CALCULATION OF STRAIN VALUES FROM STRAIN RATE CURVES ...

IEEE Ultrasonics Symposium 2000

Jan D’hooge et al.

CALCULATION OF STRAIN VALUES FROM STRAIN RATE CURVES: HOW SHOULD THIS BE DONE? J.D’hooge, F.Jamal1 , B.Bijnens1 , A.Heimdal2 , J.Thoen3 , F.Van de Werf 1 , G.R.Sutherland1 , P.Suetens Katholieke Universiteit Leuven Medical Image Computing – ESAT, 1 Dept. of Cardiology and 3 Dept. of Physics U.Z. Gasthuisberg, Herestraat 49, B-3000 Leuven, Belgium 2 GE Vingmed, Horten, Norway Abstract—The non-invasive quantification of regional myocardial function is an important goal in clinical cardiology. Myocardial strain and strain rate indices are two methods of attempting to define regional myocardial function. Several approaches to extract these indices have been proposed in the literature, one of which is to extract the strain rate information as the spatial gradient in myocardial velocities that had been estimated using Doppler myocardial imaging techniques. In order to obtain information on the strain profile, the strain rate curve is time integrated. In practice however, the strain rate curves can be post-processed in several ways and different strain indices can be extracted. As no information exists on which scheme is advantegeous, this paper attempts to define the optimal post-processing scheme for the clinical setting. I NTRODUCTION Myocardial strain and strain rate indices are two methods of attempting to define regional myocardial function. One approach towards myocardial strain estimation by ultrasound is the velocity gradient methodology in which strain rate is estimated as the spatial gradient in myocardial velocities [1]. This curve is time integrated in order to obtain a strain profile. In the literature, two types of strain have been defined: natural and Lagrangian strain. They are defined respectively as [2]: εN =

Z

L L0

dl l

and

εL =

Z

L L0

dl , L0

(1)

with l the instantaneous length, L the final length and L 0 the initial length of the object. From these equations, it is obvious that both types of strain relate as : εL = exp (εN ) − 1.

(2)

1

It can be shown that under conditions of homogeneous, linear strain, the integration of the velocity gradient, i.e. strain rate, results in the natural strain profile [3]. This curve can subsequently be converted to the Lagrangian one using expression (2). This enables the comparison with classical M-mode derived wall thickening indices and with strain values extracted using MRI tagging as these methods typically have extracted Lagrangian strain values. However, the question thus arises which type of strain indices are more robust, i.e. user independent, and should thus better be used in the clinical setting. Moreover, although a significant amount of work has been done in attempting to use the velocity gradient methodology to characterize myocardial function, no fixed acquisition and post-processing scheme has been presented. This lack of standardization could make comparison and interpretation of results published by different groups difficult, if not impossible. The goal of this paper was thus to derive an optimal acquisition and post-processing scheme, based on scientific evidence. Therefore, the following questions will be addressed: How does acquisition rate of the velocity data sets influence the extracted strain values? Which frame rate has to be used during data acquisition? Will conversion of the natural strain curve to the Lagrangian one result in a bias for data sets with limited temporal resolution? Is the extraction of the maximal strain or the extraction of the difference between the maximal and minimal strain occurring over the cardiac cycle the more robust parameter? If drifting of the strain curve occurs, should it automatically be compensated for? What is the influence of this compensation on the strain values? This paper attempts to address all of these questions by post-processing velocity data sets acquired at high frame rate in an animal model. As the answer to these questions might be different in case of pathologies (as the strain profile is usually altered), data sets were acquired both before and after induction of ischemia. In this way, the optimal methodology to extract strain values using the velocity gra-



the strain curve to return to zero at the end of the cycle (R-R interval); thus, assuming that any errors were equally spread over the heart cycle independent of e.g. the strain rate amplitude). Subsequently, the time integrated SR curves (from scheme I) were averaged over the four heart cycles (identical to the averaging of the SR curves in scheme II) and the mean SR curves (from scheme II) were time integrated in order to estimate εN . Again integration was done both with and without compensation for drifting. All curves obtained in this way, were converted to their Lagrangian correlates (εL ) by means of equation (2). Finally, strain indices were extracted from all curves both as the maximal and the maximal minus the minimal strain value over the mean cardiac cycle. In order to assess the influence of the frame rate on the extracted strain indices, the value extracted from the original data set (having the highest acquisition rate) was used as the true one. In this way, the absolute relative errors for all frame rates were calculated for all post-processing schemes. The absolute error was extracted because the change in frame rate did not result in a monotonic change of the strain indices but rather in an unpredictable relative over / underestimation of the strain indices. Subsequently, the average, absolute error at a specific frame rate was calculated over all animals. The mean of these average errors over all frame rates was used as an index for the sensitivity of the post-processing scheme/extracted parameter to the acquisition rate of the velocity data set. Moreover, based on the average errors, the minimal acquisition rate was defined in order to keep the strain estimation error smaller than 5%. The influence of the position of ED (R-top) on the strain indices was estimated by using the average strain value over all ED positions at the highest frame rate as the true one. In this way, all strain estimations were normalized to their mean value for all animals. The standard deviation of this normalized strain sequence was used as an indicator of the sensitivity of the post-processing scheme/extracted parameter to the exact position of ED. Finally, the average strain value and its standard deviation for all animals and for all processing schemes was calculated (separating the baseline from the ischemic data sets). Moreover, in order to assess the difference between the extraction of the maximal value and the difference between the maximal and the minimal value, all natural strain values extracted by any processing scheme were averaged. Identically, the influence of drift compensation and averaging – integration order was investigated.

dient approach could be defined for the clinical setting. M ETHODS : ANIMAL PREPARATION AND DATA ACQUISITION

Ten male crossbred pigs (33 ± 4 kg) were anesthetized with intravenous pentobarbital (0.4 mg/kg/min). The animals were intubated and ventilated with a mixture of air and oxygen to maintain arterial blood gas values within the physiologic range. The left main coronary artery was catheterized through the right carotid artery under fluoroscopic guidance. A PTCA balloon catheter was positioned in a proximal segment of the circumflex coronary artery in order to enable the induction of posterior wall ischemia. Colour Doppler Myocardial Imaging (CDMI) data sets were acquired in the parasternal short axis (SAx) view both at baseline and after 20 seconds of acute ischemia using a System FiVe (GE Vingmed, Horten, Norway). Moreover, apical four chamber views (A4C) of the interventricular septum were acquired from 5 healthy volunteers. All data sets were acquired over 4 consecutive heart cycles at high frame rate (180 Hz) using a 2.5 MHz transducer. In all acquisitions, the pulse repetition frequency was adjusted in order to avoid aliasing. The digital data sets were recorded during brief apnea (in the animals, by turning off the respirator) and transferred to a PC-workstation for off-line analysis. M ETHODS : DATA PROCESSING Parasternal data sets Strain rate (SR) curves were extracted offline from the CDMI data sets as the spatial gradient in myocardial velocities for a region in the posterior wall using dedicated software (TVI 6.0, GE Vingmed, Horten, Norway). In order to reduce the noise level in the SR curves, spatial averaging of the (non-scanconverted) velocity and SR data sets was performed prior to local SR curve extraction. For both data sets, the averaging consisted of five and three samples in the axial and lateral direction respectively. From the extracted high frame rate SR curve, 15 subsampled curves were extracted downto a virtual frame rate of 20 Hz, representing different acquisition rates. Subsequently, two distinct processing schemes were followed: I) all SR curves were integrated as a function of time and II) the mean SR curves over the four acquired heart cycles were calculated in order to improve the signal to noise ratio further. Averaging was based on the manual indication of the R-tops, corresponding to left ventricular end-diastole (ED), on a highresolution ECG that had been acquired simultaneously with the CDMI data set. The exact position of the R-tops was artificially varied by maximal 10 percent of the average duration of the R-R interval in order to test the influence of the definition of ED on the extracted strain indices. Moreover, integration was performed both with and without compensation for drifting (this compensation was done by forcing

Apical data sets

2

As εL can only indirectly be calculated from εN using equation (2), an intrinsic conversion error could be introduced especially at low acquisition rates as in this situation RL P the numerical approximation L0 dl/l ≈ i ∆li /li will get



Integration + averaging Drift compensation No drift compensation εN εL εN εL Max Diff Max Diff Max Diff Max Diff 6.6 4.3 6.6 4.3 3.4 3.8 4.2 3.8 6.2 3.7 6.2 3.7 5.5 4.0 6.2 4.0 6.4 4.0 6.4 4.0 4.4 3.9 5.2 3.9

worse. In order to estimate this potential error, two velocity traces were extracted from two points in the basal septum, approximately 2 cm apart (in end-diastole). The position of both points was manually tracked during the cardiac cycles based on anatomical landmarks. As in the parasternal data sets, the velocity traces were averaged over the four heart cycles acquired. Time integration of these two velocity traces resulted in the corresponding displacement curves. The displacement of both points at the end of the cycle was forced to return to zero. From these two mean displacement curves and the end-diastolic distance between the two points, the length of the virtual object was calculated as a function of time: l(t). This curve was subsequently downsampled (cf. the parasternal SR curves) and both εN and εL were directly calculated using equation (1). Moreover, εL was calculated indirectly from εN by means of equation (2). Both maximal and maximal minus minimal strain value (further called the difference strain value) were extracted as a measure for myocardial function. The difference between the direct and indirect Lagrangian strain indices was extracted as a measure of an “intrinsic conversion” error. This error was expressed in percent of the true (direct) Lagrangian index extracted at the highest frame rate.

