Current Cardiology Reviews, 2006, 2, 000-000 1

1573-403X/06 $50.00+.00 ©2006 Bentham Science Publishers Ltd.

Assessment of Cardiac Performance with Magnetic Resonance Imaging

Alistair A. Young*

Department of Anatomy with Radiology, Faculty of Medical and Health Sciences, University of Auckland, 85 Park Ave,

Grafton, Auckland, New Zealand

Abstract: A quantitative assessment of regional cardiac performance is required for the diagnosis of disease, evaluation of

severity and the quantification of treatment effect. MRI allows the noninvasive quantification of motion and deformation

in the heart, including the precise assessment of all components of deformation in all regions of the heart throughout the

cardiac cycle. In recent years, these imaging protocols have become standardized in both the research and clinical settings.

However, adoption in the routine clinical environment has been hindered by the complex and time-consuming nature of

the image post-processing. Model-based image analysis procedures provide a powerful mechanism for the fast, accurate

assessment of cardiac MRI data and lend themselves to biophysical analysis and standardized functional mapping proce-

dures. This paper reviews the current state of the art in MRI assessment of cardiac performance with an emphasis on

mathematical modeling analysis procedures. Firstly, fast and accurate evaluation of mass and volume is discussed using

interactive 4D modeling techniques. Analysis of tissue function, strain and strain rate is then reviewed. Mathematical

models of regional tissue function and wall motion allow registration between cases and across groups, enabling quantifi-

cation of multidimensional patterns of wall motion between disease and treatment groups. Finally, information on myo-

cardial tissue kinematics can be incorporated into biophysical models of cardiac mechanics and used to gain an under-

standing of how physiological tissue parameters such as contractility, ventricular compliance and electrical activation

combine to effect whole heart function.

Key Words: Cardiac performance, magnetic resonance imaging, strain, mathematical modeling.

1. INTRODUCTION

Cardiac magnetic resonance (CMR) imaging provides an abundant source of detailed, quantitative data on heart struc-ture and function. Advantages of CMR include its non-invasive nature, ability to modulate contrast in response to several mechanisms, and ability to provide high quality func-tional information in any plane and any direction. Its three-dimensional (3D) tomographic nature allows excellent views of the entire heart, irrespective of cardiac orientation and cardiac chamber shape. CMR imaging has provided detailed information on 3D ventricular shape and geometry [1, 2], regional systolic [3] and diastolic [4] strain, material micro-structure [5, 6], blood flow [7], perfusion [8] and viability [9, 10]. It is considered the most accurate method to measure ventricular volumes and systolic function [2]. The high pre-cision and accuracy of CMR [11, 12] has led to its increasing application worldwide in cardiac research trials and clinical practice. In particular, CMR offers the ability to non-inva-sively quantify regional wall motion abnormalities including regional wall thickening and strain in all regions of the heart.

However, adoption in the routine clinical environment has been hindered by the availability of the technology and the time-consuming nature of the image analysis. Imaging protocols are now becoming standardized, and dedicated CMR scanners offered by all major manufacturers are capa-ble of sampling the entire heart at high contrast to noise ratio and acceptable resolution (10-20 sections at 1x1x8 mm vox-els and 20-50 msec temporal resolution) in 10-15 minutes.

*Address correspondence to this author at the Department of Anatomy with

Radiology, Faculty of Medical and Health Sciences, University of Auck-land, 85 Park Ave, Grafton, Auckland, New Zealand; Tel: +64 9 3737599

ext 86115; E-mail: a.young@auckland.ac.nz

Analysis of the many hundreds of images that are routinely produced is a significant problem. Model-based image ana-lysis procedures provide a powerful mechanism for the fast, accurate assessment of cardiac MRI data and lend them-selves to biophysical analysis and standardized functional mapping procedures.

This review focuses on the assessment of cardiac per-formance with CMR techniques. Emphasis is placed on the quantification of regional wall motion and tissue function, including strain and strain rate, with the aid of mathematical models of cardiac structure and function. Section 2 reviews the application of interactive 4D modeling techniques to fast, accurate evaluation of mass and volume. Myocardial tissue performance is considered in Section 3, including displace-ment encoding MRI with SPAMM, HARP and DENSE methods. Quantitative methods for the evaluation of regional wall motion are considered in Section 4, in particular princi-pal component analysis and the identification of characteris-tic functional modes of motion and deformation. Finally, biophysical models of cardiac mechanics are discussed in Section 5, which enable the kinematic information obtained by CMR to be understood in terms of the underlying physi-ology of the tissue, including contractility, compliance and electrical activation.

