Artificial Intelligence to derive aligned strain in cine CMR to detect patients with myocardial fibrosis: an open and scrutinizable approach

Cine Cardiac Magnetic Resonance (CMR) is the gold standard for cardiac function evaluation, incorporating ejection fraction (EF) and strain as vital indicators of abnormal deformation. Rare pathologies like Duchenne muscular dystrophies (DMD) are monitored with repeated late gadolinium-enhanced (LGE) CMR for identification of myocardial fibrosis. However, it is judicious to reduce repeated gadolinium exposure and rather employ strain analysis from cine CMR. This solution is limited so far since full strain curves are not comparable between individual cardiac cycles and current practice mainly neglects diastolic deformation patterns. Our novel Deep Learning-based approach derives strain values aligned by key frames throughout the cardiac cycle. In a reproducibility scenario (57+82 patients), our results reveal five times more significant differences (22 vs. 4) between patients with scar and without, enhancing scar detection by +30%, improving detection of patients with preserved EF by +61%, with an overall sensitivity/specificity of 82/81%.

1 Introduction 1 Duchenne muscular dystrophy (DMD) is an X-2 chromosomal linked and the most commonly inher-3 ited muscular disorder in childhood (incidence 1:3500 4 male newborns) [1].It is caused by mutations in the dystrophin gene and, over time, induces a fibrofatty replacement of muscular tissue, ultimately leading to muscle weakness in all parts of the body [2].With increasing age, cardiac involvement is almost univer-1 sally present in DMD and manifests with dilated carhas been shown that the temporal resolution of the CMR series has a significant influence on the strain values [27].
The field has approached the problem by extracting a single strain value as descriptor of the systolic deformation [28,24,29].One option is to select the maximum of the curve (peak strain) neglecting the positional encoding within the cardiac cycle and without further systolic isolation, it can potentially include post-systolic deformation [27].A better positional alignment between patients can be achieved by determining the end-systolic frame (end systolic strain -strain between ED and ES frames) (e.g.[30,13]) or deriving the peak strain within the systolic sub-phase (peak systolic strain between ED and ES frames).However, relying solely on systolic strain values significantly reduce the information on myocardial deformation.Sub-cohorts of patients with preserved LVEF, where the systolic phase itself may be a less predictive marker, could therefore fail in the analysis.Although calculating peak strain rates and diastolic strain rates (e.g.[30,24,31]) where the deformation is integrated over a temporal interval can pose a potential solution, a systematic investigation of non-handpicked phase intervals has remained poorly explored.Such an approach would require robust CMR-based extraction of several temporal markers ('key frames') along the cardiac cycle that goes beyond the current and error-prone LV volume calculations for ES and ED determination [27].
We propose a method to derive aligned E cc and E rr cardiac strain from stacks of 2D steady-state free precession (SSFP) cine short-axis CMR to predict myocardial fibrosis in patients with DMD.For this purpose, a fully automatic Deep Learning and Machine Learning pipeline (cf. Figure 2 and 4) is introduced to derive composed (ED to key frames-ED2K ) and sequential (key frame to key frame -K2K ) strain values between five cardiac key frames that are distributed over the cardiac cycle (cf.Figure 1 b) and describe beginning and end of respective sub-phases.The key frames are extracted in a self-supervised manner (cf.Section 5.3) [32], meaning for learning this task no expert labels are required, and we show the robustness of the approach in several experiments (cf.Section 2).This constitutes 1) a novel variant to calculate strain, which allows for higher sampling along the temporal 102 axis instead of taking only the two prominent key 103 frames of ED and ES into consideration, which is the 104 current state-of-the-art [27] (cf. Figure 1).2) We 105 rely on the calculation of strain tensors from dense 106 displacement fields similarly as proposed by Morales 107 et al. [30], which constitutes an alternative to fea-   The images of this cohort have been acquired between 2018 and 2020.In this cohort, 33 patients have at least one myocardial segment with fibrosis LGE+ (57.9%), on a segment level, 187 segments out of 912 are LGE+ (20.5%).
A second retrospective cohort (DMD82) of 82 patients from the same center was acquired after model development to test the model's reproducibility on new clinical data.The images were acquired at a later stage between February 2022 and April 2023.In this sub-cohort, no biventricular ground truth or cardiac key frames were labeled.Here, 51 patients (62.2%) and 266 segments (20.27%) are LGE+.Both cohorts were treated independently at all times.Table 1 lists the cohort-wise demographical parameters grouped by LGE+/LGE-and provides an overview of p-values within and between the two cohorts.There are no statistical significant differences in any of the parameters.Table 1 in the Supplemental Material summarises the MRI-related parameters.
