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Integration of longitudinal and circumferential strain predicts volumetric change across the cardiac cycle and differentiates patients along the heart failure continuum
Journal of Cardiovascular Magnetic Resonance volume 25, Article number: 55 (2023)
Abstract
Background
Left ventricular (LV) circumferential and longitudinal strain provide important insight into LV mechanics and function, each contributing to volumetric changes throughout the cardiac cycle. We sought to explore this strainvolume relationship in more detail, by mathematically integrating circumferential and longitudinal strain and strain rate to predict LV volume and volumetric rates of change.
Methods
Cardiac magnetic resonance (CMR) imaging from 229 participants from the Alberta HEART Study (46 healthy controls, 77 individuals at risk for developing heart failure [HF], 70 patients with diagnosed HF with preserved ejection fraction [HFpEF], and 36 patients with diagnosed HF with reduced ejection fraction [HFrEF]) were evaluated. LV volume was assessed by the method of disks and strain/strain rate were assessed by CMR feature tracking.
Results
Integrating endocardial circumferential and longitudinal strain provided a close approximation of LV ejection fraction (EF_{Strain}), when compared to goldstandard volumetric assessment (EF_{Volume}: r = 0.94, P < 0.0001). Likewise, integrating circumferential and longitudinal strain rate provided a close approximation of peak ejection and peak filling rates (PER_{Strain} and PFR_{Strain}, respectively) compared to their goldstandard volumetime equivalents (PER_{Volume}, r = 0.73, P < 0.0001 and PFR_{Volume}, r = 0.78, P < 0.0001, respectively). Moreover, each integrated strain measure differentiated patients across the HF continuum (all P < 0.01), with the HFrEF group having worse EF_{Strain}, PER_{Strain}, and PFR_{Strain} compared to all other groups, and HFpEF having less favorable EF_{Strain} and PFR_{Strain} compared to both atrisk and control groups.
Conclusions
The data herein establish the theoretical framework for integrating discrete strain components into volumetric measurements across the cardiac cycle, and highlight the potential benefit of this approach for differentiating patients along the heart failure continuum.
Background
The importance of evaluating left ventricular (LV) strain in clinical imaging studies of patients across the heart failure (HF) continuum is well established [1,2,3], with strain often outperforming volumetric measures, such as ejection fraction, for risk prediction [4,5,6]. However, the integrated effects of strain ultimately determine volumetric function and thus it is important to understand the relationship between the distinct strain components and volume changes. Due to the unique muscle fiber orientation of the LV, tissue deformation occurs in well characterized complex patterns [7,8,9] which results in the shortening and lengthening of the myocardial borders in the circumferential and longitudinal direction (i.e. circumferential and longitudinal strain) [9,10,11,12]. Circumferential and longitudinal strains on the endocardial surface, in particular, determine the changes in LV volume across the cardiac cycle [13,14,15,16]. Indeed, changes in volume of a prolate ellipsoid (the shape of LV) are linearly related to changes in chamber length and quadratically related to changes in chamber circumference [15,16,17]. This strainvolume relationship helps to explain how ejection fraction can be maintained despite abnormalities in systolic strain for one component [15, 18], and informs the relative contributions of each strain component to volumetric function.
Despite a general appreciation for this strainvolume relationship, this concept has yet to translate to clinical populations or to relate systolic and diastolic strain rates to volumetric patterns of ejection and filling, respectively. As such, we leveraged a database of cardiac magnetic resonance (CMR) imaging from individuals along the HF continuum enrolled from the University of Alberta site of the Alberta Heart Study [19] to test the hypothesis that measures of systolic and diastolic function (LV ejection fraction, peak filling rate and peak ejection rate) derived from circumferential and longitudinal strain (a) correlate to goldstandard volumetime relationships, and (b) differentiate patients along the heart failure continuum.
Methods
Study population
