mathrm{T}}_{1\mathrm{\rho }}$ where there was no significant difference in gender (P>0.05, effect size=0.146). Error bars are the standard error of the mean (n=4). Scale bar=25 mm.

Figure 5.. Applying CS on the average 1 k-space data enhanced the accuracy of the biomechanical results at a varus loaded time point (t=1040 ms, frame 27).

(A) Displacement maps were compared on image average 1 and average 8 where the former showed higher noise levels resulting in discrepancy between the two averages strongly on the raw displacements prior to smoothing. Applying CS on average 1 data (average 1 - CS) did reduce the noise and error. (B) Strain maps showed a similar trend as the displacement maps where compressive strain at ${\mathrm{E}}_{yy}$ became more pronounced after applying CS, and the values were more comparable to the average 8 data. (C) The SNR measurements showed a significant increase in average 1 - CS compared to average 1. All images shown were collected on a 25-year-old male subject. Scale bar=10 mm. ***P<0.0001.

Figure 6.. CS improved the correspondence of the SA raw displacement and strain values between the average 1 and average 8 data on all time points.

(A) SA displacement and (B) SA strain versus time plots captured on a representative subject (25-year-old, male) visualized the average 1 - CS data approaching the average 8 data points. The error between the reconstruction methods was quantified as the absolute average difference for each time point and averaged for all eight subjects. Significantly reduced SA displacement and strain errors were observed after applying CS. Error bars are the standard error of the mean (n=8). *P<0.05.

Figure 7.. Image averaging and CS improved the signal intensity and smoothness on displacement and strain maps.

(A) Raw displacement $y$ maps (t=1040 ms) were compared qualitatively between images reconstructed on different averages. With more averaging the smoothness increased and noise level decreased. Images shown were collected on a 25-year-old female subject. Applying CS did show a similar effect where the displacement maps had less pixels with errors and were steadily smoothened with more averaging. (B) Quantitatively, the SNR did increase in both non-CS (NCS) and CS groups with more averaging and CS average 2 group surpassed the SNR of NCS average 7. RMSE of the displacement gradually decreased in the NCS group. RMSE at the CS group substantially improved compared to the NCS at lower image averages and moderately improved with more averaging. The two groups met between average 5 and 6. When comparing the raw displacement with respect to (wrt) the smoothed displacement of the average 8 data, CS showed significantly lower RMSE compared to the NCS group in all averages. (C) A similar trend was observed in strain. When using the raw strain (calculated from raw displacement), the RMSE was lower in the CS group for all averages. This result was consistent for either comparing to raw strain or smoothed strain (calculated from the smoothed displacement) of the average 8 data. When calculating the RMSE of the smoothed strain, NCS and CS met between average 3 and 4. Displacement $x,y$, and all strains (${\mathrm{E}}_{xx},{\mathrm{E}}_{yy},{\mathrm{E}}_{xy}$) were combined to calculate the RMSE of displacement and strain. Error bars are the standard error of the mean (n=7). Scale bar=10 mm.