Abstract
We present the development and testing of a semiautomated tool to support the diagnosis of left ventricle (LV) dysfunctions from cardiac magnetic resonance (CMR). CMR shortaxis images of the LVs were obtained in 15 patients and processed to detect endocardial and epicardial contours and compute volume, mass and regional wall motion (WM). Results were compared with those obtained from manual tracing by an expert cardiologist. Nearest neighbour tracking and finiteelement theory were merged to calculate local myocardial strains and torsion. The method was tested on a virtual phantom, on a healthy LV and on two ischaemic LVs with different severity of the pathology. Automated analysis of CMR data was feasible in 13/15 patients: computed LV volumes and wall mass correlated well with manually extracted data. The detection of regional WM abnormalities showed good sensitivity (77.8%), specificity (85.1%) and accuracy (82%). On the virtual phantom, computed local strains differed by less than 14 per cent from the results of commercial finiteelement solver. Strain calculation on the healthy LV showed uniform and synchronized circumferential strains, with peak shortening of about 20 per cent at end systole, progressively higher systolic wall thickening going from base to apex, and a 10° torsion. In the two pathological LVs, synchronicity and homogeneity were partially lost, anomalies being more evident for the more severely injured LV. Moreover, LV torsion was dramatically reduced. Preliminary testing confirmed the validity of our approach, which allowed for the fast analysis of LV function, even though future improvements are possible.
1. Introduction
Ischaemic cardiomyopathy is responsible for up to 65 per cent of the prevalence of heart failure (HF) [1]. Despite appropriate medical management, myocardial infarction initiates a remodelling process that potentially entails left ventricle (LV) dilation and mitral valve (MV) insufficiency, often proportional to the extent of damaged myocardium. To compensate for reduced ventricular function, the LV dilates to increase stroke volume through two distinct phases governed by mechanical, genetic and neurohormonal factors [2]: early remodelling, characterized by infarct expansion with wall thinning and LV dilation with subsequent increase in wall stress, and late remodelling, in which increased wall stress induces cardiomyocytes hypertrophy. Unfortunately, remodelling leads to alterations in the LV architecture towards a spherical form, further increasing wall stress, resulting in a vicious cycle leading to HF.
Imaging techniques play a pivotal role in LV function assessment in supporting clinical decisionmaking. Among them, cardiac magnetic resonance (CMR) imaging is a noninvasive technique currently considered the standard reference in the clinical evaluation of the LV.
Conventional twodimensional cine images are normally used to asses LV volume, function, mass and regional dysfunction [3,4]. However, their analysis requires slicebyslice, phasebyphase endo and epicardial boundaries detection. Even with commercial software, it requires extensive manual corrections, thus resulting in a poorly automated, time consuming and subjective analysis technique. Different techniques for CMR LV semiautomated and automated border detection have been described [5], but they suffer from different limitations: a large number of manually segmented images required to build a model database or to train the model [6], analysis limited to enddiastolic (ED) and endsystolic (ES) phases only, no continuous temporal segmentation and computational complexity [7].
TaggedCMR is widely adopted to calculate twodimensional wall strains by tracking the twodimensional motion of myocardial points (defined by tags crossing) over time; it permits rapid imaging and visualization, as well as automation [8]. However, this technique does not capture real threedimensional strains and does not allow for the analysis of the complete cardiac cycle, since the tags (i) can become less distinct, and thus more difficult to track, owing to outofplane motion of the tissue, and (ii) fade after a few timeframes, so that the analysis cannot be extended to the entire cardiac cycle. Moreover, only a few slices are acquired via taggedCMR as additional sequences to the conventional examination. The assessment of threedimensional myocardial motion using MR tagging techniques using multiple orthogonal image planes [9–11] or fully threedimensional MR tagged imaging [12] is still part of the research arena and is primarily limited by the need for lengthy image acquisition protocols and for tedious postprocessing procedures.
