Yujie Wang^{1,2}, Christopher J. Hanrahan^{3}, and Jeff L. Zhang^{1}

^{1}Vascular and Physiologic Imaging Research (VPIR) Lab, School of Biomedical Engineering, ShanghaiTech University, Shanghai, China, ^{2}School of Life Science and Technology, ShanghaiTech University, Shanghai, China, ^{3}Department of Radiology and Imaging Sciences, University of Utah, Salt Lake City, UT, United States

Muscle hyperemia after exercise is a physiologic phenomenon that could reflect muscle function and performance. For a group of human subjects, we performed dynamic BOLD scan of calf muscles immediately after in-scanner plantar flexion. To analyze the dynamic data, a kinetic model of deoxy-hemoglobin (dHb) was proposed, with exponentially decayed perfusion as determinant. A hyperemia index (HI) was defined based on the estimated perfusion parameters, and was compared to muscle perfusion measured by DCE scans. In conclusion, we proposed a quantitative model for analyzing post-exercise muscle BOLD data, and the new parameter “hyperemia index”.

$$ \frac{d[dHb]}{dt}=-F(t)*[dHb]+M $$

where $$$M$$$ relates to oxygen consumption rate, and $$$F(t)$$$ is blood flow. To simplify the model, we chose to model the muscle blood flow during exercise recovery as the following exponential decay form,

$$ F(t)=c_1e^{-c_2t}+F_0 $$

where $$$F_0$$$ is the resting level of $$$F(t)$$$, and parameters $$$c_1$$$ and $$$c_2$$$ characterize muscle hyperemia. Integration of $$$F(t)$$$ shows that $$$c_1/c_2$$$ is the area under the curve above the level of $$$F_0$$$, so we define “hyperemia index (HI)” as $$$c_1/c_2$$$. Also, we assumed a linear relationship between $$$[dHb]$$$ and R2*. In solving the above equations numerically, we estimated $$$[dHb]_0$$$ as the mean of the first 2 points, and $$$[dHb]_{\infty}$$$ as the mean of the last 3 data points. Model fitting was performed with optimization to minimize the root mean square error (RSME) between R2* data points and the fitted curve.

Based on the presence of overshoot in their R2*-vs-time curves, we separated the data into two groups (shown as different symbols in Fig. 3). The plots reveal very interesting findings. Parameter HI differentiated the “overshoot” cases from the no-overshoot ones (Fig. 3a), while the R2* difference failed (Fig. 3b). It was also noted that the cases with high DCE perfusion level could have high or low HI values.

1. Zhang JL, Layec G, Hanrahan C, et al. Exercise-induced calf muscle hyperemia: quantitative mapping with low-dose dynamic contrast enhanced magnetic resonance imaging. Am J Physiol Heart Circ Physiol. 2019;316(1):H201-H211. doi:10.1152/ajpheart.00537.2018

Figure 1: Representative examples of curve fitting. (a) A case with monotonically decreasing R2*: fitted values c1=2.3e-14, c2=2.0e-4, M=0.030 and RMSE=0.376 1/ms; (b) A case with the “overshoot” feature: fitted values c1=4.5e-3, c2=2.9e-2, M=0.027 and RMSE=0.226 1/ms.

Figure 2: Scatter
plot showing hyperemia index (HI) and DCE-measured perfusion for the muscles.
It is apparent that plantar flexion did not significantly stimulate soleus, so
both HI and perfusion for soleus were low (on the left-bottom corner).

Figure 3: (a) Linear
regression between BOLD-estimated HI and DCE-measured perfusion. Cases with
overshoot feature (blue): y=5.91e-4*x+0.0147, r=0.574; cases without overshoot feature (green): y=1.23e-4*x+0.0039, r=0.470; all the cases (black line): y=4.77e-4*x-0.0057,
r=0.6254; (b) Linear regression between change of R2* and DCE-measured perfusion. Cases with overshoot feature (blue): y=0.0112*x+0.3985, r=0.5154; cases without overshoot feature (green): y=0.0147*x+0.2766, r=0.5712; all the cases (black line): y=0.0128*x+0.3429, r=0.5779

DOI: https://doi.org/10.58530/2022/3108