École Polytechnique, Mechanical Engineering, Montréal, QC, Canada

Research center, CHU Sainte-Justine, Université de Montréal, Montréal, QC, Canada

Université de Montréal, Kinesiology, Montréal, QC, Canada

Abstract

Background

Early detection of heart failure is essential to effectively reduce related mortality. The quantification of the mechanical properties of the myocardium, a primordial indicator of the viability of the cardiac tissue, is a key element in patient’s care. Despite an incremental utilization of multi-parametric magnetic resonance imaging (MRI) for cardiac tissue characteristics and function, the link between multi-parametric MRI and the mechanical properties of the heart has not been established. We sought to determine the parametric relationship between the myocardial mechanical properties and the MR parameters. The specific aim was to develop a reproducible evaluative quantitative tool of the mechanical properties of cardiac tissue using multi-parametric MRI associated to principal component analysis.

Methods

Samples from porcine hearts were submitted to a multi-parametric MRI acquisition followed by a uniaxial tensile test. Multi linear regressions were performed between dependent (Young’s modulus E) and independent (relaxation times T1, T2 and T2*, magnetization transfer ratio MTR, apparent diffusion coefficient ADC and fractional anisotropy FA) variables. A principal component analysis was used to convert the set of possibly correlated variables into a set of linearly uncorrelated variables.

Results

Values of 46.1±12.7 MPa for E, 729±21 ms for T1, 61±6 ms for T2, 26±7 for T2*, 35±5% for MTRx100, 33.8±4.7 for FAx10^{-2}, and 5.85±0.21 mm^{2}/s for ADCx10^{-4} were measured. Multi linear regressions showed that only 45% of E can be explained by the MRI parameters. The principal component analysis reduced our seven variables to two principal components with a cumulative variability of 63%, which increased to 80% when considering the third principal component.

Conclusions

The proposed multi-parametric MRI protocol associated to principal component analysis is a promising tool for the evaluation of mechanical properties within the left ventricle in the

Background

Heart failure is a progressive disease in which the damage to the cardiac tissue can be of primary or secondary origin. It entails incapacity of the myocardium to sustain an adequate blood flow for the systemic needs of the organism. It is a major health problem approaching epidemical proportions in industrialized countries and imputing billions of dollars in the healthcare resources. It is estimated that at least one third of adults over 55 years old will develop heart failure later in life. The ultimate risk of heart failure is accrued death, with a survival rate of 35% five years after diagnosis

The mechanical properties of the myocardium are a primordial indicator of the viability of the cardiac tissue and heart failure. Uniaxial, biaxial and equibiaxial stretching tests were performed on excised ventricular samples. However, translating knowledge from freshly euthanized animals to live functioning hearts with reliable measures of the mechanical properties of the myocardium remains difficult because of the vascularity of the tissue that changes drastically immediately after death. Moreover, these mechanical properties vary according to the experimental loading protocol and the mathematical model. To solve the finite elasticity stress estimation problem, finite element models of the myocardium were constructed, from isotropic, initially spherical, membrane models

However, the mechanical properties depend on the finite element model and its validation. Thus, techniques allowing the direct measure of these properties from medical imaging were introduced. Magnetic resonance elastography was proposed with specific gradient-echo sequences to reach small echo times and low excitation frequencies adapted for the myocardium

There is an incremental utilization of multi-parametric magnetic resonance imaging (MRI) for cardiac tissue characteristics and function. Maps of the longitudinal relaxation time T1 of the myocardium after injection of a contrast product allowed quantifying changes in heart failure models, reflecting tissue fibrosis

Methods

Samples preparation

Porcine hearts (n=12) were obtained from a local slaughterhouse (Lavallée, Havelock, QC, Canada) within 2 hours of death. A square sample of 10 cm*6 cm*4 cm was dissected from the left ventricular myocardial tissue of each isolated heart and placed in a chamber filled with a tyrode saline solution (8 g of NaCl, 0.199 g of KCl, 0.204 g of CaCl2, 0.098 g of MgCl2, 1.0 g of NaHCO3, 0.053 g of NaH2PO3, and 0.998 g of dextrose within 1 l of water) at room temperature. Each sample was submitted to a multi-parametric MRI acquisition 4 to 6 hours after the tissue preparation, followed by a uniaxial tensile test one hour after the MRI acquisition.

Multi-parametric MR imaging

The chamber was placed within the head coil of a 3 Teslas whole body system (Philips Achieva X-Series) and a single slice, 5 mm thick, was taken centered within the tissue sample. Images for the quantification of T1 and T2 were acquired using a multiple inversion recovery turbo spin-echo sequence for T1 (repetition time of 2100 ms, echo time of 6.3 ms, 15 inversions times from 50 to 1900 ms) and a multi-echo turbo spin-echo sequence for T2 (repetition time of 2000 ms, 10 echo times every 15 ms). T1
^{2}. ADC and FA were calculated as described previously

The mean and standard deviation of T1, T2, MTR, FA and ADC were calculated over a square region of interest (ROI) chosen in the middle of the tissue. The sensitivity of the determination of the mean MRI parameters over the ROI to the ROI location within the slice was very low, due to a spatially uniform signal, whatever the image weighting (Figure

T1-weighted (a), T2-weighted (b) and diffusion weighted with a b-value of 1000 s/mm^{2} (c) images of one cardiac tissue sample installed in the chamber manufactured in acrylonitrile butadiene styrene by fused plastic deposit