Incorporating the involvement of the left ventricle ejection fraction (LVEF) as important clinical marker revealed an interesting picture.A LVEF threshold of = 55% was applied to further split patients with fibrosis (LGE+) into those with a preserved LVEF (LGE+ pLV EF ) and those with a reduced LVEF (LGE+ rLV EF ), similar as done by Earl et al. [33] (The first value in brackets refer to the DMD57 cohort and the second to the DMD82 ): From the 139 patients, 84 patients were LGE+ (33, 51) and 55 LGE- (24,31).From the 84 LGE+ patients 45 showed a reduced LVEF (19,26) and 39 showed a preserved LVEF (14,25).For the test cohort DMD82 only half of the LGE+ patients (26 of 51) developed a reduced LVEF.Interestingly, for the LGE-group (55) we found 10 patients (5 , 5) with a reduced LVEF (LGE− rLV EF ).Fig. 3 a) depicts the distribution of LGE+ AHA segments in the two cohorts.In both cohorts, the basal inferior, inferolateral, and anterolateral (AHA4-6), mid inferior, inferolateral, anterolateral (AHA10-12) and apical inferior, lateral (AHA15-16) segments were the most affected.The stripplots re-Figure 1: a), Traditional strain measure.In this widely established workflow, each frame of an CMR sequence is compared to the end-diastolic (ED) key frame.This results in temporally highly-resolved strain curves.Unfortunately, due to varying number of frames and variable lengths of cardiac cycles and cardiac sub-phases, strain curves are not temporally aligned between patients and an automatic comparison of each strain value is not possible.For an inter-patient comparison either the peak strain, the peak systolic strain or the end-systolic strain is considered [28] with the goal of comparing maximal deformation of the myocardium during the systolic phase, however, this assumption may not hold in certain patient cohorts.b), Proposed aligned strain measure through five key frames, derived from self-supervised contraction-relaxation curves [32].This approach identifies five cardiac key frames throughout the cardiac cycle: end-diastole (ED, end of diastolic relaxation); mid-systole (MS, maximum systolic contraction); end-systole (ES, end of systolic contraction); peak flow (PF, peak early diastolic relaxation) and mid-diastole (MD, key frame before atrial contraction at p-wave onset).This enables to derive composed (ED2K ) strain between the end-diastolic key frame and the other key frames and sequential, from one key frame to the next (K2K ).Through this alignment, the temporal information of the whole cardiac cycle can be exploited and compared between different patients.Note the different strain curves and the higher sampling of key frames along the temporal axis.Dashed lines and empty circles denote radial strain (E rr ), solid lines and dots depict circumferential strain (E cc ).E: strain, t: time.
Figure 2: High-level description of the proposed pipeline.The proposed workflow consists of five components (cf.Section 5.3).First, steady-state free-precession cine images in short-axis view are provided.Then, myocardial tissues are segmented from a supervised model.In the following, multiple key frames throughout the cardiac cycle are detected using a self-supervised method from Koehler et.al [32].Next, the shortand long-distance displacement fields between those key frames are learnt.In the fourth step radial (E rr ) and circumferential (E cc ) segment-wise strain is derived from the composed (ED2K ) and sequential (K2K ) displacement fields.Finally, the segment-wise and key frame specific strain values are used to predict patients with myocardial fibrosis.
veal that in the DMD57 cohort, every LGE+ pa-  The Deep Learning pipeline (cf. Figure 2) identifies cardiac key frames based on contraction and relaxation curves (cf.Section 5.3), as shown in previous work [32].The derived key frame specific strain (ED-MS, MS-ED, ED-PF, PF-MD; explained in Section 5.2) enables the comparison of temporally aligned (ED2K and K2K ) deformation values (cf. Figure 1 b) between patients.In this approach, strain values describe how deformation occurs towards and between key frames, making it independent of both temporal resolution and the patient-specific lengths of cardiac sub-phases.In extension to established measures such as proposed by Morales et al. [14], the strain values can be calculated in a composed (enddiastole to key frame, ED2K ) and a novel sequential (key frame to key frame, K2K ) manner (cf. Figure 1  b).Radial (E rr ) and circumferential (E cc ) strain was compared between patients with myocardial fibrosis (LGE+) and those without (LGE-).The proposed extension enables to compare strain at and between multiple key frames and segments (i.e.early diastole of AHA segment 5), thus is not limited to peak values LGE-patients and segments, likely due to the temporal misalignment of the cardiac sub-phases across patients.
We found that ED2K E cc revealed nine statistically significant differences in the AHA segments 5,6,11,12.Additionally, ED2K E rr showed statistical significance in the two AHA segments 5,11.Notably, ten out of eleven phases were systolic.In contrast, K2K E cc showed sixteen statistically significant differences in the segments 1,2,5,6,11,12,15, where eight phases were diastolic.The K2K E rr values additionally were significantly different at six segment-phase combinations (segments: 1,2,5,11,12), with all of them being systolic.
The K2K approach revealed not only more phases Figure 3: a) Distribution of LGE+ AHA segments in the DMD cohorts, indicated by absolute numbers and dots.In both cohorts, the segments 4,5,6 and 10,11,12 were LGE+ most frequently, followed by the segments 13,15,16.The stripplots provide a more detailed view of the LGE+ cardiac segments in the patients of the two cohorts.In these plots, each line stands for a single patient, and dots indicate the AHA segment that was LGE+.Note that the axes of AHA segments are sorted in descending order of the segments' LGE+ occurrence.b) Mean circumferential (E cc ) and radial strain (E rr ) violinplots for all cardiac segments between the five cardiac key frames for the ED2K and K2K approach (DMD57+DMD82).Neg: LGE-(blue), Pos: LGE+ (orange), asterisks indicate statistical significant differences without Holm-Bonferroni adjustment.Figure 1 and 2 in the Supplemental Material provide a detailed view split per segment.

and segments being significantly different between
LGE+ and LGE-segments, but pointed out the importance of diastolic strain differences between healthy and fibrotic myocardium.In summary, the FT -based strain curves with all values throughout the cardiac cycle did not reveal any significant segments.The FT -based peak strain (peak across all values) were significant in four segments, one segment for E rr and three for E cc .Compared to this clinically established baseline, the DLbased aligned ED2K derives eleven significant differences, two E rr and nine E cc segments.The sequential K2K approach facilitates a phase-specific compari-300 son, independent of previous deformations, revealing 301 22 significant differences -six in E rr and sixteen in 302 E cc segments.This enhanced discriminatory capabil-303 ity, resulting in five times more differences, is made 304 possible by the extraction of temporally aligned key 305 frames.to the traditional peak strain.In the sequential K2K 356 approach, we can assess each phase independently 357 of the preceding ones, including early systolic (ED-MS), late systolic (MS-ES), early diastolic (ES-PF), mid-diastolic (PF-MD), and late diastolic (MD-ED).Subsequent rows combine phase-specific strain values as downsampled representations of the entire cardiac cycle, and the metrics are reported for the ED2K and K2K approaches (cf. Figure 1 b).In the final rows, the n-th most frequently affected segments are selected, and only strain values from the significantly distinct phases observed in the DMD57 cohort (ED-MS, MS-ES, ES-PF) are incorporated.
A cross-validated grid-search (cf.Section 5.3) is applied to each of the different strain feature combinations to find a ML pipeline that generalise best for this feature-subset (cf.Table 2).On the crossvalidated DMD57 cohort most strain combinations achieved an accuracy > 70%.Within the FT -based experiments (first horizontal line) using all E rr values seem to be the best choice (acc: 75%).Unfortunately, either the sensitivity or the specificity is below 70%.Using the strain for a single cardiac phase (second horizontal line) enables an acc.> 80%.For the ED2K method strain from the early systolic phase (ED-MS) performs better than integrating further phases.The end-systolic (ED-ES) ED2K strain is comparable to the end-systolic strain from Morales et al. [14] and results in a similar balanced accuracy (E cc : 83%, E rr : 74%) on the validation splits.Incorporating the diastolic key frames yields a lower predictivity.In 75% of the cases E cc is more predictive and the early systolic phase (ED-MS) is more predictive than the late systolic phase (MS-ES).The most predictive single cardiac phase in the K2K method is the early diastolic phase (ES-PF) with a balanced acc. of 89% for the E cc .Combining the strain values of the five key frames (frames: 5K) improved the training scores but performed similar on the evaluation splits.The balanced acc. of the E cc is greater than 80% for all 5K experiments.The concluding section of the table displays experiments involving tasktailored strain features, derived from segment and key frame-specific investigations detailed in Section 2.2.Only strains from cardiac phases (ED2K : ED-ES and K2K : ED-MS, MS-ES, ES-PF) demonstrating significant differences in the DMD57 cohort are in-     LGE+ pLV EF patients is increased by +61% (17 of 25 are detected).This indicates that the aligned E cc strain is potentially better in detecting fibrosis in LGE+ pLV EF .However, 8 out of the 9 FN cases come from this group with fibrotic tissue but a preserved LVEF.

