# Geometry as a Confounder When Assessing Ventricular Systolic FunctionComparison Between Ejection Fraction and Strain

## Author + information

- Received February 27, 2017
- Revision received June 16, 2017
- Accepted June 18, 2017
- Published online August 14, 2017.

## Author Information

- Thomas M. Stokke, MD
^{a},^{b},^{c},^{d}, - Nina E. Hasselberg, MD, PhD
^{a},^{b},^{c}, - Marit K. Smedsrud, MD, PhD
^{b},^{c}, - Sebastian I. Sarvari, MD, PhD
^{a},^{b},^{c}, - Kristina H. Haugaa, MD, PhD
^{a},^{b},^{c}, - Otto A. Smiseth, MD, PhD
^{a},^{b},^{c},^{d}, - Thor Edvardsen, MD, PhD
^{a},^{b},^{c},^{d}and - Espen W. Remme, MSc, Dr-Ing
^{a},^{b},^{c},^{d},^{∗}(espen.remme{at}medisin.uio.no)

^{a}Department of Cardiology, Oslo University Hospital, Rikshospitalet, Oslo, Norway^{b}Center for Cardiological Innovation, Oslo University Hospital, Rikshospitalet, Oslo, Norway^{c}Institute for Surgical Research, Oslo University Hospital, Rikshospitalet, Oslo, Norway^{d}Institute of Clinical Medicine, Faculty of Medicine, University of Oslo, Oslo, Norway

- ↵∗
**Address for correspondence:**

Dr. Espen W. Remme, Institute for Surgical Research, Oslo University Hospital, Rikshospitalet, Postboks 4950 Nydalen, 0424 Oslo, Norway.

## Central Illustration

## Abstract

**Background** Preserved left ventricular (LV) ejection fraction (EF) and reduced myocardial strain are reported in patients with hypertrophic cardiomyopathy, ischemic heart disease, diabetes mellitus, and more.

**Objectives** The authors performed a combined mathematical and echocardiographic study to understand the inconsistencies between EF and strains.

**Methods** An analytical equation showing the relationship between EF and the 4 parameters, global longitudinal strain (GLS), global circumferential strain (GCS), wall thickness, and short-axis diameter, was derived from an elliptical LV model. The equation was validated by measuring the 4 parameters by echocardiography in 100 subjects with EF ranging from 16% to 72% and comparing model-predicted EF with measured EF. The effect of the different parameters on EF was explored in the model and compared with findings in the patients.

**Results** Calculated EF had very good agreement with measured EF (r = 0.95). The model showed that GCS contributes more than twice as much to EF than GLS. A significant reduction of GLS could be compensated by a small increase of GCS or wall thickness or reduced diameter. The model further demonstrated how EF can be maintained in ventricles with increased wall thickness or reduced diameter, despite reductions in both longitudinal and circumferential shortening. This was consistent with similar EF in 20 control subjects and 20 hypertrophic cardiomyopathy patients with increased wall thickness and reductions in both circumferential and longitudinal shortening (all p < 0.01).

**Conclusions** Reduced deformation despite preserved EF can be explained through geometric factors. Due to geometric confounders, strain better reflects systolic function in patients with preserved EF.

Numerous studies have reported a significant reduction in left ventricular (LV) global longitudinal strain (GLS) without a corresponding reduction of LV ejection fraction (EF) in various study populations, including patients with heart failure with preserved EF, coronary artery disease (CAD), diabetes mellitus, hypertensive heart disease, hypertrophic cardiomyopathy (HCM), and electrical disease (1–6).

The majority of longitudinally-oriented fibers are located in the subendocardium, which is considered most susceptible to myocardial disease, including ischemia. Many studies have shown that GLS detects subtle longitudinal abnormalities that do not affect EF globally (7). It remains uncertain, however, whether a small loss of longitudinal function per se is negligible for global pump function or if compensatory effects by other determinants of EF are responsible for preserving EF. A common hypothesis is that circumferential fibers in the midwall, if intact, may compensate for the loss of longitudinal mechanics to preserve LV pump function and EF (7,8). However, several studies report a significant reduction in both GLS and global circumferential strain (GCS), despite normal LVEF (1,9,10). The mechanism maintaining EF in this setting is unclear. MacIver (11,12) has proposed a geometric explanation for this apparent paradox: using a computational model of a truncated ellipsoid, he showed that increased wall thickness could effectively preserve EF. However, the computational model was not validated, and the effect of other geometric factors on EF remains incompletely described.