2. GLOBAL STRUCTURE AND FUNCTION: VEN-TRICULAR MASS AND VOLUME

The standard clinical assessment of global cardiac struc-ture and function comprises sequential 2D breath-hold cine SSFP (steady state free precession, also known as true-FISP, FIESTA, and BFFE) imaging in multiple sections covering the heart [13, 14]. In SSFP imaging, the magnetization is brought into a steady state with minimal TR (repetition time)

2 Current Cardiology Reviews, 2006, Vol. 2, No. 4 Alistair A. Young

and rephasing gradients. Tissue contrast is dependent on the ratio of T1 to T2, achieving excellent contrast between myo-cardium and blood (Fig. 1). This robust contrast mechanism facilitates the quantification of cardiac mass and chamber volume.

Fig. (1). true FISP short (top) and long axis (bottom) images, at

end-diastole (left) and end-systole (right). Contours show location

of the intersection of the 4D model with the image plane. Guide

points placed by the user are also shown.

Traditionally, LV boundaries (contours) are manually drawn on each section of a series of contiguous short-axis images and the outlined areas are converted to volumes and summed to produce estimates of volume and mass

1. Previous

studies have shown that this technique gives more accurate and reproducible estimates of volume and mass than other imaging modalities [2, 12, 15–17]. The prohibitive time nec-essary to outline the inner and outer boundaries of the LV in each section precludes this method in routine clinical prac-tice. Although many semi-automated image segmentation algorithms have been applied to this problem [18–20], they are prone to errors due to the limited temporal and spatial resolution and presence of image artifacts. User interaction is therefore required to correct errors, but this interaction must be intuitive, efficient and minimal. Guide point modeling [21] provides a fast, interactive method for accurate determi-nation of cardiac mass and volume. The basic steps of this process are outlined below.

Firstly, fiducial markers are placed on the images to de-termine the location of the LV central axis, the insertion points of the RV free wall into the septum, and the location and angulation of the mitral valve plane. A “cardiac” coordi-nate system is then defined with the origin placed on the LV central axis one third of the distance from the base to the apex, the x axis oriented toward the LV apex, the y axis ori-

1 This method of simple slice summation is often erroneously termed “Simpson’s rule”;

however, the latter is a specific quadratic integration formula typically not employed in

clinical practice.

ented towards the centroid of the right ventricle, and the z axis oriented posteriorly. A 4D (i.e. coherently continuous in space and time) finite element model of the LV is then inter-actively manipulated using guide points placed by the user on particular locations of the image (Fig. 2). The 4D model allows integration of all spatio-temporal information into a coherent whole. The contours of the model are calculated by intersecting the model with the image plane, and mass and volumes are calculated by numerical integration up to the mitral valve plane. The model updates in real time, changing the location of the contour and recalculating mass and vol-ume in response to the position of the guide points. This method has been shown to produce efficient and accurate estimates of LV mass and volume [21]. Relative positions around the heart can then be referenced by the finite element material coordinates. This allows non-rigid registration and mapping of results between cases, e.g. between different acquisitions in the same patient, or between different groups, since regions with the same material coordinate denote the same physical region in the heart.

A feature of this algorithm is the integration of long and short axis images into a coherent analysis. In particular, the 3D motion of the mitral valve plane is difficult to define in short axis images, due to partial voluming, but is easily de-termined in long axis images. Similarly the motion of the LV apex is best determined in long axis images. The smooth descent and ascent of the mitral valve plane, and numerical integration of volume up to this plane, allows the calculation of all volumes throughout the cardiac cycle and robust esti-mates of chamber ejection and filling rates. Regional analy-sis of wall thickening and regional ejection can then be cal-culated by numerical integration, allowing quantification of regional performance (Fig. 3).

3. TISSUE FUNCTION: DISPLACEMENT ENCODED

MRI

The regional wall motion and chamber function of the heart are useful parameters of cardiac performance. How-ever, they are indirect measures of tissue function. Strain, defined as the relative change in length between two states, is a direct measure of myocardial shortening and lengthen-ing. Strain can be computed from a knowledge of the dis-placements of material points within the myocardium. For small deformations, the strain is simply the gradient of the displacement field. For large strains (greater than 5%, such as occur in the heart) the strain is a non-linear function of the displacement field. The two most commonly quoted strain measures are the Lagrangian strain (typically used in MRI tagging studies) and the Eulerian strain (typically used in tissue Doppler studies). Given a small line segment of length dS in the reference state and ds in the current state, the La-grangian strain is defined as (ds

2-dS

2)/dS

2, whereas the Eule-

rian strain is defined as (ds2-dS

2)/ds

2. Strain is generally a

tensor quantity, meaning that it has different values depend-ing on the orientation of the line segment dS. At any point in the myocardium, there is a unique direction in which the extension is maximal- known as the principal lengthening direction. The direction in which the contraction is maximal (the principal shortening direction) is at right angles to the principal lengthening direction.

