MRI-radiofrequency tissue tagging in patients with aortic insufficiency before and after operation.

BACKGROUND: Magnetic resonance imaging tissue tagging is a relatively recent methodology that describes ventricular systolic function in terms of intramyocardial ventricular deformation. Because the analysis involves the use of many intramyocardial points to describe systolic deformation, it is theoretically more sensitive at describing subtle differences in regional myocardial fiber shortening when compared with conventional measures of ventricular function such as wall thickening. The objectives of this study were (1) to define sensitive indices of ventricular systolic deformation to assist the clinician in the surgical evaluation of patients with aortic insufficiency, and (2) to quantify differences in regional systolic deformation before and after surgery for aortic insufficiency. METHODS: Magnetic resonance imaging with tissue tagging was performed on 10 normal volunteers and 8 patients with chronic severe aortic insufficiency. Follow-up postoperative studies (5.4+/-1.1 months) were obtained in 6 patients who underwent Ross procedure (1 patient), David procedure (1), and St. Jude aortic valve replacement (4). RESULTS: There was no significant difference in fractional area change, overall circumferential shortening, or overall radial thickening among the normal group, the preoperative aortic insufficiency group, or the postoperative aortic insufficiency group. However, on a regional basis, there was a decrease in posterior wall circumferential strains in the postoperative aortic insufficiency group (29%+/-13% preoperative aortic insufficiency (n=6) versus 24%+/-12% postoperative aortic insufficiency (n=6), p=0.02). CONCLUSIONS: On regional analysis, there was a small but significant decrease in posterior wall circumferential shortening after operation. Magnetic resonance imaging tissue tagging is a sensitive and clinically applicable method of quantifying regional ventricular wall function before and after intervention for aortic insufficiency.

Finite element modeling and experimental verification of lower extremity shape change under load.

Prediction and measurement of residuum shape change inside the prosthesis under various loading conditions is important for prosthesis design and evaluation. Residual limb surface measurements with the prosthesis in situ were used for construction of a finite element model (FEM). These surface measurements were obtained from volumetric computed tomography. A new experimental method for modeling the shape of the in situ lower residual limb was developed based on spiral X-ray computed tomography (SXCT) imaging. The p-version of the finite element method was used for estimating the material properties from known load and displacement data. A homogeneous, isotropic, linear constitutive model with accommodation of the constitutive soft and hard tissues of the residuum was evaluated with static axial loading applied to the in situ prosthesis and compared with experimental results obtained in a human volunteer. Two FEMs were created for similar coronal cross sections of the below knee residuum under two loading conditions. Agreement between observed (from SXCT) and predicted (from FEA) residual limb shape changes inside the prosthesis were maximized with a single modulus of elasticity for the residuum soft tissue of 0.06 MPa, consistent with previously published results. This methodology provides a framework to predict and objectively evaluate FEMs and determine residuum material properties by inverse methods.

Magnetic resonance imaging provides evidence for remodeling of the right ventricle after single-lung transplantation for pulmonary hypertension.