DL Modules
So far, the results referred to the potential value of key frame based aligned strain values.However, the validity and robustness of the intermediate modules of our pipeline (cf. Figure 2) can be underpinned by established module-specific metrics.Performance is evaluated in a stratified four-fold crossvalidation manner.Four models were trained (each with 75% of the DMD57 data) per DL-task (a: semantic segmentation, b: key-frame detection and c: the deformable registration).Minor adjustments were made to Seg2D (cf. Figure 4 a) and section 5.3) and KeyFrameDet (cf. Figure 4 b) and section 5.3).Mostly, the best parameters from the origi- Applying the methods from Table 2 that results in balanced accuracy > 80%, without further modifications, on the DMD82 to estimate the robustness of various strain combinations.FT : feature tracking baseline approach from the Circle cvi42 software, ED2K : End-diastole to key frames (aligned composed), K2K : key frame to key frame (aligned sequential), ED:end-systole, MS:mid-systole, ES:end-systole, PF:peak-flow, MD:mid-diastole, 5K:include five key frames, 3K,n-seg: include ED-MS,MS-ES,ES-PF and the n most frequent segments in DMD57 (cf.Fig. 3), Err: radial strain, Ecc: circumferential strain.Up-arrows indicate increasing quality at higher values.* For ten patients of DMD82 cohort the FT method was not able to derive strain values, thus these patients are excluded in the corresponding experiments.
nal publications [32,36] were used whenever possi-492 ble to avoid dataset-driven overfitting of the models.

493
In the Supplemental Material, the main parameters

Key Frame Detection Error
With respect to the key frame detection error we report the cyclic key frame difference [32] for all five key frames on the DMD57 dataset and for the ED and ES key frame on the ACDC dataset.In terms of key strain values (cf. Figure 1) that demonstrate su-560 perior predictive capabilities (cf.Table 2 and 3) when compared to strain values obtained using recent FT -based clinical software or recent unaligned Deep Learning methods [30].The authors in [30] state a disagreement < 1% compared to the circumferential end systolic strain values from the feature tracking approach (FT ) implemented in Circle cvi42 (cvi), indicating similar predictive capabilities.
The alignment of strain values in our approach enables detailed comparisons (cf.Table 3 and Figure 2 in the Supplemental Material) on a segment-bysegment and cardiac phase basis, leading to the identification of five times more significant differences in strain between patient groups.The introduction of novel sequential (K2K ) strain values (cf. Figure 1 and Sections 5.3 and 5.3) complements the approach, particularly during diastolic phases of interest in patients with myocardial scar but preserved LVEF (cf.significant segments in Table 3 in the Supplemental Material).The study found that sequential strain values provided a higher frequency of statistically significant differences between patient groups compared to traditional composed (ED2K ) strain values, especially during cardiac relaxation (significant segments: FT peak strain (4) vs ED2K (11) vs K2K ( 22)).
Leveraging the insights from the comparative analysis in Section 2.2, the authors developed a tasktailored and resilient strain feature set based on the insights from the DMD57 cohort in Section 2.3 capable of distinguishing between patients with and without myocardial fibrosis using standard CMR data alone.This approach was cross-validated on 57 patients with a sensitivity and specificity of 0.83 ± 0.11, 0.87 ± 0.08 and after model development black-box tested on the second held-out cohort (DMD82 ) with similar performance of 0.81 and 0.84 (cf.Tables 2  and 3).This pure inference scenario on a completely separated test set ensures that insights into the generalisation capability are given without potential bias introduced by just splitting a single cohort into train and test, which often leads to overoptimistic results due to model optimisation.Both cohorts consists of challenging CMR cases but no case was excluded in our pipeline (in total 20 bad cases and 70 cases of medium quality); 14 of these cases could not even be processed with a clinical software and had to be ex-cluded in the results for the state-of-the art feature 607 tracking method.

608
A significant performance drop could be observed 609 when performing an ablation experiment in the tem-610 poral domain.We limited the ED2K strain computa-611 tion to end-systolic strain and showed that only four 612 segments with significant differences could be iden-613 tified (ED to ES -cf.Table 2 and 3 3).Fur-616 thermore, the peak systolic E cc was only able to de-617 tect half of the LGE+ pLV EF patients (cf.Section  In this study we split the patients with DMD into binary groups of patients with LGE+ segments and without.This does neither reflect the amount of fibrosis per segment nor the total amount of fibrotic tissue on the myocardium.For treatment planning it is primary important if there is fibrotic tissue at all, which is reflected in our design.More detailed failing case analysis revealed that 8 out of the 9 falsely negative predicted cases from the aligned strain approach (Table 3, 2nd last row) belong to the group of LGE+ pLV EF , questioning the relationship of late gadolinium deposition and abnormal strain in some patients.Patients with minimal late gadolinium deposition in only a few cardiac segments, despite their involvement, may not necessarily display an 'abnormal' strain pattern, backing up the argument that strain is an interesting feature itself and that most of our false predictions can be explained, increasing trust into the approach.
Multiple studies have previously investigated areas of positive LGE in patients with DMD.Reported LGE patterns in DMD include LV inferolateral (AHA5,11), anterolateral (AHA6,12), inferior (AHA4,10) and other free wall segments [30,37].Hor et al. investigated the relationship among LGE, age and LVEF in a cohort of 314 patients with DMD.
LGE was present at a higher rate in the free wall compared to the septal wall (42.7% versus 5.3%).At base and mid-cavity, anterolateral, inferolateral, and inferior segments had the highest counts of LGE positivity (n=190,165,54) [39].According to Siegel et al., segments in DMD known not to develop LGE are located inferoseptal and anteroseptal [40].Figure 3 a confirms the localisation of LGE+ segments in general.Furthermore, this work extends the localisation by temporal information regarding the cardiac phases that are affected per segment.Hor et al. reported in a cohort of 70 patients with DMD and 16 controls that global mean circumferential strain decreased with advancing age.However, in this study, only the midventricular slice was investigated and peak strain was referred to as ED-ES strain [38].Also, in a cohort of 68 patients with DMD and 15 controls it was shown that LV free wall has the greatest decline of circumferential strain in older patients with DMD.There, the lateral free wall midcircumferential segments ex-   In this study, we combine two existing models: 792 Seg2D [44] for spatial grouping (cf.Section 5.3) and 793 the KeyFrameDet model [32] for temporal alignment (cf.Section 5.3).Additionally, we propose a deformable registration model (cf.DeformReg in Section 5.3) to predict two sets of temporally aligned 3D+t displacement fields from cine CMR sequences.One displacement field describes composite (ED2K ) motion from end-diastole (ED) to predefined cardiac key frames, while the other represents sequential motion (K2K ) from one key frame to the next (cf.Figure 1).We extend Morales et al.'s Green Lagrangian strain calculation method [14] to compute sequential myocardial strain with varying polar coordinate systems per apical, mid-cavity and basal area (35%, 35%, and 30% as suggested in [26]) from the displacement fields (cf.Section 5.3).Finally, we evaluate the strain values for myocardial scar detection using cross-validated grid search with approximately 2000 different machine-Learning methods/parameters.
The model is trained jointly on five 3D CMR volumes and masks, with the masks generated by Seg2D.This model produces two displacement fields: one for composed ϕ ED2k and one for sequential ϕ k2k displacement.These fields utilize grey value registration and anatomical guidance via the myocardium mask, demonstrating the motion in similar cardiac phases among patients.For this model, a 3D + K stack of CMR sequences is defined as X, where each 3D CMR volume is denoted as x ∈ X, and the corresponding 3D myocardial mask is denoted as s ∈ S, where x k and s k refer to a 3D CMR/mask at a specific cardiac key frame K ∈ [ED, M S, ES, P F, M D].
During training, the general registration task of ϕ, M = f θ (M, F ) is addressed, with M and F representing the moving and fixed volume pair, respectively.θ represents the learnable parameters of f , ϕ represents the learned discrete displacement field, and M represents the moved volume after the spatial transformer layer applies ϕ to M .Figure 5 provides a visual description of the registration process.One forward pass of DeformReg processes the whole 3D + k volume X simultaneously.This model processes X in one forward pass, and creates temporally consecutive moving (x k ) and fixed (x k−1 ) volume pairs.Figure 5 shows the general architecture.Two vector fields ϕ are learned.The first one is ϕ k2ED , which describes the composed deformation from x k (moving) to x ED (fixed).The second one is ϕ k2k , which reflects the sequential deformation from x k (moving) to the previous x k−1 (fixed).To ensure physiological plausibility, both deformation fields ϕ k2k and ϕ k2ED are additionally applied to the corresponding myocardial mask s k .The bilinear spatial transformer layers samples grey values from the target grid x ED or x k−1 , based on the discrete vector fields ϕ k2ED and ϕ k2k and solve the deformable registration task of the moving and fixed volume pairs.The learnt displacement fields ϕ are later treated as the voxel-wise 'forward' displacement or motion over time.The learning procedure comes from the three registration losses: Figure 5: DeformReg is designed to learn and predict both short-and long-distance displacement fields, denoted as ϕ, while incorporating anatomical guidance.
This loss component uses the spatial gradient of eight neighbouring voxels to enforce local smoothness of the displacement field, following the approach introduced by Balakrishnan et al. [48].
In response to the challenge of precise registration of myocardial tissue and its boundaries caused by variations in image brightness, we incorporate a modified Structural Similarity Index measure (SSIM) as robust image similarity loss component.This loss function assesses luminance, contrast, and structural features for the two fixed and moved volume pairs: (x ED , x k • ϕ k2ED ), (x k−1 , x k • ϕ k2k ).The original SSIM measure is only defined for 2D images.Here, L SSIM is defined as .
Here, f and m refer to one fixed and moving slice where ϵ = 1 is included for smoothing purposes.Lagrangian strain tensors from a displacement field.