The availability of a reliable technique for automated endocardial and epicardial contour detection and regional wall strain calculation throughout the cardiac cycle on conventional cine CMR images would overcome these limitations, providing an exhaustive quantitative analysis of the LV.
Within the framework of the virtual pathological heart of the virtual physiological human (VPH2) project, we aim at developing two decision support tools for cardiologists and cardiac surgeons, based on LV patientspecific modelling, the functional assessment tool (FAT) and the functional predictive tool (FPT). FAT quantitatively analyses LV, by semiautomated endocardial and epicardial detection, and MV function from CMR images, thus helping defining the severity and extent of disease in patients with LV dysfunction, with or without mitral regurgitation. FPT is used for an easy and fast simulation of postoperative scenarios subsequent to different surgical procedures.
The present paper is focused on the development, testing and validation of the LVrelated capabilities of the FAT: (i) semiautomated detection of endocardial and epicardial contours for volumetric and wall motion (WM) analysis; (ii) quantification of LV volume, mass and regional WM; and (iii) computation of local strains in the myocardium. FAT contour detection was verified on a small population of subjects (n = 13), while its capability to correctly compute local LV wall strains was tested on a virtual phantom and on three real ventricles characterized by different clinical scenarios.
2. Methods
2.1. Cardiac magnetic resonance imaging
A group of 15 patients with previous myocardial infarction and regional WM abnormalities was considered. CMR studies were performed using a 1.5 T scanner (Signa Hdx, GE Healthcare, Milwaukee, WI, USA). An eightelement cardiac phasedarray receiver surface coil with breathholding in expiration and ECGgating were used for signal reception. Three standard cine longaxis slices and a stack (from 8 to 12) of contiguous cine shortaxis slices from the atrioventricular ring to the apex were acquired using a steadystate freeprecession pulse sequence (30 phases, slice thickness 8 mm with no overlap and no gap, field of view = 40 cm, reconstruction matrix 256 × 256, repetition time = 3.5 ms, echo time = 1.5 ms, flip angle 45°).
2.2. Algorithms for contours detection
The semiautomated detection of LV contours was based on regionbased image noise distribution (for LV endocardial detection) and on edgebased image gradient (for LV epicardial detection).
2.2.1. Endocardial border detection
The endocardial border detection is based on the formulation proposed by Chan & Vese [13] and on embedding in the segmentation model the a priori knowledge of the statistical distribution of grey levels in medical images [14]. In particular, concerning CMR, we note that image pixels are modelled as Gaussian distributed random variables. Then the proposed method drives the curve evolution to achieve a maximumlikelihood segmentation of the target, with respect to the statistical distribution law of image pixels.
Let us consider an image I as a real positive function defined in a domain Ω ⊂ ℜ^{2}. The grey levels are assumed to be uncorrelated and independently distributed. They are thus characterized by their respective probability density. Now, we define a closed curve C partitioning the image domain in an ‘inside’ Ω_{i} and an ‘outside’ Ω_{e} and denote with P_{i} = Π_{Ω}_{i(}_{C}_{)}p(I) the probability of the random field inside the curve and with P_{e} = Π_{Ω}_{e(}_{C}_{)}p(I) the probability outside the curve. Without any a priori knowledge about the shape of the object to be detected, we look for the curve C that maximizes the likelihood function given by the product of the inner and the outer probability [15]: P[IC] = P_{i} P_{e}.
Since the log function is strictly increasing, the maximum value of P[IC], if it exists, will occur at the same points as the maximum value of l(I,C) = log(P[IC]). This function is the ‘log likelihood’ and in many cases it is easier to work with it than with the likelihood function. Indeed, the product structure of the probability function is transformed in a summation or integral structure of the log likelihood. Passing to the continuous limit, we replace the sum with the integral and, to perform a maximumlikelihood segmentation of the target, we need to maximize the functional I with respect to variation of the curve C.