Assessment of Cardiac Performance with Magnetic Resonance Imaging Current Cardiology Reviews, 2006, Vol. 2, No. 4 3

In order to measure tissue material displacements, re-searchers have used implanted radiopaque beads [22], ultra-sonic markers [23], or natural landmarks such as the coro-nary arteries [24]. These methods have provided very useful information for research purposes but are too invasive and too sparse for clinical use. Recently, there has been consider-able clinical interest in echocardiographic tissue Doppler imaging (TDI), which allows measurement of tissue velocity along the direction of the ultrasound beam [25-27], and myocardial speckle tracking, which allows quantification of in-plane velocities [28, 29]. Spatial derivatives of the veloc-ity field give rise to strain rates, which can then be integrated through time to give myocardial strain [26]; alternatively, velocity can be integrated to give displacements and thereby strain [28, 29]. Although limited in the regions which can be imaged, and subject to errors due to through plane motion, these techniques are proving very useful in the clinical evaluation of tissue function [28-32].

Fig. (3). Wall thickness vs time in a patient with first time Q wave

myocardial infarction. Note compensatory function in remote re-

gion, and wall thinning at infarct region, after 3 months relative to 1

week. Data courtesy Dr Louis Dell’Italia, University of Alabama.

MRI also provides quantitative information on motion and deformation in the heart and offers the potential of pre-cise noninvasive assessment of all components of deforma-tion in all regions of the heart throughout the cardiac cycle corrected for through-plane motion at acceptable spatial and temporal resolution. Many of these techniques have been available for over a decade for research purposes, but the translation into the clinical domain has been hindered by the complex and time-consuming nature of the image post-processing. Recently however, there have been rapid devel-opments in the field, including the HARP analysis method and DENSE acquisition techniques. These have the potential for higher spatial and temporal resolution and faster evalua-tion procedures.

3.1. Selective Tagging

Selective saturation pulses have been employed for many years to label tissue and blood [33] and thereby obtain meas-ures of motion and blood flow [34, 35]. The basic spin preparation pulse sequence involves a selective (soft) RF 90º pulse combined with a slice select gradient (typically ori-ented orthogonal to the imaging plane) followed by a spoiler gradient designed to dephase the transverse magnetization in the tag plane. This gives rise to a signal void in the tagged slice, which can be subsequently tracked or used to label blood flow by imaging the remaining longitudinal magneti-zation. Although this technique can place magnetic tag planes at any position and orientation in the object, the num-ber of tag planes is limited by the time required for each se-lective tagging pulse.

3.2. SPAMM

In 1989 Axel and Dougherty developed an efficient non-selective magnetization preparation pulse sequence called spatial modulation of magnetization (SPAMM) [36], which (in the original 1-1 form) produces a cosine modulation of the longitudinal magnetization, as follows. First, an initial

Fig. (2). a) CIM (Cardiac Image Modeller) 3D display, showing LV model with short and long axis MR scans. The endocardial surface is

shaded, lines denote the intersections of the epicardial surface with the image planes. The mitral valve base plane is also shown. b) CIM

volumetric output gives LV volume as a function of time as part of the real time user feedback.

4 Current Cardiology Reviews, 2006, Vol. 2, No. 4 Alistair A. Young

90° radio frequency (RF) pulse rotates the longitudinal mag-netization into the transverse plane. A gradient is applied to wrap the phase of the magnetization along the gradient direc-tion. A second 90° pulse rotates the magnetization back to the longitudinal direction. After a period of time in which the transverse component has been removed due to T2 relaxation or a crusher gradient the longitudinal magnetization profile (ignoring T1 relaxation) is cosine modulated.

The magnetization preparation sequence is typically ap-plied on detection of the R-wave ECG trigger at end-diastole (ED) and is followed by an imaging sequence to acquire cine images regularly spaced through the cardiac cycle. Varia-tions on the imaging sequence include FLASH (fast low an-gle shot) [37], multi-shot EPI (echo planar imaging) [38] and SSFP (steady state free precession) [39]. The tag stripe con-trast fades with tissue T1 (about 800 msec for myocardium) and is also influenced by the imaging procedure (e.g. EPI offers greater tag persistence than FLASH due to reduced RF excitation).