953
The Vec2Strain module is an extension to the exist-954 ing approach that enables to derive sequential (K2K ) 955 strain values.

ML-based Fibrosis Detection
Finally, e) in Figure 4 refers to a feature selection and evaluation module (F eatureM L) that identifies predictive segments at cardiac phases for the task of detecting patients with myocardial fibrosis (LGE+ cf.Section 5.2).In order to quantify spatially mapped myocardial deformation at and between different cardiac key frames, the myocardium is divided into 16 segments, according to the definition of the American Heart Association (AHA) [26] and leaving out the most apical segment AHA17.Temporally down-sampled and aligned E rr and E cc values are acquired from the Vec2Strain module for ϕ k2ED and ϕ k2k .In summary, we can derive 320 strain values.In section 2.3 we report the results for various strain value combinations.During training, F eatureM L identifies AHA segments at cardiac phases that show significantly different strain values v n between LGE+/LGE-patients in the training subset.
A grid-search through more than 2000 different ML pipelines was performed to find a parameter combination that shows the best generalisation capabilities for each of the selected strain combinations.During inference, this module applies the same feature extraction and forwards the strain values for the segments and phases of interest to the trained ML model in order to get a binary classification as either LGE+ or LGE-.After the paper's acceptance, our GitHub repository, along with the experiment and model configuration files and detailed parameters, will be made publicly available.

Data Availability
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request and with appropriate data use agreement.Furthermore, on publication we will make our GitHub repository together with the detailed trainings parameter and config files publicly available.

108
ture tracking of segmented contours.3) Our compre-109 hensive analysis involves two cohorts comprising 139 110 (57+82) patients with the rare condition of DMD. 111 One cohort is used in a cross-validation manner for 112 model development and evaluation, while the other 113 was introduced thereafter to systematically test the 114 reproducibility of the approach on new clinical data.
compares the potential additional 117 value of aligned composed (ED2K ) and sequential 118 (K2K ) strain (cf.Figure 1 b).During development, 119 robust architectures were extensively sought after by 120 modifying three DL modules (cf.a-c in Figure 4 and 121 in Section 5.3).The intermediate measures for each 122 module of our final pipeline are reported briefly in 123 Section 2.4 in favour of a more detailed evaluation 124 regarding the potential value of aligned strain values 125 (cf.Sections 2.2 and 2.3).

126 2 . 1
Study Cohorts 127 This study was approved by the institutional re-128 view board of the HRPP designated reviewers at UT 129 Southwestern Medical Center, Dallas, Texas.The ex-130 empt criteria was met under 45 CFR 46.104(d).A 131 coverage analysis was not required.A clinical trial 132 agreement was not required.133 Two single-center cohorts of male patients with 134 DMD are investigated in our retrospective study.135 The patients in both cohorts underwent native CMR 136 and LGE examinations (cf.Section 5.2).Based 137 on the routine clinical reports cardiac segments are 138 labelled as either LGE-positive (LGE+) or LGE-139 negative (LGE-).The first sub-cohort (DMD57) con-140 sists of 57 patients and is used in a four-fold cross val-141 idation manner for model development and provides 142 additionally biventricular ground truth contouring at five distinct cardiac key frames together with the corresponding key frame indices (cf.Section 5.2).

