Comprehensive enhanced methodology of an MRI-based automated left-ventricular chamber quantification algorithm and validation in chemotherapy-related cardiotoxicity

Abstract.

Purpose: To comprehensively outline the methodology of a fully automated, MRI motion-guided, left-ventricular (LV) chamber quantification algorithm that enhances a similar, existing semi-automated approach. Additionally, to validate the motion-guided technique in comparison to chamber quantification with a vendor tool in post-chemotherapy breast cancer patients susceptible to cardiotoxicity.

Approach: LV deformation data were acquired with the displacement encoding with stimulated echoes (DENSE) sequence on $N=21$ post-chemotherapy female patients and $N=21$ age-matched healthy females. The new chamber quantification algorithm consists of detecting LV boundary motion via a combination of image quantization and DENSE phase-encoded displacements. LV contractility was analyzed via chamber quantification and computations of 3D strains and torsion. For validation, estimates of chamber quantification with the motion-guided algorithm on DENSE and steady-state free precession (SSFP) acquisitions, and similar estimates with an existing vendor tool on DENSE acquisitions were compared via repeated measures analysis. Patient results were compared to healthy subjects for observing abnormalities.

Results: Repeated measures analysis showed similar LV ejection fractions (LVEF), $59\%\pm 6\%$, $58\%\pm 6\%$, and $58\%\pm 6\%$, $p=0.2$, by applying the motion-guided algorithm on DENSE and SSFP and vendor tool on DENSE acquisitions, respectively. Differences found between patients and healthy subjects included enlarged basal diameters ($5.0\pm 0.5\mathrm{cm}$ versus $4.4\pm 0.5\mathrm{cm}$, $p<0.01$), torsions ($p<0.001$), and longitudinal strains ($p<0.001$), but not LVEF ($p=0.1$).

Conclusions: Measurement similarities between new and existing tools, and between DENSE and SSFP validated the motion-guided algorithm and differences found between subpopulations demonstrate the ability to detect contractile abnormalities.

1. Introduction

Administration of the anthracycline and trastuzumab types of anti-neoplastic chemotherapy agents (CTA) in breast cancer patients may lead to the development of cardiotoxicity that counters any gains in survivorship achieved with treatment.^1–4 Left-ventricular (LV) dysfunctions caused by CTA cardiotoxicity range from arrhythmias to irreversible heart failure that ultimately require managed care and guideline directed medical therapy.⁵ Therefore, CTA treatment plans require routine cardiotoxicity surveillance and close monitoring of LV contractility, which can enable early and subclinical detections of myocardial dysfunction and lead to preventive interventions with drugs such as enalapril and carvedilol.^6–12 However, the standard accepted measure of cardiotoxicity, defined as a decline in echocardiographic quantification of LV ejection fraction (LVEF), may not always provide optimal information toward subclinical detection.^2,5,7,11 In this context, scientific evidence now shows that subclinical LV contractile abnormality monitoring is effective when a number of parameters related to LV chamber quantification, including chamber volume, and 3D myocardial strain are measured.^7,11,13–19 Hence, the purpose of this study was to develop a fully automated, motion-guided LV chamber quantification algorithm, with an approach that combines MRI phase-based displacements and the quantized profile of the myocardium in parallel for boundary detection. This strategy is uniquely different from our previous effort where we used phase-unwrapped displacements for strain analysis and quantization for semi-automated chamber quantification, separately.^20,21

Hence, the purpose of our study reflects the needs of the medical community for more robust surveillance (that incorporate both LVEF and LV strain analysis via imaging modalities) toward early, subclinical detections of LV contractile dysfunction in cardiotoxicity and other cardiac diseases.^{8,11,14,15,18,19} In this regard, an ideal contractility analysis tool must provide comprehensive details regarding cardiac health via LV function analysis, while being a time-saving and least interventional procedure. Fundamental to the tool should be an automated myocardial segmentation module (algorithm), which has in the past led to the development of several post-processing approaches for MRI-based LV motion automation.^21–25 Some of the early tissue motion-guided segmentation approaches include the well-validated tagging technique that spatially modulates magnetization and harmonic phase (HARP) which isolates a single harmonic peak with each tissue element defined by a constant phase and that is tracked in time.^22,24,26 Other segmentation approaches for tissue tracking include active appearance models which depend on training sets and statistical foundations that can withstand substandard quality of data and strain encoding (SENC) which is excellent at estimating real-time, high-resolution through-plane strain.^22,27 Among the very latest innovation are artificial intelligence (AI) and machine-learning tools for motion and deformation analysis in cardiac images that can provide information on pathologies related to myocardial dysfunction.^28–35 Convolutional neural networks (CNN) and deep convolutional neural networks (DCNN) are subsets of both AI and machine learning. However, the supervised learning models with CNN and DCNN technology require manual labels and annotations, rendering which may become time-consuming and tedious. Recent efforts also include segmentation techniques with the displacement encoding with stimulated echoes (DENSE) sequence where tissue motion encoded in phase images was used for 2D myocardial boundary tracking, but these studies did not conduct 3D chamber quantification measurements, such as estimating LVEF.^25,36 Our first 3D endeavor involved implementing an image gradient-guided radial search method for boundary detection that was semi-automated and recently tested in breast cancer patients.^20,21 The novelty of this study lies in implementing an automated, motion-guided myocardial segmentation and 3D chamber quantification algorithm for detecting LV dysfunction. The uniqueness of our approach lies in combining displacements from DENSE phase-unwrapping and gradients of quantized magnitude images toward myocardial feature-tracking and segmenting in each timeframe between end-diastole and end-systole. To assess its clinical applicability, we validated the new motion-guided algorithm in a subpopulation of breast cancer patients following chemotherapy treatment, in comparison to an existing vendor tool, Circle cvi42 (Circle Cardiovascular Imaging Inc., Calgary, Alberta). Three-dimensional LV strains were analyzed following integration of the motion-guided algorithm to our existing strain analysis module.

2. Methods

2.1. Scope of Study

As mentioned, this study outlines the new methodology and validation stage for an automated, single-scan, MRI-based approach to estimating chamber quantification, which in addition to our existing 3D strain computation module has been designed for clinical applications.^21,37–39 The entire algorithm including chamber quantification, 3D strain, and torsion analysis is implemented with a Matlab (MathWorks Inc., Natick, Massachusetts) interface and functions. To analyze the aforementioned, the algorithm’s main modules perform unwrapping of phase images and quantization of magnitude images, in parallel, that are obtained with the navigator-gated, spiral, 3D DENSE sequence.^{21,36,40–43} The patient subpopulation investigated for this study were female breast cancer patients who underwent CTA-based treatment, in a subset of whom it was previously shown that differences in contractile parameters exist in comparison to healthy subjects.²⁰ For the main validation, we conducted repeated-measures ANOVA analysis between chamber quantification with the motion-guided algorithm on DENSE and steady-state free precession (SSFP) acquisitions, and similar estimates (as reference) with the Circle cvi42 vendor tool on DENSE acquisitions. All contractile parameters measured in the patient subpopulation were compared to similar measurements in an age-matched subset of healthy females.

2.2. Human Subject Recruitments

The possibility of cardiac remodeling and occurrence of LV dysfunction was tested on DENSE data acquired in 21 adult female breast cancer survivors. All patients had undergone CTA-based treatment consisting of either one of two regimens, including (1) a combination of anthracyclines for 4 cycles and cyclophosphamide and taxol or (2) a combination of taxol, carboplatin, and trastuzumab for several cycles with optional pertuzumab.²⁰ Some were under continued surveillance and managed care for cardiac comorbidities, to reduce the effect of which on cardiotoxicity analysis required a carefully planned recruitment criteria. Hence, patients with only non-acute cardiac complications that existed prior to their chemotherapy or developed following it were recruited, as we did in our previous study.²⁰ The most important recruitment criterion was a preserved LVEF ($>50\%$) that was measured via transthoracic echocardiography (TTE) at the inception of chemotherapy.^1,20,44 Radiation therapy for effectively reducing local recurrences is integral to breast cancer treatment and irradiated patients were not excluded.^7,12,13 Patients were recruited within a 12-months interval following chemotherapy such that contractility analysis was conducted when the most clinically relevant form of cardiotoxicity occurs.^8,12,45 In addition to DENSE, full LV SSFP data were acquired in patients to ensure extensive validation tests conducted on chamber quantification with the motion-guided algorithm. Both patients and healthy subjects signed informed consents based on Institutional Review Board (IRB) guidelines and patients volunteered access to their medical histories. DENSE acquisitions in $N=21$ healthy female subjects contributed to the 1:1 age-matched comparisons of contractile parameters, with subjects either newly recruited or their data taken from an existing database.^21,37–39

2.3. DENSE Acquisition and Protocols

Navigator-gated, spiral 3D DENSE data were acquired on a 1.5T MAGNETOM Espree (Siemens Healthcare, Erlangen, Germany) scanner with displacement encoding applied in two orthogonal in-plane directions and one through-plane direction.^36,39,40,43 Typical imaging parameters included a field of view of $380\times 380\mathrm{mm}$, a matrix size of $128\times 128$, an echo time of 1.04 ms, a repetition time of 15 ms, a flip angle of 20°, a voxel size of $2.97\times 2.97\times 5\mathrm{mm}$, 21 cardiac phases, an encoding frequency of $0.06\text{cycles}/\mathrm{mm}$, and simple 4-point encoding and 3-point phase cycling for artifact suppression.^42,43 The SSFP acquisition consisted of a field of view of $276\times 340\mathrm{mm}$, a matrix size of $156\times 192$, an echo time of 1.48 ms, a repetition time of 51.2 ms, 80° in flip angle, a $1.77\times 1.77\mathrm{mm}$ pixel size, slice thickness of 7 mm, and 25 cardiac phases. For receiving patient signals from the Espree, an anterior 18-channel array coil in combination with elements of the table-mounted spine array coil was used.⁴⁶ Heart rates (HR) and diastolic and systolic blood pressures (DBP and SBP) were continuously monitored during the scans.

2.4. Automated Boundary Detection

The automated motion-guided approach presented in this study is an enhancement to our validated semi-automated algorithm based on radial searches for quantized image gradients.²¹ The existing semi-automated process consists of identifying the LV boundary contours in the most basal short-axis slice at end-diastole with an ellipsoidal region of interest (ROI), following which the reference boundaries are propagated to all short-axis slices between end-diastole and end-systole as well as base to apex.²¹ The LV boundaries and intramural tissue are identified using Otsu’s method which is a non-uniform image quantization approach based on histogram bins that yield a threshold image with a distinct profile of the short-axis.⁴⁷ To move toward a fully automated algorithm, this study uniquely combined the unwrapped displacement vectors with quantization via a Hadamard product for precisely tracking a boundary point’s motion.^{25,36,38,40,43} The various aspects of the methodology for tracking the motion of myocardial boundaries that incorporate fitting pixel-based displacement trajectories, gradients from image quantization for feature detection, and polynomial smoothing with a residual-regression technique are discussed as follows.

Let the location of a myocardial boundary point at any timeframe be ${\mathit{p}}_j[t_i]$, $j\in [1\dots J]$, with components in both spatial directions ($x$ and $y$) and $t_i$ representing the time at the $i$’th timeframe. With ${\mathit{p}}_j\in {\mathbb{R}}^2$ representing its position within a deformable image domain, the boundary point’s unweighted spatiotemporal location, ${\mathit{p}}_j^{″}[t_i]$, at time $t_i$ can be assembled into an equation given by

$${\mathit{p}}_{\mathit{j}}^{″}[t_i]={\mathit{p}}_{0j}+\frac{\nabla {\mathit{g}}_j}{|\nabla g|}[t_i]\circ {\mathit{f}}_j[t_i],$$ (1)

where ${\mathit{p}}_{0j}$ is the initial myocardial boundary point location, ${\mathit{f}}_j[t_i]$ is a displacement vector from fitting the path traced by a point’s trajectory with Fourier basis functions, also equal to ${\mathit{f}}_j[t_i]=k_e{\mathit{u}}_j^{\prime }[t_i]$ with ${\mathit{u}}_j[t_i]$ the true unwrapped phase and ${\mathit{u}}_j^{\prime }[t_i]$ its fitted form and $k_e$ the encoding frequency, ${\mathit{g}}_j[t_i]$ is the pixel intensity, and $\nabla {\mathit{g}}_j[t_i]=(\frac{d{g}_j}{dx}[t_i],\frac{d{g}_j}{dy}[t_i])$ the intensity gradient calculated at the displacement location with $|\nabla g|$ its magnitude and ∘ representing elementwise products. The fitted displacement vector, ${\mathit{f}}_j[t_i]$, from the point’s trajectory at time $t_i$ is then given by

$${\mathit{f}}_j[t_i]=\frac{1}{2}{\mathit{a}}_{0,j}+\left(\sum _{n=1}^{\infty }\right({\mathit{a}}_{nj}\cos \frac{2n\pi t_i}{T}+{\mathit{b}}_{nj}\sin \frac{2n\pi t_i}{T}\left)\right),$$ (2)

where $n$ is the order of Fourier basis functions, ${\mathit{a}}_{0,j}$, ${\mathit{a}}_{nj}$, and ${\mathit{b}}_{nj}$ are the Fourier basis function coefficients, and $T$ is the total time. It is noted that the occurrence of an image gradient at the displacement point, ${\mathit{p}}_j^{″}[t_i]$, allowed a tolerance of 1 to 2 pixels based on ${\mathit{f}}_j[t_i]$. Equation (1) assumes that the pixel’s displacement vector will match an image gradient in a well-fitted manner if it is a true boundary point. However, the point’s relocation can be unacceptable due to a noisy placement arising from factors such as low signal-to-noise ratio and surrounding non-separable tissue. Hence, to achieve an accurate estimate of the point’s relocation, a spatial weighting technique based on the existence of intensity gradients found in $k$-neighboring pixels and approximated via radial basis function (RBF) interpolation was applied.^48–50 A weight, ${\lambda }_j[t_i]$, is applied that moves the point to a new location, ${\mathit{p}}_j^{\prime }[t_i]$, by a spatial increment of $\mathrm{\Delta }{\mathit{p}}_j^{\prime }[t_i]$ defined by the following set:

$${\mathit{p}}_j^{\prime }[t_i]={\mathit{p}}_{0j}+\mathrm{\Delta }{\mathit{p}}_j^{\prime }[t_i]={\mathit{p}}_{0j}+{\lambda }_j[t_i]\frac{\nabla {\mathit{g}}_j}{|\nabla g|}[t_i]\circ {\mathit{f}}_j[t_i],$$ (3a)

$$\psi ({\mathit{p}}_j)\approx \psi ({\mathit{p}}_j^{″})=\sum _{k=1}^K({\varpi }_k{\varphi }_k\Vert {\mathit{p}}_j^{″}-{\mathit{x}}_k\Vert ),$$ (3b)

$$E=\sum _{k=1}^K{[\psi ({\mathit{x}}_k)-{\mathrm{\Phi }}_k\varpi ]}^2,\mathrm{\Phi }\varpi =\mathrm{\Psi },$$ (3c)

where $\{{\mathit{x}}_k\}$ are $k$-neighboring pixel-based material points in the myocardium, ${\varphi }_k\Vert {\mathit{p}}_j^{″}-{\mathit{x}}_k\Vert$ is an RBF interpolant approximated at ${\mathit{p}}_j^{″}$ in reference to each ${\mathit{x}}_k$, ${\varpi }_k$ is the $k$’th weight, and $\psi ({\mathit{p}}_j)$ is the function observation at ${\mathit{p}}_j^{″}$. The RBF function used in Eqs. (3a)–(3c) was the local positive definite multiquadrics (MQ) RBF that has been used for mesh-free strain analysis in our previous studies.^{20,21,37,39,49} Minimizing the energy function, $E$, in Eq. (3c) is targeted to obtain the weights, $\varpi$, where $\psi ({\mathit{x}}_k)$ is the RBF function evaluated at each ${\mathit{x}}_k$, $\varpi$ is the vector of $k$ weights, $\mathbf{\Phi }$ is a 2D RBF matrix, and ${\mathbf{\Phi }}_k$ is its $k$’th row. The weights are then determined by observing the second part of Eq. (3c), where $\mathbf{\Psi }$ is a vector of $k$ function observations. If $\psi ({\mathit{p}}_j)$ now represents the displacement interpolated at ${\mathit{p}}_j^{″}$ given by the weighted true displacements of the $k$-neighboring points, then a weight ${\lambda }_j[t_i]=|\frac{\psi ({\mathit{p}}_j)}{\mathrm{\Delta }{\mathit{p}}_j^{″}[t_i]}|$ can be computed based on this observation that relocates the boundary point to ${\mathit{p}}_j^{\prime }$ in Eq. (3a). Hence, the position change for a boundary point at time $t_i$ can be estimated based on other points that demarcate true tissue motion. It is noted that the constraint, ${\lambda }_j[t_i]\frac{\nabla {\mathit{g}}_j}{|\nabla g|}[t_i]=1$, was applied when a non-zero intensity gradient was not found ($\nabla {\mathit{g}}_j=0$) at the location of a point’s Fourier-fitted displacement and given the tolerance mentioned above. This ensured that boundary points at the right ventricular–septal junction or other undistinguishable boundaries with tissue such as the liver were moved for the entire period according to their Fourier-fitted displacements. Figure 1 shows the trajectories of Fourier-fitted paths for all points within the myocardium of a patient and healthy subject for a mid-ventricular slice, which provide the neighboring paths to approximate any boundary point’s move. The net movement for a boundary point is then provided by the weighted RBF vector generated from its neighboring pixels as shown in Figs. 2(a)–2(f). The final positioning of the point involves spatial smoothing attained with a locally estimated scatterplot smoothing (LOESS) curve-fitting technique applied to specific spans of boundary points, the full extent of developing which is outlined in Appendix A.^51,52 The smoothing of the deforming boundary is illustrated in Figs. 2(g)–2(l), which requires carefully choosing a smoothing weight that does not alter the main purpose of finding tissue boundaries. The relocation of a single boundary point in the lower-left corner of the epicardium boundaries in Figs. 2(a)–2(f) that moves rightward and upward through the deformation is shown in Figs. 2(m)–2(r), where the path contributions from its neighboring pixels that lie on tissue boundaries (with non-zero quantization gradients) contribute to relocating the point at each timeframe.

Fig. 1.

The short-axis trajectories of the displacement vectors at pixel resolution are shown in (a) a patient and (b) a healthy subject following the elimination of data with non-physiological vector magnitudes, fitting with fifth-order Fourier basis functions and elimination of vectors with high angular divergence. The blue dot in each trajectory represents the beginning of the trajectory, the red dot indicates the peak systolic time point, the blue segment represents the path from start to the peak systolic point, and the red segment indicates the time between the peak systolic point and end-point.

Fig. 2.

(a)–(f) The LV image quantization at pixel resolution and unwrapped displacement data that is utilized in the Hadamard product equation for automated propagation of the 2D boundaries. (g)–(l) The raw boundaries are then smoothed with an outlier residual analysis and local quadratic regression-based LOESS curve-fitting. Solid lines represent the quantized boundaries and broken lines represent the fitted boundaries in (a)–(f). Solid lines represent the fitted current boundaries and broken lines represent the end-diastolic boundaries in (g)–(l). The systolic time instances shown from left to right and top to bottom are at $t$ = [30, 90, 150, 225, 270, and 315] ms. (m)–(r) The movement of a single boundary point (circled in yellow) in the lower-left corner of the deforming epicardium in (a)–(f) is shown. It moves according to the RBF vector approximated from the displacements of its neighboring Fourier-fitted pixels that have non-zero quantization gradients. The contributing vectors to the motion of the pixel (in yellow) are identified by the blue dots at their start.

With LOESS, a local weight, ${\omega }_j[t_i]$, based on polynomial smoothing is applied that moves the point to ${\mathit{p}}_j[t_i]$, via an incremental change, $\mathrm{\Delta }{\mathit{p}}_j[t_i]$, given by

$${\mathit{p}}_j[t_i]={\mathit{p}}_{0j}+\mathrm{\Delta }{\mathit{p}}_j[t_i]={\mathit{p}}_{0j}+{\omega }_j[t_i]{\lambda }_j[t_i]\frac{\nabla {\mathit{g}}_j}{|\nabla g|}[t_i]\circ {\mathit{f}}_j[t_i],$$ (4a)

$${\omega }_j[t_i]=\frac{{\mathit{p}}_{j,\xi }[t_i]-{\mathit{p}}_{0j}}{{\lambda }_j[t_i]\frac{\nabla {\mathit{g}}_j}{|\nabla g|}[t_i]\circ {\mathit{f}}_j[t_i]},$$ (4b)

$${\mathit{p}}_{j,\xi }[t_i]={\xi }_j({\mathit{x}}_k)\sum _{l=0}^L{b}_{lk}{\nu }_k,$$ (4c)

where $\{{\mathit{x}}_k\}$ are $k$-neighboring boundary points situated at $\{{\nu }_k\}$ which is a local span of equal spacing, ${\xi }_j({\mathit{x}}_k)$ is a residual-regression weight function for smoothing described in more details in Appendix A and $b_{lk}$ with $l\in [1..L]$ is the set of polynomial coefficients ($L=2$ for a quadratic polynomial) that determine the weighted evaluation of the point at ${\nu }_k$. Hence, a new point, ${\mathit{p}}_{j,\xi }[t_i]$, is computed with each iteration of the LOESS regression and the final position of the point at the last iteration is given by ${\mathit{p}}_j[t_i]={\mathit{p}}_{j,\xi }^F[t_i]$, $\mathrm{F}=\text{final}$.⁵¹ The LOESS fit is advantageous for retaining a curve’s local shape when it incorporates residual analysis on the $k$-neighboring data points and, in particular, eliminates the influence of noisy outliers by the weighted relocation to ${\mathit{p}}_j$ in the final fit. The final assembled matrix for all boundary points in the domain is given by

$$\mathit{P}={\mathit{P}}_0+\mathbf{\Omega }\circ \mathbf{\Lambda }\circ \mathrm{\Delta }\mathit{G}\circ \mathcal{F},$$ (5)

which is the entrywise Hadamard product (denoted by ∘) of the curve-fitting weights, $\mathbf{\Omega }$, RBF-fitted displacement weights, $\mathbf{\Lambda }$, normalized image gradients, $\mathrm{\Delta }\mathit{G}$, and fitted displacements, $\mathcal{F}$, and where each row represents a single boundary point’s spatiotemporal trajectory. Several additional constraints were applied for positioning the boundary points with Eqs. (1)–(5), which were based on physiological deformation limits for myocardial tissue as well as heuristics. The physiological limits to displacements are from Moore et al.⁵³ 3D strain evolution study, which showed maximum peak systolic displacements of 6 to 10 mm occurring in healthy LVs in the three normal directions. A majority of noisy trajectories can be eliminated using this physiological criterion as a threshold prior to the Fourier fitting. Additionally, a second constraint based on heuristics was set where a displacement vector showing noisy behavior via higher local angular deviation was removed. The basis for identifying this noise was by comparison to a threshold angle set by an initial statistical estimate of angular divergences (of more than 30° to 40° in comparison to neighboring vectors) within the ROI. Finally, the algorithm steps involved in order to implement the theory described above are as follows.