By considering the Gaussian noise distribution: 2.1where μ and σ are the average and variance of I, respectively, the corresponding loglikelihood is derived as in Chesnaud et al. [16]. Then, following the model proposed by Chan & Vese [13] and embedding in the segmentation model the a priori knowledge of statistical distribution of grey levels in CMR images [17], the final associated flow results: 2.2where A_{i} and A_{e} are, respectively, the number of pixels in W_{i} and W_{e}, and φ(x,y,0) is the initial function with the property that its zerolevel set corresponds to the position of the initial front. Typically, it is defined by φt(x,y,0) = ±d, where d is the signed distance function from each point to the initial front [18], and δ(φ)/∇φ∂φ/∂ n = 0 are the boundary conditions.
The evolution process will stop when the region probability terms of the inside regions do equal the terms of outside regions, up to regularization of boundaries (figure 1a).
To define the initial function, we require the manual placement of a single point inside the LV cavity. From a mathematical point of view, we defined a curve C, centred in the manual selected point, as the zerolevel set of an implicit real function φ taking values on the image domain Ω: 2.3
This initial circumference C undergoes the evolution described in equation (2.1) in order to maximize the functional F.
Following this step, the boundary regularization was achieved using a curvaturebased motion not allowing curvature above the mean Euclidean curvature value of the detected contour and designed to automatically include the papillary muscles in the LV cavity (figure 1b).
2.2.2. Epicardial border detection
To identify the epicardial boundary (figure 1c), we drove the evolution of an initial contour applying the wellknown Malladi–Sethian model for active contour evolution, which requires adequate boundary conditions.
The model includes a dependence of the speed on the curvature, a propagation expansion speed and an advection speed based on the image gradient: 2.4where K is the mean curvature, g is the edge indicator, ν and λ are weighting coefficients.
The edge indicator g is a nonincreasing function of the gradient of the initial image [19]: 2.5
The parameter α depends on the characteristics of the noise in the image: α controls the sensitivity to edges and therefore it was empirically set to 20 to select the contrast of the objects we want to consider in the image during the motion of the embedding. The parameter ν is used to limit the regularization of the embedding controlled by the parameter λ: these parameters were set equal to 10 and 6, respectively.
The contour evolution will have a steadystate solution when the geometry dependent and expansion terms balance the advection term [17]. At the end of this step, the epicardial boundary was also regularized applying a modified curvature motion.
2.2.3. Algorithms initialization
For endocardial detection, the regionbased approach was applied from basal to apical slices for each frame. In the basal slice, after initialization of the algorithm's parameters (radius of the initial circle, and per cent of radius decrement from one slice to the next one), the operator selected one point inside the LV cavity. Then, automatically, the applied algorithm expanded the initial circle according to the videointensity probability distribution followed by the regularizing expansion to include the papillary muscles, when present. Then, the algorithm processed the other slices, using the detected contour on the current slice (s) as initialization for the next (s + 1) slice, after reducing it by the per cent set by the operator.
For epicardial detection, this approach required a robust initialization on the first frame f. Then, for the next frame f + 1, the initialization was obtained by applying the ‘erode’ morphological operation applied to the resulting epicardial contour on the frame f.
For each slice and frames, the detected contours were then superimposed to the original image, to allow for possible corrections, if needed.
2.3. Left ventricle volume and mass quantification
The LV volume was automatically computed by summing the LV area in each slice (measured as pixel counts inside the endocardial contour) multiplied by the pixel spatial resolution and by the slice thickness (from the DICOM header). In the same way, the LV mass was computed as the difference between the LV epicardial and LV endocardial volumes, and multiplied by 1.05 to be expressed in grams.
For the automated interpretation of regional WM, the ED frame was used to define the standard segmentation scheme for the LV shortaxis view in each slice (figure 2b). In the slice at the midventricular position, the ED centroid of the LV cavity was calculated as centre of mass of the binary image representing the detected LV cavity, in which all pixels in the cavity appear ‘on’ (i.e. have value 1) and have been attributed with a unit mass, and used as the origin of segmentation.