196 2 . 2
Strain Analysis197 The study sought to assess the handling of challenges 198 in real clinical data, including extensive breathing 199 and motion artifacts.The CMR series from both 200 datasets underwent visual inspection.The following 201 brackets list the number of series per quality group, 202 the first number belongs to the DMD57 and the sec-203 ond to the DMD82 cohort.Images with no artifacts 204 are categorised as good (20 and 29), series with mod-205 erate artifacts in some slices or frames are consid-206 ered medium (30 and 40), and stacks with signifi-207 cant artifacts in nearly all slices or frames are la-208 beled as bad cases (7 and 13).Importantly, the study 209 did not exclude patients with poor data quality, and 210 it should be acknowledged that the feature-tracking 211 (FT ) based clinical software (cvi) could not provide proper strain values for 14 patients that had been neglected in the FT experiments.

Figure 3 b
) visually captures the distribution and ranges of the ED2K and K2K strain values across all patients and AHA segments.

306 2 . 3 Figure 1 b
Figure 1 b) for the task of detecting patients with 317 339 presents experiments incorporating both the entire 340 set of FT -based strain and the corresponding peak 341 strain baseline.The latter serves as a reference to 342 the method proposed by Morales et al. [14], given 343 their reported minimal discrepancies (< 1%) com-344 pared to the FT -based peak strain values from cvi. 345 All metrics express the validation score as the mean 346 ± standard deviation.The subsequent experiments 347 are based on the strain values from our work.We 348 begin our experiments by utilizing strain data from 349 specific phases (cf.Section 5.2), focusing on the dis-350 tinct information each phase offers.For the ED2K 351 approach, we compare the following phases: early 352 systolic (ED-MS), systolic (ED-ES), systolic + early 353 diastolic (ED-PF), and systolic + mid diastolic (ED-354 MD).Notably, the ED-ES phase exhibits similarity 355
in the supple-614 mental Material) with a balanced accuracy of 65% 615 on the DMD82 cohort (cf.row 6 in Table

618 2 .
3).In contrast, the aligned E cc strain resulted in 619 50% less FN cases and was able to identify +61% 620 of the LGE+ pLV EF .The improved predictive ca-621 pabilities of aligned strain to detect patients with 622 preserved LVEF and maybe less 'abnormal' systolic 623 deformations highlights the advantage of integrat-624 ing several aligned temporal strain values into the 625 decision-making process.The superior performance 626 potentially results from the fact that the same phe-627 nomenon (abnormal deformation) can be observed in 628 multiple phases leading to a more stable classifica-629 tion, and/or the information on (subtle) changes in 630 deformation only evident in single, potentially non-631 endsystolic phases, is now integrated.In contrast to 632 many prior work [14, 33, 24, 38, 29], strain values 633 at various cardiac phases are automatically detected 634 through a self-supervised approach [32] for further 635 processing without the necessity of prior handpick-636 ing of a specific phase.This makes the approach more 637 flexible and general, as different diseases certainly re-638 quire tailored combinations of strain features to reach 639 a high level of accuracy.640 Segmentation and key frame detection errors have 641 an impact on the overall performance of the classi-642 fier.The biventricular segmentation model usually 643 performs better on ED frames [37], which is an addi-644 tional challenge for the sequential strain computation 645 (K2K ) as it requires the creation of new AHA seg-646 ment masks at each key frame.However, in our single 647 experiments we could show that the approaches are 648 robust (cf.Section 2.4) and especially the choice of a 649 self-supervised approach is powerful with respect to 650 translation to other cohorts where no temporal labels 651 are given. 652

Figure 4 :
Figure 4: Overview of the individual modules of the Aligned strain value derivation pipeline for abnormal deformation detection (cf.Section 5.3).The modules a), b), and c) are represented by Deep Learning models.Module d) involves the calculation of Green Lagrangian strain tensors from dense displacement fields incorporating specialised basal, mid-cavity and apical polar coordinate systems, and e) encompasses a segment and phase specific strain feature exploration component along with a classical Machine Learning backbone that detects individuals with myocardial fibrosis in a cohort of patients with DMD.