• 1.Elimination of non-physiological and heuristically incorrect data. Fitting each pixel’s trajectory in the myocardium with Fourier basis functions to find ${\mathit{f}}_j[t_i]$ for the DENSE images. Figure 1 shows the Fourier-fitted trajectories of material points within the myocardium, which locally contribute toward the motion of each boundary point.
• 2.The initial diastolic boundary in a time-series is created by a radial search to locate pixels with quantization-based gradients (within a bounding ellipsoid) for both DENSE and SSFP images, as outlined in our previous study.²¹ Boundary points in subsequent frames are located by finding the nearest gradient ($\frac{\nabla {\mathit{g}}_j}{|\nabla g|}[t_i]$) in the quantized image, either using a search path approximated from the neighboring Fourier-fitted trajectories for DENSE (step three) or via the Otsu’s method-based radial search (as outlined in our previous study) for SSFP.
• 3.Conducting RBF fitting with the neighboring displacements to find $\psi ({\mathit{p}}_j)$ for the point’s net motion at a given timeframe and relocating it to ${\mathit{p}}_j^{\prime }$. This relocation was not conducted for points for which a new $\frac{\nabla {\mathit{g}}_j}{|\nabla g|}[t_i]$ was not found (to avoid the influence of other tissue with which sharp boundaries are not present), but the point moved based on ${\mathit{f}}_j[t_i]$. Figures 2(a)–2(f) show the relocation of the boundary at each timeframe based on the RBF vector approximated for each point from its neighboring Fourier-fitted displacements, which also depended on the availability of quantization gradients. Figures 2(m)–2(r) show the relocation of a single boundary point based on the RBF-fitted vector approximated from its neighboring Fourier-fitted pixels and availability of neighboring quantization gradients.
• 4.Applying the LOESS curve-fitting technique to obtain the smoothing weight ${\xi }_j({\mathit{x}}_k)$ with each iteration of the residual-regression analysis and the final weight ${\omega }_j[t_i]$ to get an estimate for point ${\mathit{p}}_j$. Hence, to ultimately fit the boundary by reducing the influence of outliers in both DENSE and SSFP images. Figures 2(g)–2(l) show the final LOESS fitted boundaries at each timeframe, whose extent of smoothing depends on the condition of the polynomial and the application of the smoothing weight.

To observe the influence of motion-guiding toward boundary detection, agreements were assessed between systolic areas within the detected DENSE and SSFP regional (basal, mid-ventricular, and apical) epicardium and endocardium boundaries. Following the generation of boundaries and 3D LV reconstruction, chamber quantification estimates from DENSE and SSFP images included measuring the end-diastolic diameter (EDD), end-systolic diameter (ESD), end-diastolic volume (EDV), end-systolic volume (ESV), stroke volume (SV), LVEF, and LV mass (LVM).²¹ Scatterplots of the EDD, ESD, LVEF, and LVM (in addition to regional strains and torsion) in both patients and healthy subjects were generated for visually comparing the results from the two subpopulations.

2.5. Mesh-Free Strain Analysis

Three-dimensional strain tensors were computed using the radial point interpolation method (RPIM) at each voxel in the patient’s reconstructed 3D geometries. RPIM is a numerical analysis technique based on the Galerkin weak form, and details on computing 3D LV strains via the RPIM methodology that incorporates MQ RBF shape function approximations are outlined in our previous literature.^{20,38,39,49,50,54} The LV torsion definition used in this study was the relative angle of twist between basal and apical rotations multiplied by the ratio of the mean segmental radius to the intersegment distance, details of which are given in previous studies.⁵⁵

2.6. Statistical Analysis

Means and standard deviations were computed for demographic data and LV function parameters (chamber quantification, strains, and torsion). To validate the motion-guided segmentation technique, repeated measures analysis was conducted between estimates of patient chamber quantification on DENSE and SSFP same-day acquisitions and similar estimates on the DENSE data with Circle cvi42. The repeated-‘measures analysis provided answers to two fundamental design objectives; first, to observe if differences existed between chamber quantification computed with the motion-guided algorithm versus an existing methodology, and second, to see if there were differences in results between two protocols, DENSE and SSFP. Additionally, repeated measures analysis was conducted between DENSE, SSFP, and TTE exam-based LVEF measurements in patients following chemotherapy. All repeated measures ANOVA was estimated with SPSS, Version 26 (IBM Corp., Armonk, New York) which included a Mauchly’s test for sphericity, such that any unequal variances in the differences between pairs of within-subject measurements and the possibility of an inflated $F$-test could be reported. Agreements were assessed between the DENSE- and SSFP-based regional epicardial and endocardial boundary areas to estimate geometric variances arising from motion-guided boundary searches. Bland–Altman interobserver agreements were assessed for patient strains measured within the detected boundaries, with random segmentation and strain analysis conducted by two independent users (a radiology researcher and a graduate engineer). Age-specific comparisons of the parameters were conducted between patients and age-matched healthy subjects in our database with unpaired two-sample $t$-tests and significant differences due to LV remodeling and dysfunction observed.^56,57 It is noted that while the comparison of strains between the subpopulations identify parameters that are different in patients, the main validation comprises of the three-way comparison between the chamber quantification with our motion-guided algorithm on DENSE and SSFP data and the corresponding Circle cvi42 quantification on the DENSE acquisitions.