**T1-weighted (a), T2-weighted (b) and diffusion weighted with a b-value of 1000 s/mm**
^{
2
}
**(c) images of one cardiac tissue sample installed in the chamber manufactured in acrylonitrile butadiene styrene by fused plastic deposit.**

Mechanical testing

Immediately after the MRI acquisition, the heart tissue from the left ventricle was cut into samples of 5 cm*1 cm*1 cm, which were submitted to a preloading of 2 N followed by a ramp-release preconditioning of amplitude 3 mm and constant speed of 5 mm/s to align the fibres for 5 minutes according to previous protocols

Representative pressure (Pa) - stretch curve for all the samples obtained from the traction test until failure

**Representative pressure (Pa) - stretch curve for all the samples obtained from the traction test until failure.** The resulting curve is composed of a non-linear toe region (stretch between 0 and 0.1), a linear region (stretch between 0.1 and 0.15), a plastic region (stretch between 0.15 and 0.3) and a failure region (stretch over 0.3). The Young’s modulus E is the slope of the curve in the linear part.

Relationships between mechanical properties and MRI parameters

Multi linear regressions were performed between dependent (E) and independent (T1, T2, MTR, FA and ADC) variables to verify our hypothesis. In order to account for potential interaction between MR parameters, a principal component analysis was used to convert the set of possibly correlated variables into a set of linearly uncorrelated variables. The data were rendered to Z-values by subtracting the individual results from the group’s average, and dividing by the calculated group’s standard deviation. The covariance matrix and its eigenvectors and eigenvalues were computed. The cumulative energy content for each eigenvector was used to select a subset of eigenvectors as basis vectors. The source data were then converted into the new basis. The first principal component (F1) has the largest possible variance, and each succeeding component (F2, F3, …Fn) in turn has the highest variance possible under the constraint that it is orthogonal to the preceding components. All statistical tests were performed using XLSTATS (Addinsoft, New York, United States). All results were expressed as Mean±SD and the significance of all tests was set to p≤0.05.

Results

All parameters measured (Table

**
Property
**

**
Mean±SD
**

E

46.1±12.7 MPa

T1

729±21 ms

T2

61±6 ms

T2*

26±7

MTRx100

35±5%

FAx10^{-2}

33.8±4.7

ADCx10^{-4}

5.85±0.21 mm^{2}/s

T1 in ms (a), T2 in ms (b), ADC in mm^{2}/s (c), FA (d) and FA color (e) maps calculated from the T1- and T2-weighted images and from the diffusion tensor images of the sample shown in Figure

**T1 in ms (a), T2 in ms (b), ADC in mm**^{2}**/s (c), FA (d) and FA color (e) maps calculated from the T1- and T2-weighted images and from the diffusion tensor images of the sample shown in Figure****.** For the FA color map, the colors indicate direction of fiber tracts (red transverse, blue cranio-caudal, green anterior–posterior).

Multi linear regressions showed that only 45% of E can be explained by the MRI parameters T1, T2, T2*, MTR, FA and ADC (Equation 1). The highest variance inflation factor was attributed to T2 when the regression was done on the 6 MRI parameters and to T2* when the regression was done on the remaining 5 MRI parameters (without T2). The multiple linear regression done after removing T2 and T2* (Equation 2) showed that all parameters had small and equivalent variance inflation factor and that the coefficient of determination did not change significantly (42%).

The principal component analysis reduced our 7 variables (E, T1, T2, T2*, MTR, ADC, FA) to two principal components F1 and F2 with a cumulative variability of 63%, which increased to 80% when considering the third principal component F3. The representation of the 7 variables in the (F1, F2) plane (Figure

Correlation circle representing a) the 7 variables (E, T1, T2, T2*, MTR, ADC, FA) and b) the 4 variables (E, T1, ADC, FA) in the plane of the principal components (F1, F2)

**Correlation circle representing a) the 7 variables (E, T1, T2, T2*, MTR, ADC, FA) and b) the 4 variables (E, T1, ADC, FA) in the plane of the principal components (F1, F2).**

The principal component analysis reduced the 5 variables (E, T1, MTR, ADC, FA) to two principal components F1 and F2 with a cumulative variability of 67%, which increased to 81% when considering the third principal component F3. The representation of the 5 variables in the (F1, F2) plane (Figure

Discussion

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

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

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

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

In vivo relaxometry of cardiac tissue is a well established method already used in clinical applications

Conclusions

The proposed multi-parametric MRI protocol associated to principal component analysis is a promising tool for the evaluation of mechanical properties within the left ventricular myocardium. Our

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

DP proposed the design of the study, carried out the data analysis, discussed the results and drafted the manuscript. ND participated to the results discussion and revised the manuscript. AF carried out the experiments. DC participated to the design of the study and the statistical analysis and revised the manuscript. All authors read and approved the final manuscript.

Acknowledgements

The Quebec Bio-Imaging network (Fonds de Recherche du Québec en Santé) and the Research center of the Sainte-Justine Hospital (Montreal, Canada) for the financial support.

Irene Londono, from the Pediatric Orthopaedic Laboratory (Research Center, Sainte Justine Hospital, Montreal, Canada), for her support with the tissues preservation.

Pre-publication history

The pre-publication history for this paper can be accessed here: