In cardiology, magnetic resonance imaging (MRI) provides a clinical standard for measuring ventricular volumes. Owing to their reliability, volumetric measurements with cardiac MRI have become an essential tool for quantitative assessment of ventricular function. However, as volumetric indices are indirectly related to myocardial motion that drives ventricular filling and ejection, cardiac MRI cannot provide comprehensive evaluation of ventricular performance. To overcome this limitation, the presented work sought to measure ventricular wall motion directly with optical flow analysis of real-time cardiac MRI. By modeling left ventricle (LV) walls in real-time images based on myocardial architecture, we developed an optical flow approach to analyzing LV radial and circumferential wall motion for improved quantitative assessment of ventricular function. For proof-of-concept, a cardiac MRI study was conducted with healthy volunteers and heart failure (HF) patients. It was found that, as real-time images provided sufficient temporal information for correlation analysis between different LV wall motion velocity components, optical flow assessment detected the difference of ventricular performance between the HF patients and the healthy volunteers more effectively than volumetric measurements. We expect that this model-based optical flow assessment with real-time cardiac MRI would offer intricate analysis of ventricular function beyond conventional volumetric measurements.
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The authors would like to thank Drs Jianing Pang, Mickael Bush and Xiaoming Bi for providing technical support on MRI pulse sequence programming.
FundingFunding was provided by Foundation for the National Institutes of Health (Grant No. R01EB022405).
Conflict of interestThere is no conflict of interest.
Author information Authors and AffiliationsDepartment of Cardiac Imaging, St. Francis Hospital, DeMatteis Center for Research and Education, 101 Northern Blvd, Greenvale, NY, 11548, USA
Yu Y. Li, Jason Craft, Yang Cheng, William Schapiro, Kathleen Gliganic, Elizabeth Haag & J. Jane Cao
Department of Biomedical Engineering, Stony Brook University, Stony Brook, NY, 11794, USA
Yu Y. Li
Department of Clinical Medicine, Stony Brook University, Stony Brook, NY, 11794, USA
J. Jane Cao
Correspondence to Yu Y. Li.
Additional informationAssociate Editor Umberto Morbiducci oversaw the review of this article.
Publisher's NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix AppendixThe coefficient terms Am(x,y,z,t-t') and Bmn(x,y,z,t) in Eq. 4 are given as below:
$$A_{0} \left( {x,y,z,t - t^{\prime}} \right) = \left[ {\frac{{\partial I\left( {x,y,z,t} \right)}}{\partial x}\cos \left( \theta \right) + \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial y}\sin \left( \theta \right)} \right]s_{v} \left( {z,t - t^{\prime}} \right)$$
$$A_{1} \left( {x,y,z,t - t^{\prime}} \right) = \left[ {\frac{{\partial I\left( {x,y,z,t} \right)}}{\partial x}\cos \left( \theta \right)\sin \left( \theta \right) + \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial y}\sin^{2} \left( \theta \right)} \right]s_{v} \left( {z,t - t^{\prime}} \right)$$
$$A_{2} \left( {x,y,z,t - t^{\prime}} \right) = \left[ {\frac{{\partial I\left( {x,y,z,t} \right)}}{\partial x}\sin^{2} \left( \theta \right) + \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial y}\cos \left( \theta \right)\sin \left( \theta \right)} \right]s_{v} \left( {z,t - t^{\prime}} \right)$$
$$A_{3} \left( {x,y,z,t - t^{\prime}} \right) = \left[ { - \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial x}r \sin \left( \theta \right) + \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial y}r \cos \left( \theta \right)} \right]s_{v} \left( {z,t - t^{\prime}} \right)$$