3. Results

The demographic information on age-matched patients and healthy subjects are given in Table 1, which also details existing comorbidities in patients and their chemotherapy treatment plans. The MRI scans were scheduled following a routine post-chemotherapy TTE, within a 1- to 3-day window, to ensure accuracy of comparisons between DENSE, SSFP, and TTE LVEFs. The time to recruiting patients from the end of chemotherapy was $5.7\pm 3.8$ months. Table 2 shows the results of repeated measures analysis between chamber quantification estimated from DENSE and SSFP acquisitions with the motion-guided algorithm and estimated from DENSE acquisitions with Circle cvi42. Significant differences were not found between the three different measurements, which was the important finding for validating the automated segmentation technique. The Fisher statistics from repeated measures analysis between results of patient LVEF from DENSE ($59\%\pm 6\%$), SSFP ($58\%\pm 6\%$), and post-chemotherapy TTE ($58\%\pm 7\%$) was $F(\mathrm{2,40})=1.8$, $p=0.2$ without sphericity assumption violated, showing that significant differences were not there between the measurements. Estimates of contractile parameters consisting of chamber quantification, strains, and torsion in the two subpopulations are given in Table 3, which are similar to the contractile parameters reported in our previous study.²⁰ For visual comparison, scatterplots related to the parameter means in Table 3 (for ESD, ESD, LVEF, LVM, radial, circumferential and longitudinal regional strains, and apical and mid-ventricular torsions) in each patient and healthy subject are given in Appendix D. Figures 1(a) and 1(b) show the fifth-order Fourier-fitted trajectories within the ROI in a patient and a healthy subject to which the physiological and heuristic-based constraints described previously were applied. Given in Fig. 2 are the propagations of the deforming myocardial boundaries on a mid-ventricular short-axis slice of a patient. Figures 2(a)–2(f) show the boundaries in the quantized images, which along with RBF-fitted motion-guiding and LOESS smoothing yield Figs. 2(g)–2(l). Figures 2(m)–2(r) show the motion of a single boundary point following RBF-fitting on its neighboring Fourier-fitted trajectories that lie on pixels with quantization gradients. It was observed that curve-fitting with the LOESS quadratic regression method (inclusive of residual analysis) was mostly successful in eliminating influences of noisy outliers in the magnitude images, which occurred due to poor contrast or motion artifacts. Figure 3(a) shows overlapped stacks of DENSE and SSFP short-axis slices such that similarly located boundaries could be acquired for comparing areas, cavity volumes, and LVEF between the two protocols. Figures 3(b) and 3(c) show the similarities in 3D systolic chamber and cavity dimensions estimated with SSFP and DENSE, respectively, and Fig. 3(d) shows the agreement between LVEFs estimated with the two protocols. Figure 3(e) shows a 3D LV generated with Circle cvi42 for chamber quantification, estimates of which in patients were used for validating the motion-guided algorithm (Table 2). The similarities in LV profile can be seen between Figs. 3(b), 3(c), and 3(e). Agreements between the regional systolic areas obtained with the two protocols for the epicardium and endocardium are given in Appendix B, which did not differ significantly in a similar way to their diameters (Table 2). Additionally not seen were significant differences in regional diastolic areas between the two protocols, excluding the first two frames with low contrast due to the displacement-encoded blood. This agreement found with several hundred systolic frames followed the new motion-guided segmentation process that was conducted in $\sim \mathrm{11,500}$ DENSE short-axis slices (patients and healthy subjects combined), comprising of spatiotemporal frames from end-diastole to end-systole and apex to base. With the above total number of frames processed, the automated algorithm failed in $\sim 400$ frames amounting to a segmentation success rate of $\sim 97\%$. The processing time per segmentation was less than 2 s with a 3.4-GHz Intel Core processor and 16-GB RAM in a 64-bit operating system and therefore required $\sim 8.5\min$ for processing each LV. The majority of this computational expense involved time spent in phase unwrapping, conducting the Fourier fitting, and image rendering tasks. The agreements on normal strains and torsion computed by independent observers, with the motion-guided segmentation approach integrated in the contractility analysis tool, are shown in Appendix C. Figure 4 shows trajectories of fitted contractile parameters including the three normal strains, LVEF, and apical torsion in both patients and healthy subjects. More detailed LV regional trajectories in a subset of this subpopulation are given in our previous study on cardiotoxicity with the semi-automated technique.²⁰ Temporal fitting for trajectories in Fig. 4 was with fifth-order Fourier basis functions in the same way as displacement vectors were fitted. Data were extrapolated beyond the number of cardiac phases acquired to show at least one period for each contractile parameter. It is seen from Fig. 4 that peak longitudinal strain and torsion are significantly different from healthy subjects, but not peak LVEF and radial and circumferential strains, as also given in Table 3 (and visually seen from the individual-based scatterplots in Appendix D). Furthermore, Table 3 shows the significantly different rotations between groups with it being a fundamental parameter for computing torsion. Figures 5 and 6 show short-axis slice maps for the three normal strains in a patient and healthy subject at systole. The patient LV basal diameter is slightly enlarged which is representative of the patient subpopulation and also reported in our previous study with the semi-automated technique.²⁰ Furthermore, the strain maps in Fig. 5 show reduced longitudinal strains in the patient when compared to the healthy subject in Fig. 6, but radial and circumferential strain ranges are closer between the two representatives.

Table 1.

Demograsphics in patients and healthy subjects.

Parameter	Patients	Age-matched HS	$p$-value
Demographics
Age (years)	$55\pm 8.8$	$54.5\pm 6.6$	0.9
DBP (mmHg)	$73.8\pm 11.7$	$69.5\pm 7.8$	0.2
SBP (mmHg)	$124.7\pm 14.1$	$123.8\pm 10.7$	0.9
HR (bpm)	$73.5\pm 11$	$71.2\pm 8.3$	0.5
Body mass (kg)	$72.5\pm 14.6$	$72.7\pm 12.9$	1.0
BMI ($\mathrm{kg}/{\mathrm{m}}^2$)	$27\pm 4.4$	$27.2\pm 4.4$	0.9
BSA (${\mathrm{m}}^2$)	$1.8\pm 0.2$	$1.8\pm 0.2$	1.0
Comorbidities
Hypertension	5	0	0.02*
Hypercholesterolemia	4	0	0.04*
Diabetes mellitus	5	0	0.02*
Chemotherapy dose
Doxorubicin $240\mathrm{mg}/{\mathrm{m}}^2$	14	0	—
Trastuzumab $8\mathrm{mg}/\mathrm{kg}$ loading + $6\mathrm{mg}/\mathrm{kg}/\text{cycle}$	7	0	—
Radiotherapy	7	0	—

Notes: HS, healthy subjects; DBP, diastolic blood pressure; SBP, systolic blood pressure; HR, heart rate; BMI, body mass index; BSA, body surface area.

^*Indicates significant differences between patients and healthy subjects.

Table 2.

Motion-guided and Circle cvi42-based chamber quantification.

Parameter	DENSEa	DENSEb	SSFPa	DF,DF-errorc	$F$, $p$-valuec
Dia basal (D) (cm)	$5.0\pm 0.5$	$5.0\pm 0.5$	$5.0\pm 0.5$	2, 40	0.01, 0.99
Dia basal (S) (cm)	$3.3\pm 0.4$	$3.3\pm 0.4$	$3.2\pm 0.3$	2, 40	0.14, 0.88
LV EDV (${\mathrm{cm}}^3$)	$108\pm 17$	$110\pm 21$	$109\pm 19$	2, 40	0.04, 0.96
LV ESV (${\mathrm{cm}}^3$)	$44\pm 8$	$46\pm 8$	$46\pm 9$	2, 40	0.25, 0.78
LV SV (${\mathrm{cm}}^3$)	$64\pm 14$	$64\pm 17$	$63\pm 15$	2, 40	0.07, 0.93
LV EF (%)	$59\pm 6$	$58\pm 6$	$58\pm 6$	2, 40	1.5, 0.24
LVM (gm)	$123\pm 9$	$119\pm 11$	$121\pm 12$	2, 40	1.1, 0.35

Notes: Dia, diameter; D, diastolic; S, systolic; EDV, end diastolic volume; ESV, end systolic volume; SV, stroke volume; EF, ejection fraction; LVM, LV mass; DF, degree of freedom; F, Fisher statistics.

^aEstimated with the motion-guided algorithm.

^bEstimated with Circle cvi42.

^cDegrees of freedom (DF) and $F$-test results from repeated measures analysis. The DF values indicate that sphericity assumptions were not violated.

Table 3.

Chamber quantification and strains in patients and healthy subjects.