Multiple RF pulses separated by gradients were then de-signed [40] to make the magnetization profile thinner and more square (as in the DANTE sequence [41]). This results in a graphic visualization of motion as dark stripes (tags) in the image (Fig. 4). Subsequently, Fischer et al. [42] demon-strated that unwanted signal arising from T1 relaxation could be subtracted using complementary SPAMM tagging (CSPAMM). In this method, two tagged images are ac-quired, one with positive cosine modulation and the other with negative cosine modulation. Subtraction of the two im-ages reinforces the tagged component and eliminates the untagged (relaxed) component. Although this doubles the image acquisition time, it now appears that the 1-1 CSPAMM sequence is optimal for the HARP and DENSE methods, as described below.

The SPAMM tagging method has been applied in pa-tients to quantify reduced longitudinal and circumferential shortening in patients with hypertensive LV hypertrophy [43]. In aortic stenosis, ventricular torsion is increased while circumferential midwall shortening is decreased in both chil-dren [44] and adults [45], consistent with the hypothesis of subendocardial functional impairment. Altered relaxation of LV rotation has also been quantified in pressure overload

due to aortic stenosis relative to physiological hypertrophy in athletes [46, 47]. MR tagging has proven effective in the identification of ischemia with dobutamine stress testing [48] and functional improvement after reperfused myocardial infarction [49, 50] and coronary artery bypass grafting [51]. Since strain is quantified from tags created orthogonal to the image plane, MR tagging is not subject to errors due to through plane motion, unlike traditional wall thickening measurements in which a different geometry is imaged at each time point [52]. Diastolic strain relaxation can also be quantified with MR tagging [53-55], allowing quantification of diastolic tissue function. MR tagging has also proven a useful method for quantifying changes in regional perform-ance after LV reconstruction surgery [56, 57].

3.3. HARP

In 1998 Osman et al. [58] introduced a fast analysis for MR tagged images based on the harmonic phase (HARP) image. Noting that the tagged image is spatially modulated by a cosine (in the case of a 1-1 tag pulse sequence; a sum of cosines for a DANTE type tag pulse sequence), the spatial frequency domain signal is seen to be comprised of a number of peaks, each centered on the frequency of the cosine modu-lation (Fig. 5b). The HARP technique applies a bandpass filter centered on one of the harmonic peaks (Fig. 5c). The filter is designed to pass frequency and phase components associated with the harmonic peak and remove all signal from the other harmonics. The Fourier Transform of this filtered signal is called the harmonic image. The phase of this complex image, expressed as an angle in the range [-

, ), is called the harmonic phase. This phase can be thought of as being fixed with respect to material coordinates: as the heart deforms the harmonic phase of a material point is con-stant.

The spatial resolution of the harmonic phase is deter-mined by the size of the filter used to isolate the spectral peak. If only 32x32 pixels are included in the k-space filter, then the resolution of the harmonic image is approximately 32x32 [59].

For small motions (less than a tag spacing) the compo-nent of displacement in the tag encoding direction can be calculated from the difference in harmonic phase between

Fig. (4). Five pulse SPAMM tagging sequence. a) end-diastole, b) end-systole, c) late diastole. From [81], used with permission.

Assessment of Cardiac Performance with Magnetic Resonance Imaging Current Cardiology Reviews, 2006, Vol. 2, No. 4 5

the deformed and undeformed time points. For larger dis-placements aliasing occurs, and a phase unwrapping proce-dure must be employed. The spatial derivative of the har-monic phase can be used to directly calculate the Eulerian strain.

The HARP angle is corrupted by signal from other spec-tral peaks, particularly the signal arising from T1 relaxation. To avoid corruption of the HARP image by this signal, the k-space filter is typically kept small (e.g. 32x32 pixels), result-ing in a low resolution displacement map. Kuijer et al. [60] noted that a 1-1 CSPAMM tagging procedure allows cancel-lation of the relaxed component, leaving only two peaks, either of which can be used to construct the HARP image. The size of the filter used to extract the peak can then be enlarged, resulting in a higher resolution displacement map.

HARP analysis has been recently applied to a large co-hort of asymptomatic patients with no evidence of clinical heart disease in the Multi-Ethnic Study of Atherosclerosis (MESA), demonstrating a reduction in peak systolic strain with increasing concentric hypertrophy, particularly in the left anterior descending artery territory [61]. This study sug-gests that there may be regional differences in LV systolic function in response to concentric remodeling in subclinical disease.

3.4. Phase Contrast Displacement and Velocity Mapping

The phase of the MR image can be made sensitive to velocity by employing velocity encoding and decoding en-coding gradients [62]. As in tissue Doppler ultrasound imag-ing, MR velocity images allow the simple calculation of in-stantaneous strain rate by taking the spatial derivative of the velocity field. However, if tissue strain is required, dis-placements must be reconstructed by integrating the myo-cardial velocities over time. Such a non-rigid motion track-ing procedure is described by Zhu et al. [63]. Due to through plane motion, material points are not imaged through time, leading to difficulties in the calculation of 3D displacement.

The phase of the MR signal can be made directly sensi-tive to tissue displacements (as opposed to velocities) with the DENSE technique (displacement encoding with stimu-lated echos). Applied to measure cardiac function by Aletras et al. [64], the standard phase contrast velocity imaging method was adapted to measure displacement over longer

time intervals using a stimulated echo pulse sequence. The phase of the MR image is thus directly proportional to the displacement of tissue between the displacement encoding and decoding gradients. Due to T1 relaxation, the displace-ment encoded signal fades over time, where as a non-encoded signal gains in strength. This relaxed, non-encoded signal corrupts the displacement map. Traditionally, the en-code and decode gradients in the slice direction were set to large values in order to crush the relaxed component signal: the decode gradient was thus used to both refocus the en-coded signal and defocus the relaxed component. However, large displacement encoding and decoding gradients lead to signal loss in the heart wall, due to nonhomogeneous dis-placement over a voxel (ie strain and rotation). This is a common problem with stimulated echo imaging techniques in the heart [65].

To avoid this problem, Kim et al. [66] combined DENSE with CSPAMM to achieve cancellation of the relaxed (untagged) component and thus reduce the signal loss due to tissue strain. In fact, the DENSE pulse sequence is very simi-lar to the 1-1 SPAMM sequence with the addition of a de-coding gradient that unwraps the phase shift encoded by the first gradient. The decoding gradient has the effect of shift-ing one harmonic peak to the center of frequency space, the other harmonic peak being shifted out of the readout win-dow. The techniques of SPAMM, HARP and DENSE are thus closely related and can be thought of as variants of the same displacement encoding principle. Both HARP and DENSE are designed to select one spectral peak of the SPAMM tagged signal. In HARP, the peak is selected using a software filter, whereas in DENSE the spectral peak is se-lected using hardware (i.e. the decoding gradient). Since a narrow bandpass filter is not required for DENSE, the reso-lution of the displacement map is potentially greater than HARP. However, this increased spatial resolution comes at the cost of increased acquisition time, reduced SNR, and intravoxel dephasing at high strains or rotations

2.

Analysis of DENSE images can be performed in the same way as for HARP. Spatial derivatives of phase can be

2 This signal loss due to strain arises due to the same mechanism as the signal loss in

MR diffusion imaging, which is exploited to map the diffusion tensor field in the brain

[67]. It could therefore be exploited in a similar fashion to achieve direct MR strain

tensor imaging.

Fig. (5). a) SPAMM tagged image at ES. b) Fourier transform showing harmonic peaks. c) Filter to isolate one harmonic peak. d) Harmonic

phase image, masked to the LV.

6 Current Cardiology Reviews, 2006, Vol. 2, No. 4 Alistair A. Young

used to calculate Eulerian strain at each time frame. For re-construction of displacements greater than one tag spacing, a phase unwrapping procedure must be used.

DENSE imaging has been applied to the analysis of re-gional tissue function in mice after reperfused myocardial infarction [68]; its superior spatial resolution allows the quantification of transmural variation in strain patterns. Re-cently, Wen et al. have used DENSE myocardial displace-ment mapping combined with phase contrast blood velocity mapping to estimate myocardial elastic modulus and viscos-ity [69].

4. MODEL BASED 3D ANALYSIS OF DISPLACE-

MENT AND STRAIN

As noted above, the displacement (or velocity) encoded images can be directly processed on a pixel by pixel basis to yield Eulerian strain (or strain rate) images. However, the analysis of displacement and strain in 3D requires tracking of material points through time. Also, results must be regis-tered with the heart anatomy in order to calculate clinically meaningful parameters in standardized regions of the heart. It would also be advantageous to register cases with other cases, or register to an atlas which maps regional cardiac function across population subgroups. A data mapping capa-bility would also allow fusion of data from multiple sources, e.g. CT coronary angiography with MRI tissue function. These applications are facilitated by mathematical model-based analyses. This section briefly reviews model-based analysis of displacement encoded MR images. A more com-prehensive review of MRI cardiac deformation analysis techniques is provided in [70].

In the case of SPAMM tagging, image tags can be tracked to calculate 2D displacement and deformation. Kraitchman et al. [71] described a semi-automatic interactive procedure for tracking tag intersection points. A template matching procedure was used to filter the tagged images to estimate an image intersection likelihood function. Adapting the active contour (“snakes”) formulation of Kass et al. [72], a 2D ac-tive contour mesh model comprising interconnected tag in-tersection points was then used to optimally find the best location of the stripe intersections subject to constraints on the relative displacement between neighboring tag intersec-tion points. This method was extended to track the entire stripe (including points between stripe intersections) using a 2D active “carpet” model of interconnected snakes [73]. Each stripe was modeled as a thin, flexible beam with resis-tance to stretch and bending. Stripes were connected at the intersection points (in the case of grid tagged images) and the entire mesh deformed to maximize the image derived feature values. Similar stripe tracking procedures have been developed by Guttman et al. [74] and others [70]. Recently, Qian et al. [75] have applied a Gabor filter bank to recover the displacement field from SPAMM tagged images. The result of these stripe tracking procedures provide similar displacement information to the HARP and DENSE dis-placement encoding procedures described above.

User interaction is essential to these tracking processes in order to correct errors due to image contamination and re-solve correspondence between frames in cases where the

tissue motion was greater than stripe spacing. Image con-tamination arises due to respiration and gating artifacts, stripe T1 relaxation, spin dephasing due to susceptibility, and poor image SNR.

Given a set of tagged image slices (typically in standard short and long axis orientations), in which at least three line-arly independent displacement encoding directions have been employed, the 3D displacement field can be recon-structed using a field fitting approach. The main problem in the reconstruction of 3D motion and deformation is the fact that the imaged displacements do not represent tracked 3D material points. Those material points imaged at ED (shortly after tag creation) move off the imaging plane at subsequent times due to through plane components of heart motion, so their displacements are not imaged. However, material points imaged at ES (or any other time after ED) are located on the same tag saturation plane as their corresponding tracked image stripe points at ED. The displacements of all material points can be fitted to the available data with the use of a mathematical model [73, 76]. Validation experiments with a deformable MR phantom undergoing known strains and displacements showed that the magnitude of errors in motion and strain reconstruction using this method was 6%, increasing to 16% in the transmural direction due to the rela-tively sparse tag distribution across the wall [73]. Similar model based methods have been developed for HARP [77] and velocity-encoded MRI [63].

The model-based analysis method results in a wealth of kinematic parameters describing the multi-dimensional tis-sue function. Fig. (6a) shows some of these parameters, in-cluding the principal shortening strain, which is typically aligned obliquely to all imaging planes in the approximate direction of the subepicardial myocytes. In a study of re-gional reduction in systolic strain in hypertrophic cardiomy-opathy, the greatest reduction in shortening was found in the septal region [78]. Circumferential and longitudinal shorten-ing was also shown to be dramatically reduced, with some cases showing paradoxical systolic lengthening, in the septal regions in patients with nonischemic dilated cardiomyopathy [79]. In some of these patients, ventricular reconstruction surgery resulted in normalization of septal function [79]. This regional heterogeneity in function in dilated cardiomy-opathy may be due to regional differences in wall stress; however, simple geometric indices of stress were not suffi-cient to explain the functional heterogeneity observed. In a group of patients examined late after coarctation of the aorta, slight LV hypertrophy was accompanied by reductions in strain and augmentation of torsion [80]. In a study of normal aging, diastolic strain relaxation parameters, such as peak diastolic strain rate, were shown to be impaired on a regional basis with age [81]. In patients with type II diabetes and clinical diastolic dysfunction, systolic strain parameters were shown to be reduced despite normal ejection fraction (Fig. 6b) [82]. Finally, the model can also be used to map strain information in relation to structural data from other imaging protocols. Fig. (7) shows results from a longitudinal study of reperfused myocardial infarction in mice, illustrating how the boundaries of the infarct (obtained from late gadolinium enhancement images) can be mapped onto a bullseye plot (Fig. 7a) and the ventricular model (Fig. 7b). Myocardial

Assessment of Cardiac Performance with Magnetic Resonance Imaging Current Cardiology Reviews, 2006, Vol. 2, No. 4 7

strains can then be located into infarct adjacent and remote regions for the purposes of studying the effects of ventricular

remodeling after infarction (Fig. 7c) [83].