BACKGROUND: In end-stage pulmonary hypertension (PH), the degree of right ventricular (RV) dysfunction has been considered so severe as to require combined heart-lung transplantation. Nevertheless, left ventricular (LV) and RV hemodynamics return to relatively normal levels after single-lung transplantation (SLT) alone. Accordingly, to test the hypothesis that LV and RV systolic function improves after SLT and that the dilated, thick-walled RV reverts to more normal geometry, we used cine MRI and finite-element (FE) analysis to study patients with end-stage PH. METHODS AND RESULTS: Seven patients with end-stage PH underwent cine MRI before and after SLT, and eight normal volunteers were also imaged with cine MRI. Short-axis images at the midventricular level were analyzed with customized image-processing software. The LV and RV ejection fractions, velocity of fiber shortening, RV end-diastolic (ED) and end-systolic (ES) chamber areas, and RV ES and ED wall thicknesses were calculated directly from the MRI images. Two-dimensional FE models of the heart were constructed from the MRI images at early diastole. LV and RV pressures were measured in the patients with a cardiac catheterization before and after SLT. Models were solved to yield diastolic LV, RV, and septal wall stresses. By use of a nonlinear optimization algorithm, LV and RV diastolic maternal properties were determined by minimization of the leastsquares difference between FE model-predicted and MRI-measured LV, RV, and epicardial chamber areas and circumferences. The results demonstrated a substantial reduction in RV wall stress after SLT (1.8 x 10(5) dynes/cm2 pre-SLT to 2 x 10(4) dynes/cm2 post-SLT; P < .001). The average RV diastolic elastic modulus was reduced significantly after SLT (1.5 x 10(6) dynes/cm2 pre-SLT to 1 x 10(5) dynes/cm2 post-SLT; P = .01), but there was no change in the LV elastic modulus. RV velocity of fractional shortening increased significantly after SLT (0.23 pre-SLT to 0.58 post-SLT, P = .02), and RV ED and ES wall thicknesses were reduced significantly (ED, 0.86 cm pre-SLT to 0.65 cm post-SLT, P = .03 and ES, 1.06 cm pre-SLT to 0.72 cm post-SLT, P = .005). CONCLUSIONS: These results provide evidence supporting the contention that LV and RV systolic function improved after SLT for end-stage PH and that the RV underwent significant remodeling within 3 to 6 months after lung transplantation.

Myocardial material property determination in the in vivo heart using magnetic resonance imaging.

OBJECTIVES: To determine nonlinear material properties of passive, diastolic myocardium using magnetic resonance imaging (MRI) tissue-tagging, finite element analysis (FEA) and nonlinear optimization. BACKGROUND: Alterations in the diastolic material properties of myocardium may pre-date the onset of or exist exclusive of systolic ventricular dysfunction in disease states such as hypertrophy and heart failure. Accordingly, significant effort has been expended recently to characterize the material properties of myocardium in diastole. The present study defines a new technique for determining material properties of passive myocardium using finite element (FE) models of the heart, MRI tissue-tagging and nonlinear optimization. This material parameter estimation algorithm is employed to estimate nonlinear material parameter sin the in vivo canine heart and provides the necessary framework to study the full complexities of myocardial material behavior in health and disease. METHODS AND RESULTS: Material parameters for a proposed exponential strain energy function were determined by minimizing the least squares difference between FE model-predicted and MRI-measured diastolic strains. Six mongrel dogs underwent MRI imaging with radiofrequency (RF) tissue-tagging. Two-dimensional diastolic strains were measured from the deformations of the MRI tag lines. Finite element models were constructed from early diastolic images and were loaded with the mean early to late left ventricular and right ventricular diastolic change in pressure measured at the time of imaging. A nonlinear optimization algorithm was employed to solve the least squares objective function for hte material parameters. Average material parameters for the six dogs were E = 28,722 +/- 15984 dynes/cm2 and c = 0.00182 +/- 0.00232 cm2/dyne. CONCLUSION: This parameter estimation algorithm provides the necessary framework for estimating the nonlinear, anisotropic and non-homogeneous material properties of passive myocardium in health and disease in the in vivo beating heart.

Spline surface interpolation for calculating 3-D ventricular strains from MRI tissue tagging.

A method is developed and validated for approximating continuous smooth distributions of finite strains in the ventricles from the deformations of magnetic resonance imaging (MRI) tissue tagging "tag lines" or "tag surfaces." Tag lines and intersections of orthogonal tag lines are determined using a semiautomated algorithm. Three-dimensional (3-D) reconstruction of the displacement field on tag surfaces is performed using two orthogonal sets of MRI images and employing spline surface interpolation. The 3-D regional ventricular wall strains are computed from an initial reference image to a deformed image in diastole or systole by defining a mapping or transformation of space between the two states. The resultant mapping is termed the measurement analysis solution and is defined by determining a set of coefficients for the approximating functions that best fit the measured tag surface displacements. Validation of the method is performed by simulating tag line or surface deformations with a finite element (FE) elasticity solution of the heart and incorporating the measured root-mean-square (rms) errors of tag line detection into the simulations. The FE-computed strains are compared with strains calculated by the proposed procedure. The average difference between two-dimensional (2-D) FE-computed strains and strains calculated by the measurement analysis was 0.022 +/- 0.009 or 14.2 +/- 3.6% of the average FE elasticity strain solution. The 3-D displacement reconstruction errors averaged 0.087 +/- 0.002 mm or 2.4 +/- 0.1% of the average FE solution, and 3-D strain fitting errors averaged 0.024 +/- 0.011 or 15.9 +/- 2.8% of the average 3-D FE elasticity solution. When the rms errors in tag line detection were included in the 2-D simulations, the agreement between FE solution and fitted solution was 24.7% for the 2-D simulations and 19.2% for the 3-D simulations. We conclude that the 3-D displacements of MRI tag lines may be reconstructed accurately; however, the strain solution magnifies the small errors in locating tag lines and reconstructing 3-D displacements.