The general objective was, therefore, to perform a comprehensive study of the individual geometric factors that influence EF by combining clinical data from speckle tracking echocardiography and mathematical modeling.

Two specific objectives of this study were to investigate if:

1. The contribution of longitudinal shortening to EF is so small that reduced longitudinal shortening can be compensated by small changes in other factors to preserve EF; and

2. EF can be preserved, despite reductions in both longitudinal and circumferential shortening in LVs with increased wall thickness and/or reduced end-diastolic volume (EDV).

## Methods

### Patient study

Echocardiographic examinations from 100 subjects were retrospectively included. The study population was heterogeneous to represent a wide range of EF values: 20 patients had significant CAD; 20 patients had angina pectoris without significant CAD; 20 patients had dilated cardiomyopathy (DCM); 20 patients had HCM; and 20 subjects were healthy individuals (Table 1). The inclusion criteria were adequate image quality in 3 apical views (4-chamber, 2-chamber, and long-axis) and at least 2 parasternal short-axis views (mitral valve, midventricle, and/or apical levels). Patients with exclusion of more than 6 of 18 strain segments in either apical or parasternal views were excluded. Written informed consent was obtained from all subjects.

### Echocardiography

Two-dimensional grayscale echocardiography was performed with Vivid 7 or E9 scanners (GE Vingmed Ultrasound, Horten, Norway). The frame rate was >50/s. Images were analyzed using EchoPAC version 112 (GE Vingmed Ultrasound). LV diameter and wall thickness were obtained by M-mode measurements or 2-dimensional mode. LVEF was calculated by 1 operator (SIS) using the modified Simpson’s rule based on 4- and 2-chamber images (13).

Myocardial strain was measured by another operator (TMS), blinded to EF calculations, using 2-dimensional speckle-tracking echocardiography in accordance with current recommendations (14). The endocardial border was traced at end-systole, and the thickness of the region of interest (ROI) was adjusted to include most of the myocardium, but avoiding stationary speckles close to the pericardium. Longitudinal strain was measured in the 3 apical views, and circumferential strain was measured in the 3 short-axis views. All segmental strain values were measured from the same frame in end-systole, defined by the aortic valve closure in apical long-axis view. Strains were assessed at end-systole, as this is the time when minimum volume is assessed and there is a direct geometric link between EF and strains. Strain values from the 18 LV segments were averaged to GLS and GCS.

### LV model

We modeled the LV as a thick-walled, truncated ellipsoid (Figure 1A) (15), and derived the analytical mathematical relation for EF as a function of GLS, GCS, end-diastolic (ED) LV wall thickness (w), and ED short-axis diameter (d), as shown in Equation 1 (Online Appendix 1 shows how the equation was derived):

The speckle tracking ROI is placed manually, and its center may not be exactly at the midwall. In the model, we therefore included a factor (f) with value between 0 and 1 to prescribe the actual center of the ROI between the endocardium (f = 0) and epicardium (f = 1) for the individual patient (Figure 1B). Commonly, the epicardial ROI border is drawn inside stationary speckles close to the pericardium, whereas the endocardial ROI border is drawn inside the typically distinct and easily trackable speckle pattern in the subendocardial region. This shifts the center of ROI inward from the midwall. The f value was “eyeballed” in each of the 6 projections, and the average was used as input in the equation. The default value of f = 0.33 was accepted for most patients and was consequently used as a default value in the model simulations.

Shortening in the circumferential and longitudinal directions results in wall thickening, which contributes to ejection. The magnitude of wall thickening depends on the degree of myocardial compressibility. As pressure increases during systole, some myocardial blood is squeezed out of the wall, effectively compressing the wall (16); a 5% to 10% reduction in myocardial volume during systole has been reported (17). We consequently included a compressibility constant, c, in the model to incorporate this effect. It was set to 0.95, which means that the myocardial volume was assumed to shrink 5% during systole.

For the convenience of other investigators, the equation is implemented in Online Appendix 2.