Parameter	Patients	Age-matched HS	$p$-value
Chamber quantification
Dia basal (D) (cm)	$5.0\pm 0.5$	$4.4\pm 0.5$	0.0*
Dia basal (S) (cm)	$3.3\pm 0.4$	$2.7\pm 0.4$	0.0*
LV EDV (${\mathrm{cm}}^3$)	$108\pm 17$	$111\pm 18$	0.7
LV ESV (${\mathrm{cm}}^3$)	$44\pm 8$	$42\pm 11$	0.5
LV SV (${\mathrm{cm}}^3$)	$64\pm 14$	$69\pm 13$	0.3
LV EF (%)	$59\pm 6$	$63\pm 6$	0.1
LVM (gm)	$123\pm 9$	$126\pm 10$	0.1
LVM/BSA ($\mathrm{gm}/{\mathrm{m}}^2$)	$68\pm 8$	$71\pm 9$	0.4
Strains and torsion
$E_{\mathrm{cc}}$ basal	$-0.18\pm 0.03$	$-0.20\pm 0.02$	0.2
$E_{\mathrm{cc}}$ mid	$-0.20\pm 0.03$	$-0.21\pm 0.03$	0.3
$E_{\mathrm{cc}}$ apical	$-0.22\pm 0.03$	$-0.24\pm 0.04$	0.2
$E_{\mathrm{cc}}$ global	$-0.20\pm 0.03$	$-0.21\pm 0.03$	0.1
$E_{\mathrm{ll}}$ basal	$-0.14\pm 0.02$	$-0.19\pm 0.04$	0.0**
$E_{\mathrm{ll}}$ mid	$-0.15\pm 0.02$	$-0.21\pm 0.04$	0.0**
$E_{\mathrm{ll}}$ apical	$-0.16\pm 0.03$	$-0.23\pm 0.04$	0.0**
$E_{\mathrm{ll}}$ global	$-0.15\pm 0.02$	$-0.21\pm 0.04$	0.0**
$E_{\mathrm{rr}}$ basal	$0.38\pm 0.05$	$0.38\pm 0.05$	0.8
$E_{\mathrm{rr}}$ mid	$0.32\pm 0.04$	$0.34\pm 0.04$	0.2
$E_{\mathrm{rr}}$ apical	$0.26\pm 0.04$	$0.27\pm 0.03$	0.1
$E_{\mathrm{rr}}$ global	$0.32\pm 0.06$	$0.33\pm 0.06$	0.4
Rotation basal (°)	$-1.50\pm 1.10$	$-4.50\pm 2.10$	0.0**
Rotation mid (°)	$5.50\pm 1.50$	$8.30\pm 1.90$	0.0**
Rotation apex (°)	$8.30\pm 2.10$	$11.70\pm 2.50$	0.0**
Torsion basal (°)	$0.00\pm 0.00$	$0.00\pm 0.00$	—
Torsion mid (°)	$4.80\pm 1.00$	$7.70\pm 1.30$	0.0**
Torsion apical (°)	$6.00\pm 1.10$	$9.70\pm 1.40$	0.0**

Note: Dia, diameter; HS, healthy subjects; D, diastolic; S, systolic; EDV, end diastolic volume; ESV, end systolic volume; SV, stroke volume; EF, ejection fraction; LVM, LV mass; rr, radial; cc, circumferential; ll, longitudinal.

^*Indicates significant differences between patients and healthy subjects at $p<0.01$.

^**Indicates significant differences at $p<0.001$.

Fig. 3.

(a) LVEF were computed from myocardial boundaries detected using the automated chamber quantification algorithm in stacks of similar SSFP and DENSE short-axis images as shown in a patient. The DENSE short-axis slices are surrounded by the green rim and SSFP slices by the red rim. (b) and (c) Similarities in SSFP and DENSE image-based estimates of 3D systolic LV chamber and cavity dimensions. (d) Bland–Altman agreement between DENSE and SSFP LVEFs in $N=21$ patients. (e) A 3D systolic LV estimated with Circle cvi42.

Fig. 4.

Trajectories of global circumferential, longitudinal, and radial strains (mm/mm), LVEF (%), and apical torsion (°) in the patient subpopulation ($N=21$) and age-matched healthy subjects ($N=21$). The broken vertical line at 290 ms indicates the end point of image acquisition, beyond which data were extrapolated using the fifth-order Fourier fit to complete the systolic period. HS, healthy subjects.

Fig. 5.

Two-dimensional short-axis slice maps of radial, circumferential, and longitudinal strains generated with the automated strain analysis algorithm in the apical, mid-ventricular, and basal LV of a patient at the systolic timeframe.

Fig. 6.

Two-dimensional short-axis slice maps of radial, circumferential, and longitudinal strains generated with the automated strain analysis algorithm in the apical, mid-ventricular, and basal LV of a healthy subject at the systolic timeframe.

4. Discussion

This study introduced and validated an automated, motion-guided methodology for chamber quantification toward determining LV contractile parameters, with tests conducted in a subpopulation of breast cancer patients who have enhanced risks of developing cardiotoxicity. Systolic contractile parameters of the LV were computed by combining phase-unwrapped displacements and image quantization for chamber quantification, which is the novel addition to our contractility analysis tool, and mesh-free RPIM strain analysis, which is an existing component of this tool.^21,37–39 Figure 1 shows that physiological trajectories of tissue displacement can be obtained with this novel contractility analysis approach and Fig. 2 represents successfully attaining segmentations in $\sim 97\%$ of frames processed. The primary goal of validating the motion-guided algorithm in a patient subpopulation was accomplished following the repeated measures analysis (Table 2) that showed differences were not there when quantifications were conducted with three different techniques, including computations with Circle cvi42. Thus, validating the motion-guided algorithm in comparison to both an existing tool and a gold-standard protocol, SSFP (also visually represented by the LVEF agreement in Fig. 3), was indeed an important outcome of this study. Also noted is that these similarities were achieved for several thousand short-axis slices successfully undergoing the contractility analysis steps. It was proven yet again by the Fisher statistical result from the next repeated measures analysis showing that a significant difference between DENSE-, SSFP-, and TTE-based LVEFs did not exist. Some early attempts to automate segmentation have been conducted with SSFP, tagged, HARP, SENC, and also DENSE images, which met with various levels of success, a few of which outcomes are discussed next.^22–25,27 In a similar study by Spottiswoode et al.²⁵ to automate 2D segmentation using DENSE phase images, the authors reported average endocardial segmentation errors of $0.46\pm 0.12$ and $0.46\pm 0.16\text{pixels}$ for slice-following and conventional cine DENSE, respectively, and segmentation failures in 0.72% of the images due to incorrect phase-unwrapping. However, their algorithm was based entirely on the DENSE phase images, without incorporating edge information from the magnitude images, and neither did they conduct 3D analysis toward chamber quantification. DENSE-based segmentation was also conducted by Gilliam and Epstein²³ who used both magnitude and phase images, and compared their algorithm to semi-manual analysis using distance-weighted linear interpolation across all datasets. They found the RMSE of all material points within the myocardium to be 0.35 mm ($\sim 0.125\text{pixels}$) and as their method was 2D without through-plane motion, they did not attempt chamber quantification. Among other segmentation techniques, Zhang et al.⁵⁸ conducted an MRI study to develop a fully automatic framework for chronic MI delineation via deep learning on non-contrast cardiac cine data and did not find differences between the non-enhanced and late gadolinium-enhanced analyses in per-patient MI area (6.2 versus $5.5{\mathrm{cm}}^2$, $p=0.3$). In a recent study conducted by Bai et al.³⁰ on automated segmentation with fully convolutional network on a large-scale cardiac dataset from the UK Biobank, the authors showed insignificant differences in segmentation between a subgroup with cardiovascular diseases (Dice score of 0.87) versus the entire set of healthy subjects and patients (Dice score of 0.88). We report the validation results of our study via repeated measures analysis (in comparison to chamber quantification with Circle cvi42 with significant differences not found), where it was seen that the motion-guided technique with accurate quantization levels, phase-unwrapping, and smoothing can be applied toward designing a tool that saves valuable time and manual effort. However, while automating segmentations in $\sim 97\%$ of the images indicate a high success rate, there is potential for failure under certain circumstances, which generally occur due to a lack of contrast (or quality) in the magnitude images in the timeframes following the peak systolic phase or similarly from unwrapping errors. Differences in segmented areas between SSFP and DENSE were non-significant and the low biases and narrow limits from assessing their agreements are given in Appendix B. Differences were expected (but not found) due to detecting each boundary point in SSFP images via radially locating the quantization gradients, which without displacement vectors constraining its motion (that we apply to the DENSE images) could result in overestimating the area of the myocardium.²¹ Appendix C shows the low interobserver agreement biases for contractile parameters estimated in patients and the limits not surpassing $\sim 0.06$ in strain magnitude and less than 1.5° in torsional agreement. The extent of these agreements indicates soundness of the motion-guided approach and additionally support the findings of subclinical myocardial abnormalities detected via some of these parameters. Determining these LV contractile parameters that significantly differed between CTA-treated patients and age-matched healthy subjects was also an important finding of this study, which were in longitudinal strain, torsion, and the basal diameter distortion as detailed in Table 3 and visually seen in Figs. 4–6. Figure 5 shows the same effect in relation to reduced longitudinal strains (in comparison to the healthy subject in Fig. 6) that was shown with the 3D LV map in our previous study.²⁰ The above key findings are inclusive of not finding significant differences in LVEF (also circumferential and radial strains) measurements between patients and healthy subjects. It is noted that the differences in LV function observed between the patients and healthy subjects identify the parameters that may differ following CTA treatment, but it does not validate the chamber quantification algorithm. The validation for the motion-guided algorithm is provided by the three computations on chamber quantification and the repeated measures analysis as comprehensively outlined in Sec. 2.6 and discussed above.