$$A_{4} \left( {x,y,z,t - t^{\prime}} \right) = \left[ { - \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial x}r^{2} \sin \left( \theta \right) + \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial y}r^{2} \cos \left( \theta \right)} \right]s_{v} \left( {z,t - t^{\prime}} \right)$$
$$A_{5} \left( {x,y,z,t - t^{\prime}} \right) = \left[ { - \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial x}rz \sin \left( \theta \right) + \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial y}rz \cos \left( \theta \right)} \right]s_{v} \left( {z,t - t^{\prime}} \right)$$
$$B_{0n} \left( {x,y,z,t} \right) = \left[ {\frac{{\partial I\left( {x,y,z,t} \right)}}{\partial x}\cos \left( \theta \right) + \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial y}\sin \left( \theta \right)} \right]\mathop \sum \limits_{{t^{\prime} = 0}}^{{t_{a} }} s_{w} \left( {z,t - t^{\prime}} \right)T_{n} \left( {\frac{{t^{\prime}}}{{t_{a} }}} \right)$$
$$B_{1n} \left( {x,y,z,t} \right) = \left[ {\frac{{\partial I\left( {x,y,z,t} \right)}}{\partial x}x\cos \left( \theta \right) + \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial y}x \sin \left( \theta \right)} \right]\mathop \sum \limits_{{t^{\prime} = 0}}^{{t_{a} }} s_{w} \left( {z,t - t^{\prime}} \right)T_{n} \left( {\frac{{t^{\prime}}}{{t_{a} }}} \right)$$
$$B_{2n} \left( {x,y,z,t} \right) = \left[ {\frac{{\partial I\left( {x,y,z,t} \right)}}{\partial x}y\cos \left( \theta \right) + \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial y}y \sin \left( \theta \right)} \right]\mathop \sum \limits_{{t^{\prime} = 0}}^{{t_{a} }} s_{w} \left( {z,t - t^{\prime}} \right)T_{n} \left( {\frac{{t^{\prime}}}{{t_{a} }}} \right)$$
$$B_{3n} \left( {x,y,z,t} \right) = \left[ { - \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial x}\sin \left( \theta \right) + \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial y}\cos \left( \theta \right)} \right]\mathop \sum \limits_{{t^{\prime} = 0}}^{{t_{a} }} s_{w} \left( {z,t - t^{\prime}} \right)T_{n} \left( {\frac{{t^{\prime}}}{{t_{a} }}} \right)$$
$$B_{4n} \left( {x,y,z,t} \right) = \left[ { - \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial x}x \sin \left( \theta \right) + \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial y}x \cos \left( \theta \right)} \right]\mathop \sum \limits_{{t^{\prime} = 0}}^{{t_{a} }} s_{w} \left( {z,t - t^{\prime}} \right)T_{n} \left( {\frac{{t^{\prime}}}{{t_{a} }}} \right)$$
$$B_{5n} \left( {x,y,z,t} \right) = \left[ { - \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial x}y \sin \left( \theta \right) + \frac{{\partial I\left( {x,y,z,t} \right)}}{\partial y}y \cos \left( \theta \right)} \right]\mathop \sum \limits_{{t^{\prime} = 0}}^{{t_{a} }} s_{w} \left( {z,t - t^{\prime}} \right)T_{n} \left( {\frac{{t^{\prime}}}{{t_{a} }}} \right)$$
where n={0, 1, 2,…, N} is the order of the Chebyshev polynomial Tn(t), I(x,y.z,t) represents a real-time image voxel (x,y) in the slice z and at the time t, (r,θ) is the radial coordinates of the image voxel (x,y) in the slice z, ∂I(x,y,z,t)/∂x represents the partial derivative of the real-time image along the x direction and ∂I(x,y,z,t)/∂y along the y direction, sv(z,t) and sw(z,t) are the systole/diastole and expiration/inspiration binary indicator functions (Fig. 2(c)), and [0,ta] is the data acquisition window.
About this article Cite this articleLi, Y.Y., Craft, J., Cheng, Y. et al. Optical Flow Analysis of Left Ventricle Wall Motion with Real-Time Cardiac Magnetic Resonance Imaging in Healthy Subjects and Heart Failure Patients. Ann Biomed Eng 50, 195–210 (2022). https://doi.org/10.1007/s10439-022-02907-2
Received: 19 July 2021
Accepted: 01 January 2022
Published: 12 January 2022
Issue Date: February 2022
DOI: https://doi.org/10.1007/s10439-022-02907-2
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