An additional point was then manually placed at the junction between the right ventricular free wall and the interventricular septum. Starting from that point, the LV cavity was divided into six 60° wedgeshaped segments, corresponding to those used for visual assessment and grading of WM. For each segment, regional fractional area (RFA) in per cent of regional ED area was automatically calculated throughout the cardiac cycle using a fixedcoordinate reference system. From these six curves in each slice, RFA change (RFAC) was computed as the difference between the maximum and minimum value of RFA, expressed in per cent of the regional ED area. For each segment, these values were used to automatically interpret WM as normal (RFAC ≥ 50%) or abnormal (RFAC < 50%) (figure 2a).
2.4. Validation of left ventricle volume and mass quantification
For validation purposes, data calculated through our semiautomated procedure were compared with the manual measurements performed by an expert cardiologist. The latter analysed CMR data using commercial software (MASS v. 6.1, Medis, Leiden, The Netherlands) installed on the MRI workstation and proceeded into the conventional analysis of these images by manual tracing LV endo and epicardial contours. Then, LV ED and ES volumes (EDV and ESV, respectively) and mass were measured using standard volumetric techniques. The same number of slices included for the reference value assessment by the expert were included in these computations, to avoid bias owing to the inclusion of a different number of slices.
Moreover, dynamic images were reviewed and regional WM was interpreted in three slices selected at apical, mid and basal levels. In each of these slices, the six regional segments (anterior, lateral, anterolateral, septal, inferior and posterior) were qualitatively graded as normal or abnormal, thus providing the ‘gold standard’ for WM interpretation.
The results obtained from the automated analysis were then compared with the reference values by (i) linear regression and Bland–Altman analyses for LV volumes and mass; (ii) levels of agreement between the cardiologist WM grades and the automated classification of regional WM.
Sensitivity, specificity and accuracy for the automated interpretation of WM were also computed.
2.5. Calculation of left ventricle local strains and left ventricle torsion
Local strains in the LV myocardium were calculated through the following four steps:

— A slicebased reconstruction method [20] was used to obtain smooth, threedimensional endocardial and epicardial surfaces, discretized into threenode triangular elements, from the sampled previously detected contours (figure 3a,b).

— In the ED frame, endocardial and epicardial surfaces were divided into six longitudinal sections and three circumferential sections, for a total of 18 sectors (figure 3c). For each sector, its eight vertices were identified and the corresponding local principal curvatures calculated as in Vieira & Shimada [21].

— The eight vertices of each sector were tracked throughout the subsequent timepoints by means of a nearest neighbour search, assuming that the position of a given point P on the LV surface and the surface's local shape in P change continuously throughout the cardiac cycle, and thus undergo small changes in a sufficiently short timeframe. Briefly, at the timepoint t, the position of P on the triangulated surface S_{t} is x_{t}. At t + 1, the triangulated surface S_{t}_{+1} is deformed, and P has moved to its new position x_{t}_{+1}, estimated as the position of the node in S_{t}_{+1} that minimizes the following function: 2.6where x_{t + 1,}_{i} is the position of the ith node on the surface S_{t + 1}, x_{t} and x_{0} are the known positions of P at t and at ED, K_{1} and K_{2} are the curvature tensor principal components and a_{1}, a_{2}, a_{3} are three positive scalar coefficients defined as: 2.7
In the first term of φ, x_{t}_{+}_{i} − x_{t} is the displacement needed to move P from its initial position x_{t} to its new one. The second term accounts for the change in local shape experienced by the surface, where and are the concomitant changes in local principal. In both terms, quadratic quantities are considered; thus, their convex linear combination is minimized if both terms are minimized. The coefficients a_{1} and a_{2} were set to 0.2 and 0.8, respectively, accordingly with a preliminary sensitivity analysis. The third term of the function is active only for t ≥ 12, i.e. for the diastolic timepoints, and enforces the return of the tracked point P to its initial position. The nearest neighbours search provided the timedependent position of the eight vertices of each of the 18 sectors of the LV myocardium and, thus, the corresponding timedependent displacements.