Background research on the consistencies of results between this study and previous ones was conducted.^9,13,59 Primarily, the similarities found with other studies were that LV remodeling and dysfunction occur when similar CTA doses of anthracyclines and trastuzumab are administered either separately or in combination.^13,59 Additionally found were similarities to studies which show myocardial dysfunction related to subclinical cardiotoxicity can be detected with altered global and regional strains, either independently or earlier to significant reductions in LVEF.^{2,9,11,13,15,60} These studies reported reductions in peak systolic strains with longitudinal strain dropping by 20% and torsional reductions of 50% without seeing any LVEF reductions, which are similar to the findings from this study (Table 2 and Fig. 4).^9,60 This study also showed that strain-based analysis can detect impaired LV functionality within a short period following chemotherapy, such as the studies by Motoki et al.⁹ and Sawaya et al.¹³ The enlargement in basal diameter with preserved LVEF has been seen in previous studies such as the recent CECCY trial which randomized 200 patients with breast cancer tumors receiving anthracyclines and who received a placebo or carvedilol until chemotherapy completion.⁶¹ The explanation for this enlargement lies in cardiomyopathy developing in some patients, which generally arise within a few weeks of concluding chemotherapy and may last several months as reported by the CECCY trial and Cardinale et al. studies.^1,12,61 The enlarged basal diameter as well as reductions in strain and torsion were also shown in our previous study with the semi-automated approach to chamber quantification.²⁰ These similarities with our previous study provide additional validation for the fully automated, motion-guided algorithm we present here. Delays in reaching the peak longitudinal strain and apical torsion were observed, which have been reported in previous studies on LV dysfunction.^62–65 From the results, we observed that delays between peak longitudinal strains in the posterior and lateral segments caused peak global longitudinal strain to delay, which after reviewing previous literature could be attributed to the presence of myocardial wall dyssynchrony.^62–64 The delay in peak torsion can similarly be attributed to delayed, as well as depressed and disorganized, apical untwisting compared to normal basal untwisting, as previously reported in patients with DCM.^55,65 Similarities not found with existing studies include not finding a reduction in peak systolic radial strain which studies have reported dropping by $\sim 40\%$ or in peak systolic circumferential strain dropping by $\sim 15\%$.^7–10,13,14 In summary, a novel and fully automated motion-guided chamber quantification algorithm toward LV contractility analysis was presented and validated versus an existing tool and another protocol in a post-chemotherapy patient subpopulation, which then provided evidence of subclinical abnormalities in those patients (via comparisons to healthy subjects). We perceive the application of our motion-guided algorithm toward automated ground-truth labeling in a deep learning segmentation tool that we have recently developed.^66,67 Indeed, in the context of chamber quantification via deep learning segmentation of the myocardium, our algorithm can bypass the commonly encountered, tedious task of manually generating the ground-truth labels prior to training a network for optimal accuracy.

The first limitation of this study is that this is not a longitudinal study where the effects of chemotherapy are analyzed in relation to pre-chemotherapy strains. We were limited in our resources due to this being a pilot study and hence, attempted identifying any differences in LV function that arise due to chemotherapy via the comparisons we made to healthy subjects. The second limitation is that the influence of existing comorbidities cannot be quantified and their effects isolated from the contractility analysis on cardiotoxicity. The compounding effects of LV abnormalities due to hypertension, hypercholesterolemia, diabetes, and others have been reported as non-separable with biomarker analysis in a number of previous studies and currently a statistical model for separately considering each comorbidity does not exist.^{1,8,12,13,59,68} However, the recruitment criteria for this study were designed for the least impact of comorbidities on strain parameters by ensuring that only patients with pre-chemotherapy LVEF higher than 50% and comorbidities rated NYHA class II or less were selected. The third limitation lies in not investigating the effect of manually contouring the LV boundaries, which can be an extremely tedious process for the full LV. While manual contouring does attain human perspective regarding LV shape (and function), the prospect of individually contouring more than 10,000 image frames was beyond practical consideration for this study. A fourth limitation was that segmentation with Circle cvi42 was not fully automated and required considerable manual interventions. The reason for this could be the presence of black blood in DENSE images in contrast to the white blood found in SSFP that is most likely used for feature detection. However, finding the specific cause underlying this limitation requires investigating proprietary vendor information, which currently lies beyond the scope of this study. A final limitation is that with cine DENSE only a portion of the cardiac cycle starting with end-diastole is imaged. Since Fourier coefficients are obtained by discrete Fourier transforms of the data at uniform time intervals over the entire period, displacements for each spatial coordinate need to be extrapolated from the available end point back to the start. The extrapolation can be avoided by conducting a least squares fit of the already overdetermined system (more data points and equations than unknowns), but it remains to be seen if discrete transforms over the entire contraction period from actual physiological data show trajectories of the parameters that are different.

5. Conclusion

This study introduced an automated, myocardial motion-guided chamber quantification algorithm based on DENSE acquisitions. It was validated in comparison to an existing tool and gold-standard protocol in a breast cancer patient subpopulation susceptible to cardiotoxicity following chemotherapy. Additionally, the study’s outcome reveals cardiac remodeling and dysfunction (enlarged basal diameter, reduced longitudinal strain, and torsion) in the patient subpopulation with completion of treatment. In conclusion, the findings emphasize the contractility analysis tool’s ability for both chamber quantification and strain computations.