Mechanical dysfunction in the border zone of an ovine model of left ventricular aneurysm.

BACKGROUND: The pathophysiology of regional mechanical dysfunction in the border zone (BZ) region of left ventricular aneurysm was studied in an ovine model using magnetic resonance imaging tissue-tagging and regional deformation analysis. METHODS: Transmural infarcts were created in adult Dorsett sheep (n = 8) by ligation of the distal homonymous coronary artery and were allowed to mature into left ventricular aneurysms for 8 to 12 weeks. Animals were imaged subsequently using double oblique magnetic resonance imaging with radiofrequency tissue tagging. Short axis slices were selected for analysis that included predominantly the septal component of the aneurysm as well as adjacent BZ regions in the anterior and posterior ventricular walls. Dark grid patterns of magnetic presaturations were placed on the myocardium and tracked as they deformed during the diastolic, isovolumic systolic, and systolic ejection phases of the cardiac cycle. Regional ventricular wall strains were calculated in BZ regions and regions remote from the aneurysm and compared with strains measured in corresponding regions from normal control sheep (n = 6). RESULTS: Diastolic midwall circumferential strains (fiber extensions) were relatively preserved, but abnormal circumferential lengthening strains were observed in the BZ regions during isovolumic systole. Peak circumferential strains ranged from 0.04 to 0.07 in the BZ regions but averaged -0.05 in the normal hearts (p = 0.002 for the anterior BZ and p = 0.001 for the posterior BZ). Midwall end-systolic fiber strains were depressed in the anterior BZ (-0.03 to -0.09 for the BZ versus -0.11 for the normal heart, p < 0.0001) but not in the posterior BZ (p = 0.19). CONCLUSIONS: Our data support the theory that the stretching of BZ fibers during isovolumic systole contributed to a reduction in fiber shortening during systolic ejection and thus reduced the overall contribution of these fibers to forward ventricular output.

An inverse approach to determining myocardial material properties.

Passive myocardial material properties have been measured previously by subjecting test samples of myocardium to in vitro load-deformation analysis or, in the intact heart, by pressure-volume relationships. A new method for determining passive material properties, described in this paper, couples a p-version finite element model of the heart, a nonlinear optimization algorithm and a dense set of transmural measured strains that could be obtained in the intact heart by magnetic resonance imaging (MRI) radiofrequency tissue tagging. Unknown material parameters for a nonlinear, nonhomogeneous material law are determined by solving an inverse boundary value problem. An objective function relating the least-squares difference of model-predicted and measured strains is minimized with respect to the unknown material parameters using a novel optimization algorithm that utilizes forward finite element solutions to calculate derivatives of model-predicted strains with respect to the material parameters. Test cases incorporating several salient features of the inverse material identification problem for the heart are formulated to test the performance of the inverse algorithm in typical experimental conditions. Known true material parameters can be determined to within a small tolerance and random noise is shown not to affect the stability of the inverse solution appreciably. On the basis of these validation experiments, we conclude that the inverse material identification problem for the heart can be extended to solve for unknown material parameters that describe in vivo myocardial material behavior.

An experimental method for evaluating constitutive models of myocardium in in vivo hearts.