5. MULTIDIMENSIONAL QUANTIFICATION OF

CARDIAC PERFORMANCE

Since the mathematical models employed for motion analysis are registered to the anatomy of the heart, they can be used to construct a probabilistic atlas of cardiac function and derive statistical descriptions of characteristic patterns of regional wall motion in health and disease. This leads to the quantification of differences in regional cardiac performance

between disease or treatment groups. However, due to their multidimensional nature, the differences in regional wall motion parameters between groups are difficult to character-ize succinctly. Many parameters are required to describe regional performance (including regional shortening, rota-tion, wall thickening and displacement).

One powerful technique for the statistical interpretation of multidimensional data is principal component analysis (PCA), which describes the major sources of variation by a set of orthogonal components (also known as “modes”) [84]. The modes are ranked in order of highest to lowest variabil-ity, thereby showing which variations are most strongly pre-

Fig. (6). a) Three dimensional ventricular deformation and myocardial strains. (Left) Small line segments in the left ventricle, orthogonally

oriented in the circumferential (C) and longitudinal (L) directions at end-diastole. (Right) Corresponding line segments at end-systole. Thus,

circumferential strain is equal to ((C’-C)/C) x 100%, longitudinal strain is equal to ((L’-L)/L) x 100%, and torsional shear strain is equal to

90- . Maximal shortening occurs in the direction of the line segment P at end-diastole (deformed to P’ at end-systole), so that principal strain

is equal to ((P’-P)/P) x100%. B) Time evolution of principal shortening strain in a group of patients with type II diabetes (closed circles) and

normal volunteers (open circles), showing reduced peak systolic strain and reduced peak diastolic strain rate in the patient group. From [82],

used with permission.

Fig. (7). a) Late gadolinium enhancement contours (black dots) projected into a bullseye map. The LV apex is the middle of the plot; outer

circle denotes LV base; A: anterior; S: septal; P: posterior; L: lateral. Convex perimeter enclosing the hyperenhancement contours is shown

as a solid line. b) Finite element model (endocardial surface shaded) with hyperenhancement contours (light crosses) and 3D infarct bound-

ary (grey crosses). c) Strain map at midwall in relation to 3D infarct boundary. From [83], used with permission.

8 Current Cardiology Reviews, 2006, Vol. 2, No. 4 Alistair A. Young

sent in the data and which variations can be neglected as insignificant. Thus, a database of models of heart shape and motion can be characterized by a set of orthogonal modes and their associated variance. This substantially reduces the number of significant parameters by distinguishing the modes that truly differentiate the groups and eliminating modes that are insignificant. Given two such database distributions de-scribing different patient groups, statistical comparisons can be made to determine the differences in shape and motion. Similarly, given a new case, a comparison could be made with the database to see which components best describe the patient’s cardiac performance.

Fig. (8) shows the first three modes of deformation in a group of 15 normal volunteers. The PCA was applied to ED and ES models simultaneously, and models of each state are shown at the -2 and 2 extremes of variation. To date, these methods have been hampered by the lack of large scale databases of patient groups. The effectiveness of these meth-ods to detect regional wall motion abnormalities will be en-hanced with the growth of such databases of normal and ab-normal cases.

Fig. (8). Coupled end diastolic and end systolic models subjected to

a principal component analysis. Top panel shows mean ED and ES

shapes. Next three panels show first three principal modes of de-

formation in the group. Left and right sides show the two extremes

of the deformation modes, i.e. mean plus and minus two standard

deviations. From [85], used with permission.

Although the PCA provides orthogonal (i.e. mathemati-cally uncoupled) modes of deformation, the modes may not correspond to any intuitive or easily understood deformation. In an attempt to provide more clinically understandable modes of deformation, Park et al. [86] defined several sim-ple modes of deformation, including torsion, longitudinal and circumferential shortening. Recently, Remme et al. [87] described similar “clinical” modes of variation and used these to characterize the differences between healthy volun-teers and patients with type II diabetes. Fig. (9) shows the definition of the modes of ventricular deformation, and Fig. (10) shows the distribution of the amount of each mode pre-

sent in a group of 15 healthy volunteers relative to a group of 30 patients with type II diabetes with clinical evidence of diastolic dysfunction but normal systolic chamber function [87].