— A continuous displacement field was reconstructed within each sector by treating the latter as an eightnode isoparametric hexahedral finite element. A local system of coordinates s = (s_{1}, s_{2}, s_{3}) was defined, with s_{i} ∈ [−0.5;0.5] and with s_{1}, s_{2}, s_{3} aligned, respectively, along the local circumferential, radial and axial directions of the LV in a cylindrical reference system with the zaxis on the LV long axis. Coordinates and displacements of each point within the sector were estimated by interpolating the coordinates and the displacements of the eight vertices via linear shape functions: 2.8
The strain tensor was computed as: 2.9where C is the right CauchyGreen strain tensor, F is the deformation gradient tensor, defined as F = ∂x/∂X, i.e. the derivative of the current position x as regards to the initial position X, and H is the displacement gradient tensor, defined as ∂u/∂X, i.e. the derivative of the displacement u as regards to the initial position X. H was computed as: 2.10where J is the Jacobian matrix that maps the global coordinates onto the local ones, i.e. J = ∂X/∂s.
In particular, the strain tensor E was assessed at the centre of each sector (s_{1} = s_{2} = s_{3} = 0).

— For the six vertexes at the basal end of the endocardial surface, and for the six vertexes at its apical end, the timedependent average rotation angle θ_{rot} was computed. In an orthonormal reference system x,y,z centred in the LV centre of mass, with the zaxis aligned with the longaxis, θ_{rot} was defined as: 2.11
Positive values of θ_{rot}(t) corresponded to a counterclockwise rotation as seen from the LV apex. The ventricle torsion was computed as: 2.12
2.6. Validation of local strains calculation
The validation of the method for strains calculation consisted of two steps.
First, we tested its capability to compute strains on objects with simple geometry undergoing simple deformation processes. For this purpose, a virtual phantom, consisting in an ideal, axialsymmetric ventricle was defined and discretized into tetrahedral elements (figure 4a). By means of a commercial finiteelement solver (ABAQUS, Simulia Inc., Dessault Systèmes), we simulated its inflation and deflation under the effect of a cyclic, timedependent inner pressure. The phantom was divided into 18 sectors. The corresponding strains were computed by nearest neighbour tracking of the sectors' vertices, and compared with the values computed by the commercial solver for the tetrahedral elements located at the centre of each sector.
Second, we assessed the method's capability to compute strains in the presence of more complex motion patterns, characterized by nonuniform expansion and deflation, and by torsion. We analysed a normal subject (SUBJECT1), with EDV and ejection fraction (EF) equal to 130 ml and 72 per cent, and two patients affected by late ischaemic pathology: SUBJECT2 (EDV = 117 ml, EF = 44%, anterolateral infarction), and SUBJECT3 (EDV = 378 ml, EF = 16%, anterior and inferiorlateral infarction). For each subject, we computed timedependent basal and apical rotation angles, torsion and regional.
3. Results
3.1. FAT validation
Of the 15 patients, two were excluded for artefacts in the images that precluded correct performance of the algorithm without heavy manual correction. The semiautomated analysis was then feasible in 13/15 (87%) patients.
The time required to process a single frame (ED or ES) from base to apex, for both endo and epicardial contours detection, was approximately 1 min using a standard PC. An example of the detected contours for ED and ES frames at three levels of the LV is shown in figure 5.
Good correlations were found with the reference values for LV EDV (y = 0.99x + 5.1, r^{2} = 0.99), and ESV (y = x + 4.34, r^{2} = 0.99), as well as with their derived parameters SV (y = 0.98x – 0.24, r^{2} = 0.97) and EF (y = x − 1.56, r^{2} = 0.98). For LV mass, a good correlation was found (ED, y = 1.07x + 5.41, r^{2} = 0.81; ES, y = 0.97x + 12.86, r^{2} = 0.74).