788 5 . 3
Model definition 789An automatic pipeline is proposed (cf.Fig.4) with 790 the following modules. 791 ) , where n belongs to the set [k2ED, k2k].S F 898 and S M are the concatenated fixed and moving mask 899 pairs associated to the composed and sequential dis-900 placement fields ϕ k2ED and ϕ k2k .Each image sim-901 ilarity loss component and its corresponding regu-902 lariser are assigned unique weights to control their 903 influence on the learning process, denoted as λ k2ED , 904 λ k2k , λ DICE , and λ reg .These losses propagate their 905 gradients back into the same encoder and optimise 906 simultaneously to account for both short-and long-907 distance deformations while adhering to anatomical 908 structure and smoothness constraints.A consistent smoothness regulariser L s (ϕ) is part of the three registration losses:

928 pair in x k− 1 929 while σ 2 f and σ 2 m
and x k , µ f and µ m represent the average, represent the variance of a N × N 930 region in f and m. σ f m is the co-variance of f and 931 m, and ϵ 1 and ϵ 2 are variables introduced to prevent 932 instability.The parameters are chosen as defined in 933 the original paper [49].The same image similarity 934 measure is used to learn the traditional composed 935 displacement field ϕ k2ED in Eq. 2. 936 For anatomical regularisation of the deformation 937 fields, a DICE component, as introduced by Milletari 938 et al. [50], is employed as image similarity measure 939 for the myocardial mask s k and the moving counter-940 part s k−1 • ϕ k2k : 941 L DICE (s k , s k−1 • ϕ k2k ) = 1 − 2 × |s k ∩ (s k−1 • ϕ k2k )| + ϵ (|s k | + |s k−1 • ϕ k2k |) + ϵ ,

942943
Vector2strainFollowed by d) (cf.Figure4), a Vector2strain 944 module (Vec2Strain) that interprets ϕ k2k and ϕ k2ED 945 and derives the voxel-wise radial and circumferential 946 strain (E rr /E cc ) over time.E rr and E cc values are 947 then assigned and averaged for the 16 AHA segments.948 This results in 16 segmental strain values for each 949 ED2K and K2K strain measurement, each of which is 950 temporally aligned due to K across patients.Morales 951 et al. [14] proposed a solution to calculate the Green952

Table 1 :
Characteristics of the two DMD cohorts.
tistically significant differences between LGE+ and

Table 2 :
Binary classification of patients as LGE+ or LGEmean values for the cross-validation splits of the DMD57 cohort Mean±SD validation measures for the four folds of DM D57 cv

Table 3
Deep learning based peak systolic E cc on the DMD82 cohort (cf.row six in Table3): 33 true positive (TP, LGE+ classified as LGE+), 12 false positive (FP, LGE-classified as LGE+), 19 true negative (TN, LGE-, classified as LGE-), 18 false negative (FN, LGE+ classified as LGE-).From the 18 FN cases, 13 patients have fibrotic segments but showed a normal LVEF (LGE+ pLV EF ), indicating that most FN cases are from this group and second the peak systolic strain seems not a sufficient marker to detect fibrosis in this patient group (only 52% are detected).Deep Learning based aligned E cc strain feature on the DMD82 cohort (cf.2nd last row in Table3): 42 TP, 6 FP, 25 TN, 9 FN and from the 9 FN cases, 8 belong to the LGE+ pLV EF group.Compared with the Peak systolic E cc strain the number of detected 418ducibility scenario in Table3.Those strain com-419 binations that resulted in a ML model with an av-420 erage balanced accuracy higher than 80% were se-421 lected together with the strain experiments from the 422 FT -based method to evaluate their reproducibility on 423 new clinical data.The reproducibility cohort DMD82 424 is processed by the chained and fixed pipeline of DL-425 models (FrameDet • Seg2D • DeformReg; cf.Figure4264 and Section 5.3), the corresponding feature selec-427 tion approach and the fitted ML pipeline (cf.Section 428 5.3).429The experiments with the FT values dropped to a 430 balanced accuracy < 60%.Interestingly, the strain 431 values of the early systolic phase (ES-MS) in the 432 ED2K approach are more robust (acc.: 77%) than 433 the peak strain from ED to ES (acc.: 65%).Further-434 more, from the distinct phase experiments (K2K ) 435 the diastolic phases ES-PF and MD-ED showed a 436 smaller generalisation gap than the systolic phases.437Theearly diastolic (ES-PF) K2K strain is still the