Strain, Strain Rate, and the Force Frequency Relationship in Patients with and without Heart Failure


The aim of this study was to examine the effect of heart rate (HR) on indices of deformation in adults with and without heart failure (HF) who underwent simultaneous high-fidelity catheterization of the left ventricle to describe the force-frequency relationship.


Right atrial pacing to control HR and high-fidelity recordings of left ventricular (LV) pressure were used to inscribe the force-frequency relationship. Simultaneous two-dimensional echocardiographic imaging was acquired for speckle-tracking analysis.


Thirteen patients with normal LV function and 12 with systolic HF (LV ejection fraction, 31 ± 13%) were studied. Patients with HF had depressed isovolumic contractility and impaired longitudinal strain and strain rate. HR-dependent increases in LV+dP/dt max , the force-frequency relationship, was demonstrated in both groups (normal LV function, baseline to 100 beats/min: 1,335 ± 296 to 1,564 ± 320 mm Hg/sec, P < .0001; HF, baseline to 100 beats/min: 970 ± 207 to 1,083 ± 233 mm Hg/sec, P < .01). Longitudinal strain decreased significantly (normal LV function, baseline to 100 beats/min: 18.0 ± 3.5% to 10.8 ± 6.0%, P < .001; HF: 9.4 ± 4.1% to 7.5 ± 3.4%, P < .01). The decrease in longitudinal strain was related to a decrease in LV end-diastolic dimensions. Strain rate did not change with right atrial pacing.


Despite the inotropic effect of increasing HR, longitudinal strain decreases in parallel with stroke volume as load-dependent indices of ejection. Strain rate did not reflect the modest HR-related changes in contractility; on the other hand, the use of strain rate for quantitative stress imaging is also less likely to be confounded by chronotropic responses.

Analysis of deformation by two-dimensional echocardiography and Doppler tissue imaging has expanded the methodology for noninvasive assessment of left ventricular (LV) chamber function. Strain and strain rate can be used to evaluate global LV function, and, importantly, regional analysis of myocardial deformation may provide increased sensitivity to identify abnormal myocardium.

Deformation imaging also provides quantitative information to assess LV contractile responses during exercise or pharmacologic stress. These stimuli augment inotropic state but also modulate preload and afterload. In vivo, LV inotropic state or contractility can be measured using catheterization-based methods that interpret pressure development in the context of preload and afterload conditions. Understanding whether contractility and its acute modulation can be represented by deformation imaging remains an important challenge. For example, in animals, strain has been shown to correlate more closely with load-dependent ejection phase indices, including stroke volume (SV), rather than inotropic state. Although ventricular deformation occurs in part during ejection, it has been hypothesized that strain rate may be sufficiently load independent to index ventricular contractility.

Increases in heart rate (HR) are a fundamental inotropic stimulus to the myocardium, a property known as the force-frequency relationship (FFR). The FFR contributes to the net LV inotropic effect of exercise and most pharmacologic stimuli used in diagnostic stress testing. At the same time HR is a stimulus to contractility, its effect to decrease preload is also well understood. We therefore aimed to determine the extent to which HR influences the measurement of strain and strain rate in the human ventricle. Measurements were obtained in patients with and without heart failure (HF) in whom the FFR was determined at the same time by catheterization-based measurements of isovolumic contractility.



Patients referred for the assessment of nonacute chest pain syndromes were recruited into the normal LV function group if normal LV systolic function was documented by two-dimensional echocardiography. Clinical evidence of HF (i.e., HF with preserved ejection fraction) was a specific exclusion criterion for this group. Patients in the HF group were recruited from a specialized HF clinic and underwent catheterization as part of the clinical evaluation. Inclusion into this group required stable New York Heart Association class II or III symptoms and an LV ejection fraction < 35% measured by echocardiography on the day of the study. In both the normal LV function and HF groups, patients with valvular heart disease, acute coronary syndromes, coronary revascularization within 6 months, or severe triple-vessel CAD were specifically excluded. Women of childbearing potential were also excluded. All patients were in normal sinus rhythm, and specific exclusion criteria also included a QRS duration > 110 msec, evidence of atrioventricular block, or the presence of a permanent pacemaker for bradycardia support or resynchronization therapy. Implantable defibrillators for primary prophylaxis were allowed in the HF group if there was no evidence of pace dependency.

This protocol was approved by the Mount Sinai Hospital Research Ethics Board. All patients gave written informed consent.

Cardiac Catheterization Procedures

All diagnostic and study procedures were performed at the Cardiac Catheterization Research Laboratory at the Mount Sinai Hospital. Before catheterization, venous blood was sampled for measurements of hemoglobin, creatinine, and estimated glomerular filtration rate. Patients were minimally sedated and fasting, and all medications were withheld on the morning of the procedure. These protocols are well established within our laboratory. To control HR, a 6-Fr bipolar pacing catheter was advanced to the high right atrium from the right femoral vein under fluoroscopic guidance. The pacemaker catheter was aligned with a programmable stimulator (Prucka CardioLab; GE Healthcare, Milwaukee, WI). A 7-Fr micromanometer-tipped catheter was then positioned in the left ventricle from the femoral artery. Femoral artery pressure was recorded from the sidearm of the sheath. LV pressure and the first derivative of LV pressure were continuously displayed and acquired (1,000 Hz) online, allowing serial sampling of LV+dP/dt max . Control measurements before intervention were recorded only after three serial sampling intervals demonstrated LV+dP/dt max values within 5%.

Pacing Protocol

After instrumentation and determination of the threshold for the pacing, a 10-min rest period was allotted. Three HR conditions were then studied: resting HR, then right atrial (RA) pacing at 80 and 100 beats/min (cycle length, 750 and 600 msec). If the resting HR was >75 beats/min, pacing at 80 beats/min was omitted. If Mobitz type 1 or 2:1 atrioventricular block occurred at any pacing condition, the pacing rate was reduced in increments of 5 beats/min until 1:1 conduction was reestablished for 30 sec; RA pacing at the prespecified rate was then reattempted.

Within the first minute of each HR condition, the stability of RA pacing capture was established. The continuous hemodynamic recording was annotated at the beginning of the second minute of each HR condition for the acquisition of femoral arterial pressure and the LV pressure waveform inscribed by the micromanometer-tipped catheter. Echocardiographic images were acquired during the second to fifth minutes of each HR condition, as described below.

Echocardiographic Image Acquisition

Two-dimensional echocardiographic imaging and Doppler acquisition were performed using a GE Vivid 7 system with an M4S matrix sector array probe (2–5 MHz; GE Healthcare) by a research echocardiographic technician blinded to the patient’s clinical information as well as the hemodynamic information being simultaneously acquired. The chronometers for both the imaging system and the hemodynamic recording system were synchronized to ensure that offline analysis of LV pressure was simultaneous with the time-stamped echocardiographic image frames. Analysis of imaging data was performed on an offline EchoPAC workstation (GE Healthcare).

Before pacing, for the measurement of SV, echocardiographic imaging was used to determine the LV outflow tract dimension and cross-sectional area, calculated as (LV outflow tract dimension/2) 2 × 3.14. The pulsed-wave Doppler aortic flow spectrum was then obtained in the apical five-chamber view, and transducer placement was marked on the chest wall for repeated acquisition.

At each HR condition, after the first minute of steady pacing, standard grayscale two-dimensional images were acquired in the apical four-chamber view at 60 to 95 frames/sec. At least five cardiac cycles were acquired for each condition and stored in cine loop format for subsequent speckle-tracking analysis, as well as end-systolic and end-diastolic LV volumes using standard echocardiographic techniques. Pulsed-wave Doppler aortic flow spectrum was also reestablished, and further simultaneous acquisition of the time velocity integral and LV pressure over three to five consecutive beats was performed. No pacing condition exceeded 5 min.

Data Analysis

For each HR condition, the annotated interval for analysis was interrogated offline by the research analyst in our laboratory, who was blinded to the nature of the study. Per beat of the LV pressure recording, LV+dP/dt max , peak LV systolic pressure, and LV end-diastolic pressure were determined as previously reported in our laboratory. For each beat, the preceding RR interval was recorded, and if it was not within 2% of the planned pacing cycle length, the specific beat and the subsequent five beats were discarded.

LV longitudinal strain and strain rate as assessed by speckle tracking were analyzed from the stored apical four-chamber images. For each HR, the best quality image was selected, and the endocardium was traced. The region of interest was accepted for analysis after adequacy of the tracing for speckle tracking was determined by an automated tracking quality system and confirmed by observation of tracking in real time. At least five cardiac cycles were reviewed, with a minimum of three cycles analyzed if image quality was optimal. The ventricular chamber was divided into six segments (apical, mid, and basal septum and apical, mid, and basal lateral wall), and six segmental strain curves were analyzed. Peak segmental and global longitudinal systolic strain and strain rate measurements were determined from these curves. These measurements were recorded as absolute values. Stored two-dimensional images and Doppler measurements were also used to calculate LV end-diastolic volume (Ved), LV end-systolic volume (Ves), and SV. Ejection fraction was calculated using the modified Simpson’s method. The time stamp from echocardiographic frames identified the cardiac cycle from which to obtain simultaneous LV and arterial pressure. Hemodynamic measurements were not significantly different when derived from the single cardiac cycle or taken as a mean of 10 cycles either preceding or following the beat analyzed for echocardiographic variables.

Using a method of timed intervals derived from the high-fidelity LV pressure recording, simultaneous acquisition of the Doppler-derived SV allowed the generation of approximated pressure volume loops, and external stroke work could be calculated.

Statistical Analysis

All data are presented as mean ± SEM. Analysis was performed using StatView version 5.0.1 (SAS Institute Inc., Cary, NC). Between-group comparisons of baseline characteristics were made using Student’s t tests for continuous variables and χ 2 analysis for categorical variables. The effect of HR on hemodynamic and echocardiographic variables was analyzed using a two-way analysis of variance for repeated measures, using pacing stage as one factor and disease state (normal LV function or HF) as the other. As applicable, post hoc pairwise comparisons were then performed with Bonferroni-Dunn tests. Relationships between indices of deformation and hemodynamic variables were examined using linear regression analysis. Variables related to changes in deformation by HR were similarly examined. Variables demonstrating significant correlations with indices of deformation were selected to enter into stepwise regression. P values < .05 were required for statistical significance. In our laboratory, the standard deviation of LV+dP/dt max in patients with and without HF is approximately 20%. A sample size of 10 patients per group retains 90% power to detect a change in LV+dP/dtmax of 25%.


Study Groups

Twenty-five patients were recruited for this study, 13 in the normal LV function group (seven men, six women) and 12 in the HF group (seven men, five women). The baseline characteristics of the study patients, comorbid conditions, and medical therapies are described in Table 1 . Use of angiotensin receptor blockers, adrenergic receptor antagonists, and diuretics was more frequent in the HF group. All patients underwent coronary angiography. In the normal LV function group, all patients had patent epicardial coronary arteries. One patient had previously undergone single-vessel percutaneous coronary intervention >12 months before the present study and had a persistently patent stent. Three patients in the HF group had ischemic etiologies of LV systolic impairment with revascularization that occurred ≥12 months before the present study. Coronary angiography demonstrated either stent (one patient) or aortocoronary bypass graft (two patients) patency not requiring repeat revascularization. The rest of the HF group was confirmed to have a nonischemic etiology of LV dysfunction.

Table 1

Baseline characteristics

Variable Normal LV function ( n = 13) HF
( n = 13)
Age (y) 59 ± 8 56 ± 11 .54
Height (cm) 172 ± 8 171 ± 8 .67
Weight (kg) 79 ± 14 79 ± 21 .99
Body surface area (m2) 1.91 ± 0.17 1.91 ± 0.27 .92
Hemoglobin (g/L) 139 ± 17 143 ± 13 .59
Cholesterol (mmol/L) 5.3 ± 1.5 4.9 ± 1.0 .57
Estimated glomerular filtration rate (mL/min) 81 ± 22 79 ± 25 .81
Creatinine (μmol/L) 84 ± 25 88 ± 22 .65
Hypertension 6 4 .51
Diabetes mellitus 2 4 .29
Hypercholesterolemia 8 1 .005
Coronary disease 1 3 .49
Adrenergic antagonists 4 10 .008
Angiotensin system antagonists 5 10 .008
Diuretics 2 8 .009
Digoxin 0 3 .05

Data are expressed as mean ± SEM or as numbers.

Resting Hemodynamic and Echocardiographic Variables: Normal LV Function and HF

All hemodynamic and echocardiographic measurements for both groups at rest and in response to RA pacing are presented in Table 2 . At rest, patients with HF demonstrated impairment of LV isovolumic contractility as measured by LV+dP/dt max and significantly higher filling pressures. LV chamber enlargement and impaired LV ejection fraction were also evident in the HF group. Global peak longitudinal systolic strain and peak strain rate were significantly depressed in the HF group. At rest, impairment of longitudinal strain and strain rate were correlated with depression of LV+dP/dt max ( Figure 1 ).

Table 2

Resting LV hemodynamic and echocardiographic measurements and the effect of increasing HR by RA pacing

Pacing condition Group Resting measurements 80 beats/min 100 beats/min P value, NLV vs HF P value, effect of HR P value for interaction
Heart rate NLV 66 ± 11 .03
HF 76 ± 10
LV+dP/dt max NLV 1,337 ± 207 1,465 ± 289 1,604 ± 359 ∗,† <.0001 <.001 .02
HF 970 ± 207 985 ± 205 1,083 ± 233 ∗,†
LVSP (mm Hg) NLV 123 ± 24 122 ± 22 120 ± 22 .42 .04 .78
HF 128 ± 21 129 ± 20 126 ± 21
LVEDP (mm Hg) NLV 9 ± 4 7 ± 4 5 ± 5 ∗,† <.0001 <.01 .07
HR 18 ± 9 17 ± 9 16 ± 9
Ves (mL) NLV 28 ± 8 26 ± 8 26 ± 10 <.0001 .73 .31
HF 127 ± 57 131 ± 59 132 ± 58
Ved (mL) NLV 98 ± 15 89 ± 16 83 ± 16 <.001 .01 .06
HF 184 ± 69 184 ± 69 181 ± 65
SV (mL) NLV 70 ± 13 62 ± 14 57 ± 13 ∗,† .04 <.0001 .06
HF 49 ± 27 45 ± 23 43 ± 20
Ejection time (msec) NLV 298 ± 32 269 ± 22 243 ± 16 ∗,† <.001 <.0001 <.01
HF 237 ± 30 232 ± 22 206 ± 18 ∗,†
EF (%) NLV 72 ± 7 70 ± 8 69 ± 10 <.0001 .05 .95
HF 27 ± 10 25 ± 10 24 ± 10
CO (L/min) NLV 4.6 ± 1.3 5.1 ± 1.2 5.7 ± 1.3 .07 <.0001 .25
HF 3.5 ± 2.1 3.5 ± 2.1 4.2 ± 2.1 ∗,†
SW (mm Hg · mL) NLV 5,614 ± 1,457 4,973 ± 1,419 4,580 ± 1,290 ∗,† .13 <.0001 .20
HF 4,181 ± 2,554 3,842 ± 2,118 3,640 ± 1,814
Peak SS (%) NLV 18.0 ± 3.5 13.2 ± 6.3 10.8 ± 6.0 ∗,† <.01 <.0001 <.01
HF 9.4 ± 4.1 8.7 ± 4.8 7.5 ± 3.4
Peak SSR (%/sec) NLV 1.1 ± 0.3 1.2 ± 0.2 1.1 ± 0.9 .04 .65 .79
HF 0.8 ± 0.2 0.9 ± 0.2 0.9 ± 0.3

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Jun 11, 2018 | Posted by in CARDIOLOGY | Comments Off on Strain, Strain Rate, and the Force Frequency Relationship in Patients with and without Heart Failure

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