Bland–Altman analysis resulted in minimal bias and narrow limits of agreement in LV ED and ES volumes, and derived parameters. Conversely, a significant overestimation and wider limits of agreement were found for LV mass. In particular, the bias expressed as error%/mean of the gold standard values resulted less than 10 per cent in all parameters, except ED LV mass (table 1). Figure 6 visualizes the results obtained in LV volumes and mass, considering ED and ES measurements together.
As regards the automated detection of LV WM, the time needed to process a single slice (30 frames), for endocardial contour detection, and for regional WM analysis, was approximately 1 min. The gold standard interpretation resulted in 135 segments evaluated as normal, and 99 as abnormal.
Figure 2 shows an example of the regional WM curves, as well as the scheme used for their quantification. Of the analysed 234 segments (13 patients × 6 sectors × 3 slices), 77 were automatically classified as true positive, 115 as true negative, 20 as false positive and 22 as false negative, based on the selected 50 per cent threshold. These counts resulted in 77.8 per cent sensitivity, 85.1 per cent specificity and 82 per cent accuracy in the automated interpretation of WM.
3.3. Left ventricle local strains
3.3.1. Analysis of the virtual phantom
Figure 4 shows the good agreement between the local strains of the virtual phantom computed with our method and the finiteelement solution, the maximum difference being equal to 14 per cent.
3.3.2. Analysis of the real ventricles
For normal SUBJECT1, the measured regional strain curves (figure 7) provided uniform strain patterns over all myocardial segments; in the systolic phase, all sectors contracted circumferentially and thickened radially. Circumferential shortening increased from the basal region to the apex: peak absolute values ranged from 15 to 21 per cent for the sectors of the basal and mid region, and from 19 to 26 per cent for the apical sectors. Similarly, the observed thickening was progressively more relevant going from the ventricular base to the apex: plots showed maximum values of 51–70%, 69–100% and 72–125% for the sectors in the basal, mid and apical region, respectively. Apical and basal maximal systolic rotations and maximal torsion were 7.8°, −2.8° and 10.2°, respectively (see figure 9, top panel).
In the pathological subjects, the normal waveform of timedependent strains, coherence between sectors at the same level, and trends characterizing the changes from the basal to the apical region, were lost.
For SUBJECT2 (figure 8, top panel), in the basal region, circumferential shortenings showed a slower dynamics, with maximal values ranging from 12 to 20 per cent. In the mid and apical regions, progressively more irregular patterns and lower maximal values (from 5% to 12% and from 3% to 5%, respectively) were computed. As regards radial thickening, four of the basal sectors showed values from 40 to 80 per cent, whereas much lower values (13% and 22%) were observed in the remaining two sectors. In the mid and apical regions, maximum thickening ranged from 36 to 120 per cent and from 2 to 88 per cent, respectively. Apical and basal maximal systolic rotations and maximal torsion were 2.6°, −3.1° and 4.9°, respectively (figure 9, mid panel).
SUBJECT3 showed even more abnormal circumferential shortenings and radial thickenings (figure 8, bottom panel). None of the 18 sectors shortened by more than 8 per cent, thus indicating very poor contraction of the myocardium. Maximal thickening values ranged from 5 to 38 per cent, from 0 to 38 per cent and from 3 to 50 per cent in the basal, mid and apical sectors, respectively. Moreover, two sectors in the mid and apical regions experienced thinning. Apical and basal maximal systolic rotations and maximal torsion were 1.7°, −0.7° and 2.1°, respectively (figure 9, mid panel).
For each of the three subjects, the computation of strains, rotation angles and torsion required about 60 min on a standard desktop PC with single CPU (Intel core2@1.86 Ghz).
4. Discussion
In this paper, we presented a new tool for LV analysis from CMR imaging, characterized by two novel aspects when compared with previous approaches [22].