### Model validation

The derived mathematical relation in Equation 1 was validated with clinical echocardiographic data by comparing the EF predicted by the model (EF_{model}) with the measured EF (EF_{measured}). For model prediction, the measured GLS, GCS, wall thickness, and short-axis diameter were used as input variables for Equation 1.

### Influence of GLS on EF

The derived equation was used to assess the effect of GLS on EF. The contribution of GLS to EF was found from plotting EF as function of an isolated change in GLS, keeping the 3 other parameters (GCS, wall thickness, and short-axis diameter) constant. This was compared to a similar analysis of the effect of GCS on EF.

EF may be unaffected if a reduction in longitudinal shortening is compensated by a change in 1 of the other parameters. We quantified the isolated change required in GCS, wall thickness, or diameter to keep EF unchanged if GLS was reduced. For this purpose, Equation 1 was reformulated and solved for GCS, w, or d, respectively. Subsequently, the derivative with respect to GLS was assessed. This derivative quantified the required change in GCS, w, or d to keep EF constant for a given change in GLS.

A change in ED short-axis diameter corresponds to a change in EDV. It may be more intuitive to understand how EF relates to EDV than diameter. We therefore report the corresponding change in volume for changes in diameter. The volume of the ellipsoid model (15) is:

### Preserved EF with both reduced longitudinal and circumferential shortening

We further investigated how wall thickness or EDV could be altered to maintain EF in a setting with reductions in both longitudinal and circumferential shortening. The model was used to plot EF as a function of GCS = GLS for cases with increasing wall thickness or with changes in EDV. How much thicker the wall or smaller the LV had to be to accommodate a percentage point reduction in shortening was calculated. We also derived the relation between EF and strains in HCM and DCM cases where both wall thickness and EDV were changed simultaneously.

### Comprehensive analysis of the dependence of EF on all factors

To provide a full analysis of the effect of all 4 factors (GLS, GCS, wall thickness, and EDV) on EF, we plotted EF as a function of varying 1 of the variables at a time, keeping the remaining factors constant. The plots were repeated for different values of the constant level of 1 of the other factors at a time. In this manner, we could investigate the effect of a specific variable, as well as the interaction of a variable with an alteration of each of the others.

### Statistical analysis

Continuous data are presented as mean ± SD. Categorical variables are presented as numbers and percentages. Linear regression analysis was used to compare measured EF and strains. Validation of model-predicted EF with measured EF was performed by intraclass correlation and Bland-Altman plot. The quality standards for correlations were defined as: very good: r∈<1.0, 0.8>; good: r∈<0.8, 0.6>; moderate: r∈<0.6, 0.4>; poor: r∈<0.4, 0.2>; and very poor: r∈<0.2, 0>. Differences between patient groups and control subjects were compared by an unpaired Student *t* test.

## Results

### Correlation between EF and myocardial strain

In the total study population, there was a very good correlation between EF_{measured} and GLS (R^{2} = 0.68; p < 0.0001) (Figure 2A). Interestingly, the slope of the relation was flatter for patients with EF ≥50% (slope = −0.6), suggesting that GLS can vary more in this patient group with less effect on EF, compared with patients with EF <50% (slope = −1.6). Notably, 8 (40%) of the HCM patients with increased wall thickness had longitudinal shortening worse than 15%, whereas their EF was >50%, contributing to the flatter relation between GLS and EF at high EFs. The results were qualitatively similar for the relations between EF_{measured} and GCS (Figure 2B).

### Model validation

There was a very good agreement between EF_{model} and EF_{measured} (r = 0.95) (Figure 3A) when measured GLS, GCS, wall thickness, and diameter were used in Equation 1 to calculate EF_{model}. The mean difference between EF_{model} and EF_{measured} was −1.2 ± 4.4 percentage points. The model appeared to be valid for all EF values, as there was no apparent systematic skewing of the data in any of the patient groups with a wide range of EF (Figure 3B). Furthermore, the model appeared valid for both spherically and elliptically shaped ventricles, as the model performed equally well (p = 0.86) in the DCM and HCM patient groups who had long-/short-axis diameter ratios of 1.3 ± 0.1 and 1.7 ± 0.2 (p < 0.001), respectively.

