We confirmed our hypothesis that a relationship exists between the Young’s modulus and the MRI parameters of the left ventricular myocardial tissue, and that this relationship may be in part non linear. Principal component analysis is very useful to reduce the dimensionality of a data set by projecting high dimensional data into a lower dimensional space. For the first time to our knowledge, a multi-parametric MRI acquisition composed of relaxation times mapping, magnetisation transfer and diffusion tensor imaging followed by a mechanical test in traction were performed on fresh porcine cadaveric hearts.
Hyperelastic properties or coefficients of the exponential stress-stretch relation were reported from bi-axial traction tests performed on bovine heart samples, but the stress-stretch curves showed various Young’s moduli from 2-7 kPa
[46–49] to 150 kPa
[45, 50]. An elastic modulus of 30 kPa was reported for muscle strips of rats left ventricular walls tested in biaxial traction
. The stiffness modulus of human samples increased from 100 to 300 kPa with increasing collagen content
. There is a large variation between the reported moduli, but they are smaller than the ones we measured (46 MPa) on samples of porcine left ventricular walls, because of the different mechanical protocols in uniaxial or biaxial traction. Along-fibre moduli of 4-100 kPa were reported from finite element modeling
. Effective shear stiffness of 10-15kPa was reported from magnetic resonance elastography performed in vivo on pigs
. However, much higher stiffness coefficients were found in the fibre direction (2.6GPa) from ultrasonic velocity measurements on freshly excised ovine hearts
The relaxation times we measured in this study on the isolated porcine left ventricular wall tissue were in the same range as the ones reported in the literature on animals or humans. Relaxography of excised rat myocardium showed T1 values of 907±77 ms, T2 values of 32±6 ms and T2* values of 32±6 ms
. T2 values of 50-60 ms
 and T2* values of 35±3 ms
 were measured on healthy volunteers while T2* values of 27±20 ms were measured on patients with myocardial fibrosis
. T1 values of 1100±67 ms and 950-1050 ms were measured in vivo on domestic farm pigs
 and normal volunteers
[57–59] respectively. However, no measures of MTR, ADC or FA were reported on the heart.
The relationship found between the Young’s modulus and the MRI parameters is the basis for the development of an indirect tool for the in vivo evaluation of the mechanical properties of cardiac tissues. However, these relationships vary between biological tissues and the degenerative state of the tissue. Equivalent experiments were done on intervertebral discs and showed that 45 to 80% of the Young’s modulus, the aggregate modulus, the radial permeability and the axial permeability can be explained mostly by MT and diffusion sequences
. On the skeletal muscle, up to 78% of the Young’s modulus can be explained by relaxation times, magnetization transfer and diffusion coefficients suggesting a linear relationship
. However, both studies showed changes in the relationships when the tissue is degenerated with a significant modification of the mechanical properties, suggesting that before the use of this technique to quantify the mechanical properties in vivo on patients suffering from various diseases, the relationships have to be defined for each degeneration state of the tissue that mimics the pathology.
There were some limitations to this study which warrant further investigations. The low number of tissue samples was due to the difficulty to obtain the animals’ heart within two hours of death from the slaughterhouse. Our strict observation of the 2-hour window, in contrast, permitted the uniformity of the test results however. Another limitation relates to the chamber used for the MRI acquisition, which was manufactured in acrylonitrile butadiene styrene by rapid prototyping (fused plastic deposit). The limit of this method is that small air bubbles can be trapped during the fused plastic deposit, even if high-density presets are used. Nevertheless, artifacts on the relaxation time images were removed using a filter that suppresses high values (more than 2500 ms in T1, 200 ms in T2). For the diffusion images, the use of a multi-shot echo-planar-imaging sequence decreased the distortion induced in the images by the air bubbles. Diffusion tensor imaging is often limited by a lower signal to noise ratio than in relaxation time imaging, but an estimated signal to noise ratio of 105 for our b=0 image confirms the reliability of our ADC and FA measures in the cardiac muscle tissue. From an analytical perspective, the mechanical behaviour of the cardiac muscle tissue is known to be hyperelastic
[11–15] which warrant the experimental data to be fitted with a hyperelastic model instead of a linear model.
In vivo relaxometry of cardiac tissue is a well established method already used in clinical applications
[25–30]. The in-vivo sensitivity of MTR measurements to infarct and inflammation was proved
. However, the application of diffusion tensor imaging of cardiac tissue in-vivo remains challenging, but the feasibility has already been demonstrated and should be available in the near future. Thus our method could be transferred to in an in-vivo study in which the mechanical properties as determined by multi-parametric MRI could be compared to the mechanical properties as determined from cine-MRI or cine-tagging-MRI associated to finite element modeling