The Alberta Heart Study (NCT02052804)[19] was approved by the Health Research Ethics Boards at the University of Alberta, University of Calgary, and Covenant Health, and written informed consent was obtained prior to data collection. This substudy of the larger clinical trial only included individuals enrolled from the University of Alberta site of the larger trial so that study procedures were uniformly performed on the same CMR scanner with the same acquisition parameters. Patients were subdivided into four groups (Table 1): (1) Healthy control participants with no evidence of coronary artery disease, hypertension, diabetes mellitus, organ disease or replacement therapies; inflammatory or autoimmune conditions, and no history of cardiac medications. (2) Participants at risk for the development of HF, with either hypertension (defined as ≥ 3 medications or LV hypertrophy as evidenced by an electrocardiogram or by elevated gendermatched LV mass index on an imaging test), and/or history of diabetes and > 45 years of age, and/or presence of obesity (defined as body mass index > 30 kg/m^{2}). Exclusion criteria included signs and symptoms of HF (i.e. dyspnea or fatigue) and known prior HF. (3) Patients with clinically diagnosed HF with preserved ejection fraction (HFpEF) with a LV ejection fraction > 45%. (4) Patients with clinically diagnosed HF with reduced ejection fraction (HFrEF) and a LV ejection fraction < 45%.
CMR protocol
All CMR examinations were performed utilizing a 1.5T clinical MRI system (Sonata; Siemens Medical Solutions, Erlangen, Germany), and all image acquisitions were retrospectively gated using an electrocardiogram and performed during breathholds at endexpiration. LV morphology and function were measured from a series of shortaxis balanced steadystate free precession cine images spanning the entire LV, along with two and fourchamber longaxis images. Typical imaging parameters were: slice thickness of 8 mm with 2 mm gap between slices, echo time of 1.3 ms, repetition time of 2.6 ms, flip angle of 51°, field of view of 300×400 mm, and matrix size of 144 × 256, 930 Hz/pixel bandwidth, rate 2 GRAPPA parallel imaging and 10–14 views per segment reconstructed to 30 phases over the cardiac cycle for an acquired temporal resolution of 29–40 ms.
Enddiastolic and endsystolic LV volumes and mass were measured using commercially available image analysis software, Syngo Argus, (Siemens Healthineers) by an experienced CMR interpreter (I.P.). In a subset of individuals (n = 79), LV volumetime relationships were determined, using commercially available software (version 5.6.8 cvi^{42}; Circle Cardiovascular Imaging Inc., Calgary, Alberta, Canada), by manually delineating the endocardial borders of each shortaxis slice at enddiastole, and during each cardiac phase between endsystole and diastasis by a single blinded interpreter (T.J.S.), as previously described [20]. The LV basal and apical boundaries were identified using the longaxis views to further define the extent of the LV chamber. Papillary muscles and trabeculae were included as part of the ventricular lumen. LV volumes were calculated by the summation of the volumes for each shortaxis slice. PER_{Volume} and PFR_{Volume} were defined as the maximal LV volumetric change between sequential temporal phases, normalized to the LV enddiastolic volume [20].
Endocardial strain and strain rate
Global endocardial LV strain/strain rate were assessed using commercially available software (version 5.13 cvi^{42}; Circle Cardiovascular Imaging Inc., Calgary, Alberta, Canada), modified by the developers to export strain values derived from the endocardial border. Briefly, the endocardial and epicardial borders of the LV were manually traced at enddiastole and endsystole using a series of shortaxis cines spanning the LV from base to apex, along with a horizonal long axis image (4chamber) and vertical long axis image (2chamber). The most basal shortaxis slices that included LV outflow tract and the most apical slices without clear delineation of the luminal border were excluded from the analysis. Following this, the feature tracking algorithm was applied, and quality of tracking was confirmed throughout the whole cardiac cycle. Feature tracking analysis was performed by a single experienced interpreter (M.D.N), blinded to the clinical condition of each participant. Intraobserver reliability, expressed as the mean ± SD of the coefficient of variation, are as follows: circumferential strain, 1.3 ± 1.0%; systolic circumferential strain rate, 4.9 ± 7.4%; early diastolic circumferential strain rate, 3.4 ± 2.5%; late diastolic circumferential strain rate, 3.9 ± 3.8; longitudinal strain, 4.1 ± 4.2%; systolic longitudinal strain rate, 6.7 ± 7.6%; and early diastolic longitudinal strain rate, 6.4 ± 3.9%. Interobserver reliability, expressed as the mean ± SD of the coefficient of variation, are as follows: circumferential strain, 4.8 ± 5.0%; systolic circumferential strain rate, 6.9 ± 7.7%; early diastolic circumferential strain rate, 4.4 ± 7.1%; late diastolic circumferential strain rate, 4.6 ± 3.2; longitudinal strain, 4.7% ± 5.7%; systolic longitudinal strain rate, 7.0 ± 6.0%; and early diastolic longitudinal strain rate, 8.5 ± 7.7%.
Integrated strain and strain rate
We used the integration of both circumferential and longitudinal endocardial strain and strain rate to calculate LV ejection fraction (EF_{Strain}), the peak ejection rate (PER_{Strain}), and peak filling rate (PFR_{Strain}) based on the following theoretical framework:
where V is LV volume, k is a shape constant, C is the basal shortaxis circumference, and L is LV length. This approximate volume is used here only to represent the linear and quadratic contributions of length and circumference to volume, respectively. Based on Eq. 1, LV EF can be calculated by,