### Influence of GLS on EF

GLS had a moderate effect on EF, as shown in Figure 4A. When GLS changed from 0% to −20% (Figure 4A), EF increased by only 16 percentage points, from 43% to 59%. GCS had a substantially greater effect: EF increased by 36 percentage points, from 23% to 59%, when GCS changed from 0% to −20%. The effect of the 2 strains can also be derived from the slope of their relation to EF. GLS had a relatively flat slope: a 1 percentage point increase in longitudinal shortening increased EF by 0.8 percentage point, whereas a 1-percentage-point increase in circumferential shortening increased EF by 1.8 percentage point.

Figures 4B to 4D quantify how a reduction in longitudinal shortening can be compensated to keep EF unaltered by an isolated change in GCS, wall thickness, or EDV, respectively: a 1–percentage point reduction in longitudinal shortening is compensated by a 0.5–percentage point increase in circumferential shortening, ∼0.9-mm increased wall thickness, or a 6- to 9-ml reduction in EDV, depending on the operating range of the other variables.

### Preserved EF with reductions in both longitudinal and circumferential shortening

Figure 5A shows EF as a function of global strain (GCS = GLS) for ventricles with wall thicknesses ranging from 0.5 to 2.5 cm. In an LV with a 1-cm-thick wall, EF = 50% if global strain is −16.0%, whereas only −13.0% is required if the thickness is 2 cm. Hence, a 1-cm-thicker wall requires 3.0 percentage points less global shortening to maintain EF. Figure 5B shows EF as a function of global strain for ventricles with EDV ranging from 50 to 450 ml. In an LV with EDV = 150 ml, EF = 50% if global strain is −16.6%, whereas only −14.5% is required if EDV = 50 ml. Hence, in this range of volumes, a 100-ml-smaller ventricle requires 2.1 percentage points less global shortening to maintain EF.

The combination of a thick wall and smaller ventricle is typical in HCM patients and vice versa in DCM patients, who typically have concentrically or eccentrically remodeled ventricles, respectively. Figures 5C and 5D show EF as a function of GLS when the mathematical model was used to simulate HCM and DCM cases, respectively. In the HCM case, substantial reduction of systolic shortening (GCS = GLS = −11.7%), still produced an EF of 50%, falsely indicating preserved systolic function. In contrast, the DCM case required 18.0% shortening or more to maintain EF >50%.

Figure 5E shows EF as a function of end-diastolic and -systolic volumes for different wall thicknesses and strains. Despite severely reduced shortening, EF can be high in small ventricles as the wall thickness to cavity size ratio gets abnormally high.

Consistent with the demonstrated effect of increased wall thickness in the mathematical model, the 20 HCM patients in our study had increased wall thickness and a tendency to shorter diameter and smaller volumes compared with the 20 control subjects, but had similar EF, despite significant reductions in both longitudinal and circumferential shortening (Table 2).

### Comprehensive analysis of the dependence of EF on all factors

Figure 6 shows a systematic, comprehensive analysis of the influence of all 4 factors on EF. The first and second rows illustrate the relationships between EF and either GLS or GCS, respectively, for 5 different constant values of the other parameters. The slope of the relation between GLS and EF was less than one-half of the slope for GCS, meaning GLS contributes less than one-half as much to EF as GCS.

Wall thickness substantially influenced EF: a 1-cm increase in thickness increased EF by approximately 13 percentage points (Figures 6G and 6H). The relation between EDV and EF was nonlinear (Figures 6J to 6L). The slope was steepest for smaller volumes: a 50-ml ventricle had 8 percentage points higher EF than a 150-ml ventricle with otherwise normal shortening and wall thickness. The relation was relatively flat for dilated ventricles (i.e., a 100-ml difference in EDV of 2 dilated but otherwise identical ventricles only marginally altered EF).

There was a distinct interaction between wall thickness and EDV (Figures 6I and 6L): in a ventricle with reduced EDV, wall thickness has a substantial effect on EF, whereas the effect is smaller in dilated ventricles. Similarly, Figure 6E shows that a change in GCS affected EF more in thick- than thin-walled ventricles.

Figure 7 shows that the relation between global strain and EF is nonlinear, that is, the slope is almost halved at high compared with low strains, consistent with the measurements showing a reduced slope between EF and strains for EF above 50%.