6. BIOPHYSICAL MODELS OF CARDIAC PER-

FORMANCE

Despite advances in the study of molecular bases of car-diac disease, the mechanical bases underlying cardiac dys-function during the development of ischemia, diabetic car-diomyopathy, hypertrophy and heart failure remain poorly understood. Global and local kinematic performance parame-ters such as ejection fraction, tissue strain, rotation and dis-placement are indicative of underlying physiological proc-esses. In order to understand the physiological bases of dys-function, a detailed knowledge of the geometry, microstruc-ture, tissue compliance, activation and wall stress is required, together with the ability to combine these characteristics into

Fig. (9). Nine systolic “clinical” modes of deformation. In a)-c) and

g)-i) the thick lines correspond to the original ED mesh while the

thin lines and shaded surfaces correspond to the mesh created for

the respective deformation mode. a) Longitudinal shortening mode,

illustrated at the epicardial surface. b) Wall thickening mode,

whereby the endocardial surface is moved inwards (the epicardial

surface, not shown, is left unchanged). c) Hinge mode, illustrated

by a longitudinal slice of elements. d) Twisting of the endocardial

base, illustrated by a schematic of the LV where the endocardial

surface is rotated at the base with gradually decreasing rotation

towards apex while the epicardial surface is fixed. e) Twisting of

the endocardial apex. f) Twisting of the epicardial apex. g) Longi-

tudinal-radial shearing, illustrated by a longitudinal slice of ele-

ments. h) Tilting mode, illustrated at the endocardial surface. i)

Septal bulging, illustrated at the epicardial surface where the sep-

tum is to the left. From [87], used with permission, © IEEE.

Assessment of Cardiac Performance with Magnetic Resonance Imaging Current Cardiology Reviews, 2006, Vol. 2, No. 4 9

a coherent continuum. Finite element model enable accurate representation of heart geometry [88, 89], microstructure [90, 91, 92], material properties [93, 94], stress [95-99], perfusion [100-101], cellular electromechanics [102] and activation [102, 97, 103, 104]. Cellular mechanisms including mem-brane channel characteristics, excitation-contraction coup-ling and cross-bridge cycling dynamics can be incorporated into a continuum description of the whole organ. This ap-proach is now forming part of a world-wide effort to model the cellular, structural, mechanical and electrical properties of the heart in order to provide a framework to predict and

understand the effect of disease and treatment on cardiac function [105]. Fig. (11) shows an overview of the biophysi-cal modeling components.

By adjusting the biophysical parameters in these models, it is possible to determine the effect on functional perform-ance. In a preliminary study, Stevens et al. [106] investigated the effect of ventricular compliance on end diastolic volume and systolic function using a mathematical simulation of the entire cardiac cycle incorporating the Frank-Starling mecha-nism. It is also possible to estimate biophysical parameters

Fig. (11). The biophysical model of the heart comprises geometry (a), fibrous microstructure (b), stress (c), perfusion (d) and activation (e).

Fig. (10). Normal vs type II diabetes comparison of systolic modes of heart deformation. The mean coefficient value for each PCA mode for

the normal subjects is marked with a short horizontal bar while the vertical line shows the ±SD variation. The coefficients for the patients are

indicated with a number for each patient. A slight horizontal spread from the mode line is included to visually separate the subjects. From

[87], used with permission, © IEEE.

10 Current Cardiology Reviews, 2006, Vol. 2, No. 4 Alistair A. Young

such as heart muscle compliance (stiffness) from CMR data. Augenstein et al. validated such a procedure for estimating myocardial stiffness in isolated arrested hearts from tagged MR images and LV pressure [107]. Remme et al. [108] have investigated the complexity of finite elasticity material laws for the purposes of material parameter estimation, noting that simplifications may be necessary for imaging applications. Recently, Wen et al. have proposed a method for simplified in vivo wall compliance measurements from DENSE and blood velocity imaging [109].

CONCLUSIONS

CMR imaging offers a wealth of detailed, precise infor-mation on cardiac performance. The application of these methods in the clinical domain has increased markedly in the last few years. The standardization of imaging protocols and the advent of fast model-based analysis procedures will aid the establishment of large clinical databases of CMR data and derived models or cardiac shape and function. These model databases will facilitate registration across groups and modalities, enabling fusion of information from other sources and statistical analysis of regional wall motion performance parameters in relation to disease processes. In the future, biophysical models of stress, activation and cellular physiol-ogy will allow the interpretation of these data in terms of the underlying physical processes.

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