The former consists in the automation of a relevant part of the procedure needed to recognize endocardial and epicardial contours.
The latter consists in the calculation of myocardial local strains through a Lagrangian approach, i.e. by actually tracking different portions of the myocardium in space throughout its deformation process.
In this study, on a small population of subjects, we tested the features of the software that allows for LV endo and epicardial borders detection for volumetric and WM analysis. Moreover, we tested the capability to correctly compute local LV wall strains on a virtual phantom and applied it to three LVs characterized by different clinical scenarios.
4.1. Automated detection of contours for analysis of volumetric and wall motion analysis
CMR imaging provides accurate measurements of LV volumes, EF and mass, nevertheless, the quantification of volumes is based on timeconsuming manual tracing of endocardial and epicardial boundaries in multiple slices. The subjective nature of this procedure limits the reproducibility of volume measurements and consequently of the set of derived parameters. The proposed combined automated endocardial and epicardial border detection procedure overcomes these limitations by allowing manual intervention just to optimize the automated detected contours. Despite this advantage, the proposed approach was not completely reliable in several LV basal slices, owing to the presence of the aorta. In this case, manual tracing was performed in order to provide a reliable contour. The technique could be easily applied to all frames in the cardiac cycle, on a different number of slices of fixed thickness for each frame.
4.2. Analysis of left ventricle strains and torsion
For validation purposes, we first applied our method for strain estimation on a simplified virtual phantom. The computed strain curves well agreed with the ones yielded by a commercial finiteelement solver throughout the whole cardiac cycle, confirming that our method fulfils the minimum requirement of being accurate in presence of simple motion patterns. The application of the method on three real subjects showed its capability to capture more complex motion and strain patterns.
In the healthy subject, physiologically meaningful strain curves were found: consistently with previous findings [23,24] almost uniform circumferential shortening and increasing thickening were assessed from LV base to apex. Moreover, LV torsion was consistent with data from tagged MRI and Doppler tissue imaging [25], both in terms of timecourse and maximal values.
In the ischaemic patients, we found a decrease in peak systolic circumferential and radial strains, in agreement with the expected loss of contraction properties following infarction, as well as in peak systolic torsion, consistently with previous findings [26]. Moreover, regional inhomogeneity and dyssynchrony of the strain pattern were detected. These abnormalities were more evident in SUBJECT3, consistently with his much lower EF.
Thus, in these preliminary tests, the calculation of rotations, LV torsion and local strains based on nearest neighbour search appeared able to provide realistic results.
However, the method suffers from some limitations. First, even though the metrics adopted in the nearest neighbour algorithm include a term aimed at enforcing the return of the tracked points to their initial position, computed timedependent strains showed residual values around 5 per cent at the end of the cardiac cycle. This issue is reported also in other recent studies [27]; possible causes include the natural aperiodicity of LV deformation owing to heartrate variability, and the inherent limitations of CMR acquisitions.
Second, in order to compute strains within each of the 18 LV wall sectors, we treated each of them as a firstorder isoparametric hexahedral element. However, it does not allow for capturing the nonnegligible curvature of the endocardial and epicardial surfaces of the sectors. To this aim, we plan to move to the use of higher order elements.
5. Conclusions
In the reported preliminary testing, the FAT tool resulted effective in computing LV volumes, myocardial strains and torsion from conventional cine shortaxis CMR images. Obtained results were in agreement with manual ground truth values, and with reported literature. Although not fully automated, our method required minimal user interaction, thus improving repeatability. FAT capability in capturing regional functional features may be of use in the interpretation of the remodelling process following myocardial infarction; this information could be useful in the clinical decisionmaking process and potentially used as input for patientspecific LV modelling tools.
Acknowledgements
The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/20072013) under Grant agreement no. 224635.
Footnotes

One contribution to a Theme Issue ‘The virtual physiological human’.
 Received November 15, 2010.
 Accepted March 1, 2011.
 This Journal is © 2011 The Royal Society