## Discussion

The derived mathematical model corresponded very well with echocardiographic measurements and shows how EF is highly dependent on the different geometric factors. The model provides mathematical evidence for the moderate contribution of longitudinal shortening to EF, and the substantially higher effect of circumferential shortening (Central Illustration). It shows how EF remains normal in a small ventricle with a thick wall and reductions in both longitudinal and circumferential shortening. The dependency on wall thickness and EDV confound the use of EF as an index of systolic function, and support the use of strain as an alternative.

### Correspondence between measurements and model

The very good agreement between measured and model-predicted EF demonstrates that the model incorporated the most important geometric factors that determine EF. The measurements showed that the relation between strains and EF in patients with EF ≥50% was characterized by a substantially flatter slope than in patients with EF <50%. This is of clinical importance due to the frequently-observed discrepancy that a patient may have EF ≥50%, suggesting normal systolic function, while there is reduced systolic shortening. Several factors may explain the flatter relation in preserved EFs. In a ventricle with thick wall and/or reduced EDV, the EF remains high despite a substantial reduction of strain (Figures 5C and 6G to 6L). The 8 subjects with the lowest GLS and EF >50% had HCM (Figure 2A), supporting this explanation. Consistently, the mathematical model also showed that the slope of the relation between EF and strain is flatter in preserved EF (Figures 6A, 6D, and 7).

The flattening of the slope at high strains (Figure 7) has another interesting implication, as it means that more of the stroke volume is ejected during the first than during the last part of shortening. From the slopes in Figure 7, it can be deduced that 44% less blood is ejected for an additional percentage point shortening at higher strains compared with lower strains. To increase cardiac output, this geometric relation favors increased heart rate, as opposed to increased shortening.

### Geometric factors and EF

As can be seen from Equation 1 and Figures 4 and 6, EF is dominated by its quadratic dependency on GCS, whereas there is a weaker linear relation between EF and GLS. Thus, the major contribution to EF comes from circumferential shortening. These results are consistent with the computational simulations of MacIver (12), who used a slightly simpler geometric model than ours. The mathematical expression we present is advantageous over computational simulation methods, as it provides a direct equation that investigators can easily implement and allows for direct validation. Our results are in apparent contrast to the results of Carlsson et al. (18), who calculated the longitudinal contribution to stroke volume as the descent of the valve plane multiplied by the fixed ED *epicardial* short-axis area at the equator and found that this theoretical volume made up ∼60% of the total measured stroke volume. However, the theoretical volume incorporates substantial circumferential shortening, as it effectively includes the inward motion of the endocardium caused by wall thickening. Hence, the theoretical volume will overemphasize the pure longitudinal contribution. To exclude the circumferential contribution, an alternative would be to multiply by the ED short-axis area to the *midwall* instead of the *epicardium* (i.e., zero midwall circumferential shortening), which would have given results more in line with ours.

We systematically investigated each geometric factor’s influence on EF and its interaction with other factors. Our results showed that EF could remain constant for a large range of longitudinal shortening and also circumferential shortening, although to a lesser degree, as can be seen by the large horizontal spread of the lines in Figure 6. Effectively, this means that myocardial function can vary greatly without changing EF.

The model demonstrates the important effect that differences in wall thickness have on EF. As the ventricular wall shortens in the longitudinal and circumferential directions, the wall thickens due to the limited compressibility of the myocardium. Thus, a thicker wall thickens more in absolute terms than a thin wall, and the endocardium moves further inward, reducing the short-axis radius. The radius has a quadratic effect on the ejected volume, as the short-axis area is a function of the square of the radius. Hence, less fiber shortening is required to produce a similar EF in a thick-walled ventricle compared with a thin-walled ventricle. This was recently demonstrated in patients with hypertensive heart disease by Rodrigues et al. (19), who discouraged the use of EF in these patients, whereas MacIver (11) previously proposed a method for wall thickness correction of EF.

In our model, we also illustrate the effect of short-axis diameter or EDV on EF. This relation was nonlinear, and moderate changes in EDV do not influence EF much in dilated ventricles. However, for ventricles with EDV in the normal and particularly in the subnormal range, a small ventricle will have higher EF than a moderately larger ventricle, despite identical shortening and wall thickness.