6. Appendix A: Locally Estimated Smoothing Curve Fitting Theory

The following outlines the methodology for the LOESS curve-fitting technique that was applied to specific spans of boundary points and its position estimated based on nearest $k$-neighboring points.^51,52

Let $\{{\mathit{x}}_j\}$ be a set of $j\in [1\dots M]$ position vectors for points on a curve in a given domain where ${\mathit{x}}_j\in {\mathbb{R}}^2$. Second, define $M$ equally spaced locations for the range of $\{{\mathit{x}}_j\}$ values and call these ${\nu }_j$. The LOESS curve will be evaluated at each of the equal ${\nu }_j$ spacings, where the fitted value is designated as $\widehat{{\mathit{x}}_j}({\nu }_j)$. Third, establish an integer parameter $\alpha$ that determines the span length of the $k$-neighboring points from which the LOESS fit is determined. Hence, for each local span, the number of points used for approximation is $k=[1\dots K]\in 1\dots \alpha M]$ and the vector of equally spaced locations is $\{{\nu }_k\}$. Let $b_{lk}$ with $l\in [1..L]$ be the set of polynomial coefficients ($L=2$ for a quadratic polynomial) that determine the function at ${\nu }_k$. In which case, the value of the curve estimated locally is $\widehat{{\mathit{x}}_j}({\nu }_k)$, given by⁵²

$$\widehat{{\mathit{x}}_j}({\nu }_k)={\xi }_j({\mathit{x}}_k)\sum _{l=0}^L{b}_{lk}{\nu }_k^l,$$ (6)

where ${\xi }_j=r_j{\rho }_j({\nu }_k)$ is the overall residual-regression smoothing function consisting of a local tricubic weight function, ${\rho }_j({\nu }_k)$, and a bicubic regression residuals-based weight function, $r_j$.

Now define $\mathrm{\Delta }{\nu }_k=\frac{{\nu }_k-{\nu }_k^{*}}{\max ({\nu }_k-{\nu }_k^{*})}$ as the spatial difference between any point within the local span, ${\nu }_k$, and the point being evaluated, ${\nu }_k^{*}$. This will make $\mathrm{\Delta }{\nu }_k<1$ for any point inside the local span and $\mathrm{\Delta }{\nu }_k\ge 1$ for any point outside the span of $k$-neighbors. The LOESS tricube neighborhood weight function approximated at the $j$’th curve point is given by

$${\rho }_j({\nu }_k)=\{\begin{array}{ll}{(1-{\mathrm{\Delta }}_{(j)}{\nu }_k^3)}^3,& |{\mathrm{\Delta }}_{(j)}{\nu }_k|<1\\ 0,& |{\mathrm{\Delta }}_{(j)}{\nu }_k|\ge 1\end{array}.$$ (7)

It is noted that the tricube weight function given in Eq. (7) is zero outside the local span which removes the influence of any points outside the span from contributing to the weighted approximation. And the LOESS regression residual-based weight function for each point on the curve is given bys

$$r_j=\{\begin{array}{ll}{(1-{\left(\frac{e_j}{6M}\right)}^2)}^2,& |e_j|<6M\\ 0,& |e_j|\ge 6M\end{array},$$ (8)

where $e_j$ is the residuals for each boundary point with $e_j={\mathit{x}}_j-\widehat{{\mathit{x}}_j}({\nu }_k)$ and $M=\text{median}(|r|)$ is the median absolute deviation of all residuals. Now use the combined tricube and residual weights to estimate a new set of coefficients, $b_{lk}$, which minimize the expression given by⁵²

$$E=\sum _{k=1}^K{\xi }_j({\rho }_k){({\mathit{x}}_j-[\sum _{l=0}^L{b}_{lk}{\nu }_k^l\left]\right)}^2,$$ (9)

${\xi }_j({\rho }_k)$ can now be recalculated via several iterations until convergence is achieved and a final point $\widehat{{\mathit{x}}_j}({\nu }_k)$ found.

7. Appendix B: Regional Systolic Area Agreement between Processed DENSE and SSFP Acquisitions

Regional systolic area agreements between DENSE and SSFP following LV chamber quantification analysis with quantization, RBF motion-guiding, and the LOESS-based curve fitting of the myocardial contours. The agreements were assessed with Bland–Altman analysis on the basal, mid-ventricular and apical sub-regions in $N=21$ patients (Fig. 7).

Fig. 7.

Regional systolic area agreement between DENSE and SSFP following quantization, RBF-motion-guiding, and fitting with LOESS approximations. The subregions include the base, mid-ventricle, and apex in each of $N=21$ patients.

8. Appendix C: Interobserver Bland–Altman Agreement on 3D Strains and Torsion in Post-Chemotherapy Breast Cancer Patients

Interobserver agreements assessed for left-ventricular radial, circumferential, and longitudinal strains (estimated at the apical, mid-ventricular, and basal segments) and torsions (mid-ventricular and apical estimate) with Bland–Altman analysis. The measurements were conducted on $N=21$ patients by each of two medical imaging researchers (Fig.  8).

Fig. 8.

Interobserver Bland–Altman agreements assessed for radial, circumferential, and longitudinal strains (estimated at the apical, mid-ventricular, and basal segments) and torsion (mid-ventricular and apical estimate), which were computed with the 3D strain analysis algorithm in patients. The measurements were conducted on $N=21$ patients by each of two research observers.

9. Appendix D: Scatterplots of Chamber Quantification and Strains in Individual Patients and Healthy Subjects

Scatterplots of LV chamber quantification parameters (LVEF, LV mass, diastolic, and systolic diameters), strains (basal, mid-ventricular, and apical in the circumferential, longitudinal, and radial directions) and torsion (basal, mid-ventricular, and apical) in the cohorts of breast cancer patients ($N=21$) and healthy subjects ($N=21$) (Fig. 9).

Fig. 9.

Scatterplots of LV chamber quantification parameters and strains in the cohorts of breast cancer patients ($N=21$) and healthy subjects ($N=21$).

Biographies

Julia Kar is an assistant professor of mechanical engineering and pharmacology at the University of South Alabama (and a former NIH fellow) who specializes in cardiac mechanics and left-ventricular contractile function analysis. She has done extensive research in heart failure with advanced MRI-based computations of regional myocardial strain. As the PI of an NIH grant, she is in charge of a study to detect cardiotoxicity in breast cancer patients who receive chemotherapy, with computations of regional strain-based contractile metrics in the left-ventricle.

Michael V. Cohen is a professor of cardiology and physiology in the Department of Physiology, University of South Alabama. He has been pioneering studies in the phenomenon of cardiac pre- and post-conditioning and the concept of salvage of ischemic myocardium for 25 years. As a cardiologist, he is also interested in studying the occurrence of mechanical dysfunction that occurs with cardiotoxicity and in developing clinical cardio-protective strategies.

Samuel A. McQuiston is a graduate of the Medical School at Louisiana State and an associate professor at the College of Medicine, University of South Alabama where he holds prestigious positions as program director of radiology and residency program director of radiology. He is certified by the American Board of Radiology. He is ideally suited for conducting MRI scans on chemotherapy patients and, through his exclusive background in cardiac reading, provide expert opinion on left-ventricular abnormalities detected from chemotherapeutic treatment in breast cancer.

Christopher M. Malozzi is a graduate from Philadelphia College of Osteopathic Medicine in Philadelphia and is an assistant professor at the University of South Alabama’s Division of Cardiology. His clinical and translational interests include non-invasive cardiovascular imaging and the management of heart failure. He provides expert opinion on the presence of cardiotoxicity in patients for Dr. Kar’s NIH grant, by evaluating their clinical exams and medical histories.

Disclosures

We confirm that none of the authors have any competing interests in the paper. Hence, there are no potential conflicts of interest with any entities within the University of South Alabama or outside including institutes, organizations, and commercial ones.

Code, Data, and Materials Availability

Data related to this project can be obtained from the Open Science Framework repository at URL: https://osf.io/3t64z/ and DOI: 10.17605/OSF.IO/3T64Z or upon request to the corresponding author.