where EDV and ESV are the LV enddiastolic and endsystolic volume, respectively. As, peak longitudinal and circumferential strain (LS and CS, respectively) are calculated as:
where, L_{0} and C_{0} represent lengths at enddiastole and L_{1} and C_{1} represent lengths at endsystole, you can solve for L_{ESV} and C_{ESV} by the following:
Substituting these formulas into Eq. 2 gives,
which is simplified to,
where LS and CS represent peak longitudinal strain (average of the 2 and 4chamber long axis images) and peak circumferential strain (average of the two most basal LV slices that do not contain LV outflow tract), expressed as absolute decimal values, respectively. Briefly, Eq. 7 links the commonly measured fractional changes in linear dimensions of the heart (length and circumference) to corresponding fractional change in volume, which is the ejection fraction.
EF is the volumetric analog to peak systolic strain, and like strain has a value throughout the cardiac cycle, EF(t), and similarly the time rate of change of EF(t) is akin to strain rate, at any time in the cardiac cycle, based on the rate of change of the ventricular volume.
V(t) is LV volume at any point in time, V_{0} is the initial (enddiastolic) volume, dEF(t)/dt is the time derivative of EF(t) at a given point in time, and dV(t)/dt is the time derivative of volume at a given time. Equation 8 shows that dEF(t)/dt is the rate of change of volume (i.e. ejection rate during systole and filling rate during diastole), normalized to peak volume (enddiastolic volume). Normalization of filling rates by V_{0} in this representation corrects for the effects of heart size on filling rates, and maintains the units of strain rate (/s) [21].
LV strain and strain rate can be related to the normalized filling rate dEF(t)/dt using the volume model introduced above:
Using the Lagrangian strain relationship in Eqs. 3 and 4 one can write,
where CSR is the circumferential strain rate derived using all available shortaxis slices and LSR is longitudinal strain rate.
Substituting Eqs. 9 and 10 in Eq. 8, volumetric rates of change can be calculated as:
and thus, the normalized PER_{Strain} and PFR_{Strain} can be estimated from longitudinal and circumferential strains and strain rates. Similar to Eq. 7 above, Eq. 11 links the commonly measured fractional changes in linear dimensions of the heart (length and circumference) and their rates of change (i.e. strain rates) to the corresponding rates of volume change. Importantly, dEF(t)/dt in Eq. 11, like the strains and strain rates it is derived from, is a normalized measure of volumetric function that is independent of the heart volume, with units of (s^{−1}), similar to strain rates. PER_{Strain} was determined as the peak rate of blood ejection during systole and PFR_{Strain} was determined as the peak rate of volumetric filling in early diastole, equivalent to the s’ and e’ on the integrated strain curve, respectively.
Statistical analysis
All statistical analyses were performed using SPSS (version 25, IBM SPSS Statistics, Armonk, NY) and GraphPad Prism (version 9.3.1, GraphPad Software, San Diego, CA). Our first hypothesis was that EF_{Strain}, PER_{Strain} and PFR_{Strain} correlate to gold standard EF_{Volume}, PER_{Volume} and PFR_{Volume}. We tested this, in a subset of randomly selected participants (n = 79), using Pearson’s or Spearman’s correlation, as appropriate, and Bland–Altman plots.
To test our second hypothesis that EF_{Strain}, PER_{Strain} and PFR_{Strain} could differentiate between patients along the HF continuum, group differences were assessed across the entire cohort of individuals (n = 229) by oneway analysis of variance or the Kruskal–Wallis test, as appropriate. Tukey’s and Dunn’s posthoc corrections were performed when significant group main effects were observed in normally and nonnormally distributed variables, respectively.
Categorical data were assessed by the Pearson’s chisquared test after adjusting for multiple comparisons and presented as counts and percentages. Normal distribution and homoscedasticity were assessed with the Shapiro–Wilk test. Continuous data are presented as means ± standard deviation when normally distributed and median and interquartile range when not. The study alpha was set to α = 0.05.
Results
Participant characteristics for the validation cohort are shown in Table 1.
EF_{Strain} was closely related to EF_{Volume} (r = 0.94, P < 0.0001; Fig. 1), with a bias of 0.56% (95%CI: 10.7 to 9.6%). Likewise, PER_{Strain} and PFR_{Strain} were moderately related to their volumetime equivalents PER_{Volume} and PFR_{Volume} (r = 0.73, P < 0.0001 and r = 0.78, P < 0.0001, Fig. 2), with a bias of − 0.017 s^{−1} (95%CI: − 1.10 to 1.07 s^{−1}) and 0.33 s^{−1} (95%CI: − 0.74 to 1.41 s^{−1}), respectively.
The integrated strain approach was then applied across the entire cohort, with the patient characteristics, LV morphology and individual strain components for each of the groups found in Tables 2 and 3. EF_{Strain}, PER_{Strain}, and PFR_{Strain} successfully differentiated patients along the HF continuum (Fig. 3A–C), with HFrEF patients demonstrating worse EF_{Strain}, PER_{Strain}, and PFR_{Strain} than all other groups, and HFpEF having less favorable EF_{Strain} and PFR_{Strain} compared to both AtRisk and controls.