We also demonstrated significant interaction between EDV and wall thickness: reduced EDV in combination with a thicker wall amplifies each other’s effect on EF. This combination is common in concentric LV hypertrophy, and can explain the common finding of preserved EF in these patients, whereas systolic shortening is substantially reduced. Many patients with heart failure and preserved EF may fall into this category, and would actually be classified with systolic dysfunction if evaluated by strain.

### Clinical implications

The results show that EF can be unaltered despite significantly reduced LV function. Particularly, longitudinal shortening may vary significantly, as it has less effect on EF than circumferential shortening. Wall thickness has a substantial effect on EF and, in concentrically remodeled ventricles with thick walls and small cavities, EF remains high despite considerably reduced shortening. Hence, EF is not a good measure of systolic function in many patient groups, and assessment of strain seems to be a better quantification of systolic function. Although many patients fall into the category of heart failure with preserved EF, very few of these would present normal shortening.

Longitudinal shortening might potentially be a more sensitive marker of systolic dysfunction, which typically affects the subendocardial region first. If circumferential shortening is also reduced, thus implicating the circumferential fibers in the midwall, it may suggest a more transmural dysfunction.

### Study limitations

The model in Equation 1 is based on simplified geometric assumptions about the LV. Longitudinal strain was calculated from the change of the long-axis diameter, as opposed to the change in arc length of the elliptical long-axis geometry, the latter requiring numerical calculations and not allowing an analytical solution. Effects of twist and asymmetric geometries are not included. However, the validation in 100 subjects with various pathologies and ventricular dimensions, including spherically- and elliptically-shaped LVs, showed very good agreement between estimated and measured EF, which suggests that there is little to gain by applying more advanced mathematical models, and that the simple model includes the most important geometric variables affecting EF. The simple geometric approach is attractive, as it conveniently provides an analytic expression that is accessible for many more investigators than when advanced mathematical modeling is required.

## Conclusions

The paradox of reduced myocardial shortening in the presence of preserved EF is explained mathematically through geometric factors, where EF can be constant for a large variation in shortening if other geometric factors are altered to compensate. Increased wall thickness and/or reduced ED volume augment EF, and therefore can maintain a normal EF despite reduced shortening. EF is quadratically dependent on circumferential shortening and only linearly dependent on longitudinal shortening; hence, EF is less sensitive to a reduction in longitudinal shortening. Our findings suggest that strain measurements reflect systolic function better than EF in patients with preserved EF.

**COMPETENCY IN MEDICAL KNOWLEDGE:** In ventricles with increased wall thickness and/or reduced EDV, EF is higher for the same degree of global myocardial shortening. Despite reductions of both longitudinal and circumferential shortening, the EF can be preserved in ventricles with thick walls and/or reduced EDV. Since alterations in LV geometry may compensate for reduced shortening, measurement of EF may not accurately reflect overall ventricular systolic function. Reduced longitudinal shortening is more easily compensated as it contributes less to EF than circumferential shortening.

**TRANSLATIONAL OUTLOOK:** Further studies are needed to compare the accuracy of EF indexed to ventricular wall thickness and EDV with measurements of strain for assessment of ventricular systolic function.

## Appendix

## Appendix

For a mathematical proof and the equation preprogrammed in a spreadsheet, please see the online version of this article.

## Footnotes

This work was supported by the Center for Cardiological Innovation, funded by the Research Council of Norway (RCN grant number 203489/o30). Dr. Stokke was funded by a grant from the Medical Student Research Program at the University of Oslo and the Research Council of Norway. Dr. Remme was funded by the K.G. Jebsen Foundation. All other authors have reported that they have no relationships relevant to the contents of this paper to disclose.

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- Abbreviations and Acronyms
- CAD
- coronary artery disease
- DCM
- dilated cardiomyopathy
- ED
- end-diastole/diastolic
- EDV
- end-diastolic volume
- EF
- ejection fraction
- GCS
- global circumferential strain
- GLS
- global longitudinal strain
- HCM
- hypertrophic cardiomyopathy
- LV
- left ventricle/ventricular
- ROI
- region of interest

- Received February 27, 2017.
- Revision received June 16, 2017.
- Accepted June 18, 2017.

- 2017 The Authors

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