A new experimental method for the evaluation of myocardial constitutive models combines magnetic resonance (MR) radiofrequency (RF) tissue-tagging techniques with iterative two-dimensional (2-D) nonlinear finite element (FE) analysis. For demonstration, a nonlinear isotropic constitutive model for passive diastolic expansion in the in vivo canine heart is evaluated. A 2-D early diastolic FE mesh was constructed with loading parameters for the ventricular chambers taken from mean early diastolic-to-late diastolic pressure changes measured during MR imaging. FE solution was performed for regional, intramyocardial ventricular wall strains using small-strain, small-displacement theory. Corresponding regional ventricular wall strains were computed independently using MR images that incorporated RF tissue tagging. Two unknown parameters were determined for an exponential strain energy function that maximized agreement between observed (from MR) and predicted (from FE analysis) regional wall strains. Extension of this methodology will provide a framework in which to evaluate the quality of myocardial constitutive models of arbitrary complexity on a regional basis.

Ventricular interaction in the pathologic heart. A model based study.

The effects of direct ventricular interaction and interaction mediated by the pericardium on the diastolic left ventricle (LV) were quantified using idealized models of five pathologic conditions. Two-dimensional (2D) mathematical models were constructed in long and short axis views of four pathologic LV conditions and the normal heart (NL): dilated cardiomyopathy (DCM), concentric LV hypertrophy (HYP), chronic anterior-apical infarction in a normal shaped LV (CAINL), and CAI in a dilated LV (CAID). To assess the effects of RV pressure increase on the LV mechanical state, RV pressure was systematically increased for several LV pressures and changes in the LV diastolic pressure-area relationships, and LV free wall and septal principal stresses and strains were quantified. At higher RV pressures, with pericardial effects included in the models, the pressure-area relationship was similar for all models, indicating that, at these higher pressures, the effects of RV and pericardial pressures are more important than global LV shape, wall thickness, or material properties in determining the pressure-area relationship. There were significant differences among models in the changes in LV free wall and septal stress and strain after an increase in RV pressure. These models may be of use in predicting interaction in the corresponding clinical state.

Mathematical three-dimensional solid modeling of biventricular geometry.

The characterization of regional myocardial stress distribution has been limited by the use of idealized mathematical representations of biventricular geometry. State-of-the-art computer-aided design and engineering (CAD/CAE) techniques can be used to create complete, unambiguous mathematical representations (solid models) of complex object geometry that are suitable for a variety of applications, including stress-strain analyses. We have used advanced CAD/CAE software to create a 3-D solid model of the biventricular unit using planar geometric data extracted from an ex vivo canine heart. Volumetric analysis revealed global volume errors of 4.7%, -1.3%, -1.6%, and -1.1% for the left ventricular cavity, right ventricular cavity, myocardial wall, and total enclosed volumes, respectively. Model errors for 34 in-plane area and circumference determinations (mean +/- SD) were 5.3 +/- 6.7% and 3.8 +/- 2.7%. Error analysis suggested that model volume errors may be due to operator variability. These results demonstrate that solid modeling of the ex vivo biventricular unit yields an accurate mathematical representation of myocardial geometry which is suitable for meshing and subsequent finite element analysis. The use of CAD/CAE solid modeling in the representation of biventricular geometry may thereby facilitate the characterization of regional myocardial stress distribution.

Regional myocardial stress distribution from magnetic resonance image-based mathematical models.

The instantaneous regional stress distribution within the myocardium, which cannot be directly measured, has been estimated using improved numerical methods and nonaxisymmetric biventricular geometry. To do this, we have employed computer-aided solid mathematical modeling to generate a three-dimensional representation for an ex vivo canine biventricular unit using magnetic resonance imaging. A two-dimensional transverse section was isolated from the solid mathematical model for regional stress analysis using p-version finite element analysis. Loading conditions and material property descriptions were taken from published reports. Analyses showed the maximum principal stresses to range from -1.76 X 10(5) to 8.52 X 10(5) dynes/cm2 during systolic loading, and from -3.85 X 10(4) to 1.13 X 10(5) dynes/cm2 during diastolic loading. This study demonstrates that magnetic resonance image-based solid mathematical biventricular models are suitable for regional stress analysis using p-version finite element analysis. p-Version finite element analysis using magnetic resonance image-based cardiac representations facilitates in vivo stress-strain analyses and may allow the clinical estimation of regional myocardial stress.