Discussion
Circumferential and longitudinal deformation of the LV occurs simultaneously in systole and diastole, with each component contributing to LV ejection and filling, respectively. Here, we extend previous literature examining this strainvolume relationship, by showing that LV ejection fraction, along with peak ejection and peak filling rates, can be accurately derived by integrating discrete strain components along the cardiac cycle. The utility of this approach is highlighted by demonstrating that each integrated component effectively differentiates participants along the HF continuum.
Impaired LV strain is a wellestablished indicator of poor clinical status in a variety of populations [15, 18, 22,23,24]. However, interpretation of LV strain is often complicated when one principal strain component is elevated while the other is reduced [15, 18, 25, 26]. The potential major advantage of integrating circumferential and longitudinal strain to calculate LV ejection fraction, over conventional discrete strain approaches, is that both measures are condensed into a single measure of overall LV volumetric function. Indeed, LV ejection fraction is the product of circumferential and longitudinal tissue deformation, each contributing independently to volumetric changes across the cardiac cycle. This strainvolume relationship therefore helps to explain how ejection fraction can be maintained (or even increase) despite abnormalities in systolic strain in one direction [15, 18], providing valuable insight into the relative contributions of each strain component to volumetric function (as illustrated in Fig. 4).
The integration of circumferential and longitudinal strain rates to predict peak ejection and peak filling rates extends prior reports that have focused only on LV ejection fraction [13,14,15,16]. While the clinical utility of assessing peak ejection and peak filling rates is well established [20, 21, 27,28,29,30,31,32,33], the approach is typically dependent upon either invasive LV catheterization methods [21, 29] or on manual contouring of images of the LV to generate volumetime relationships [20, 27]. Indeed, invasive LV hemodynamic assessment is associated with high risk and is often not feasible in many clinical and subclinical populations. While noninvasive assessment of volumetric ejection and filling rates using imagebased volumetime curves avoids many of these limitations, this approach is timeconsuming and highly userdependent, reducing its overall clinical utility and feasibility. Thus, the proposed integrated strain approach offers a major advantage, given that most strain analysis is semiautomated, with minimal user input. Integrating circumferential and longitudinal strain rates is also attractive because it has the potential to reduce the overall number of endpoint measurements reported and expresses the results in volume normalized units of measure.
Experimental Considerations. The theoretical framework for which the integrated strain concept is based is specific for endocardial strain and strain rates only. Indeed, due to the gradual change in fiber orientation and associated strain seen from the LV endocardial to midwall layers [7, 10,11,12], inclusion of information not exclusive to the endocardial border invalidates the mathematical assumptions of the current work. This is important, because strain is typically reported as a transmural strain. However, strain outputs denoted as “endocardial” often do not reflect strain from the endocardial border, but rather a region of myocardium from the endocardiumtomidwall (e.g. 33% of the inner LV layer). Future studies wishing to adopt this integrated strain approach should therefore be cognizant of this important distinction.
Limitations
The sample size was relatively small, and it remains unknown whether integrating strain is superior for predicting clinical outcomes compared to traditional (discrete) global strain measures. However, these hypothesis generating results show that the integrated strain approach can successfully differentiate patients along the heart failure continuum, highlighting it’s clinical potential.
Conclusions
With these considerations in mind, the data herein establish the theoretical framework for integrating discrete strain components into a single measure of LV ejection and filling rate. The data show that LV ejection fraction, along with peak ejection and peak filling rates, can be accurately derived by integrating discrete strain components along the cardiac cycle. The utility of this approach is highlighted by demonstrating that each integrated component effectively differentiates participants along the HF continuum.
Availability of data and materials
The datasets generated during and/or analyzed during the current study are not publicly available as data analysis remains ongoing but are available from the corresponding author on reasonable request.
Abbreviations
 CMR:

Cardiac magnetic resonance
 EF_{Strain} :

Ejection fraction from the integrated strain approach
 EF_{Volume} :

Ejection fraction from the volumetime relationship
 HF:

Heart failure
 HFpEF:

Heart failure with preserved ejection fraction
 HFrEF:

Heart failure with reduced ejection fraction
 LV:

Left ventricular
 PER_{Strain} :

Peak ejection rate from the integrated strain approach
 PER_{Volume} :

Peak ejection rate from the volumetime relationship
 PFR_{Strain} :

Peak filling rate from the integrated strain approach
 PFR_{Volume} :

Peak filling rate from the volumetime relationship
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Funding
National Institutes of Health (R01HL136601); American Heart Association (18PRE33960358, 835833); Alberta InnovatesHealth Solutions (AIHS, grant #AHFMR ITG 200801018). Alberta Health Services and Alberta HEART investigators kindly contributed to this study.
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TJS analyzed and interpreted the data, wrote the initial draft of the manuscript. APO analyzed and interpreted the data and contributed to editing the manuscript. DJC provided statistical support for the data analysis. JAE, JRD, TA, JGH, DIP contributed to the collection of the patient data, helped interpret the data and edit the manuscript. RBT and MDN contributed to the conception and design of the study, data analysis and interpretation and drafting of the manuscript. All authors read and approved the final manuscript.
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Samuel, T.J., Oneglia, A.P., Cipher, D.J. et al. Integration of longitudinal and circumferential strain predicts volumetric change across the cardiac cycle and differentiates patients along the heart failure continuum. J Cardiovasc Magn Reson 25, 55 (2023). https://doi.org/10.1186/s12968023009692
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DOI: https://doi.org/10.1186/s12968023009692