Table 1: Magnitude of the relative error of the different strain indices induced by changes in frame rate of the normal (first row) and ischemic (second row) velocity data set. Row three gives the average value of rows one and two. All values are given in percent. Integration of the strain rate curves was done prior to averaging over the different heart cycles. Averaging + integration Drift compensation No drift compensation εN εL εN εL Max Diff Max Diff Max Diff Max Diff 6.7 4.7 6.7 4.7 5.6 4.5 6.9 4.5 6.8 4.7 6.8 4.7 9.0 4.8 10.2 4.8 6.7 4.7 6.7 4.7 7.3 4.6 8.5 4.6

R ESULTS All results of the parasternal data sets are summarized in Tables 1-6. In these tables, “Max” stands for the maximal strain value, while “Diff” stands for the difference strain value over the cardiac cycle. The minimal frame rate required to keep strain estimation errors smaller than 5% was 66 and 75 Hz for the normal and ischemic data sets respectively both for the natural and Lagrangian strain data sets. The results in tables 1 and 2 show that integration of the SR curves prior to averaging over the different heart cycles results in general in strain indices that are less sensitive to the acquisition rate of the velocity data sets. They show that extracting the difference strain index rather than the maximal value over the cardiac cycle, reduces effects induced by acquisition rate of the CDMI data set independent of the post-processing scheme. Moreover, for the difference strain index it seems better not to compensate for any drifting of the integrated strain rate curve. Both natural and Lagrangian strain estimates show the same sensitivity to the frame rate. Tables 3 and 4 show that reversing the order of averaging and integration has a minimal influence on the sensitivity to the exact definition of ED unless no drifting of the strain curves is allowed. In this case, it is slightly better to start with the integration of the SR curves. On the average, drifting strain curves were more sensitive to the position of ED with the exception of the difference, natural strain index. As for the frame rate dependency, the difference strain index always performed better than the maximal strain in-

Table 2: Cf. Table 1. However, averaging of the strain rate curves was done prior to integration. dex. Moreover, Lagrangian strain estimates showed to be more sensitive to the position of ED as well. The maximal “intrinsic conversion” error was observed at the lowest aquisition rate (20 Hz). The maximal error was 0.5% and 5.3% for the maximal and difference strain index respectively. When extracting the difference between maximum and minimum, the conversion error became larger than 1% for frame rates below approximately 140 Hz. D ISCUSSION

3

In general, the sensitivity of the strain indices on acquisition rate and accurate definition of ED is comparable. This means that in order to define the optimal post-processing scheme, both effects are equally important. From this point of view, our results show that extracting the natural, difference strain index is the most robust one as this parameter minimizes the influence of both user dependent variables. In general, our results show that the effect of drift compensation depends on the processing scheme and strain index extracted. However, as it is better to extract difference strain values, our results show that it is probably better not to compensate for this drifting. The precise origin of the drifting is not known although several potential factors have been suggested [3]. As drifting is physically impossible, it is im-



portant to remark that correction for drifting will probably be important when extracting diastolic strain indices. However, this was not attempted in this paper. The order of integration and averaging of the SR curves showed little or no influence on the extracted parameters although integration first showed to perform slightly better. However, the influence of this post-processing choice can probably be neglected over that of the acquisition rate of the data. In order to avoid relative errors larger than 5%, the frame rate should minimal be around 70 Hz. In order to achieve this, it might be necessary to limit the field of view of the sector image during acquisition and to acquire separate CDMI data sets for the individual walls. Unfortunately, this makes comparison of strain (rate) profiles between wall more complicated and less accurate. When comparing strain values extracted using the velocity gradient method with classical wall thickening indeces extracted with M-mode echocardiography or with values obtained with MRI tagging, the conversion of natural to Lagrangian strain has to be done prior to correlation. If only the maximal strain value is extracted (as in MRI), the intrinsic conversion error can be neglected. Moreover, our study suggests that high frame rate acquisition (> 70 Hz) is required in order to resolve all cardiac events and to minize strain (rate) estimation errors. Table 5 shows that extracting Lagrangian strain values or difference strain indices results in a significant increase of the mean values. However, table 6 shows that neither the order of integration/averaging nor drift compensation results in a significant change. Finally, it should be remarked that, although maximal strain has been used as a marker for systolic function in the literature, it might not be the best index as it has been observed that maximal strain can occur after aortic valve closure, i.e. after end-systole. Extraction of the end-systolic strain seems thus more relevant to assess systolic function. Investigating the sensitivity of this parameter to frame rate and the definition of ED is left for future work.

Integration + averaging Drift compensation No drift compensation εN εL εN εL Max Diff Max Diff Max Diff Max Diff 7.2 3.2 8.7 3.2 7.7 2.6 8.9 3.9 5.3 1.9 6.2 1.9 5.4 1.7 6.2 2.5 6.2 2.5 7.4 2.5 6.5 2.1 7.5 3.2 Table 3: Magnitude of the relative error of the different strain indices induced by changes in the exact position of end diastole for the normal (first row) and ischemic (second row) data sets. Row three gives the average value of rows one and two. All values are given in percent. Integration of the strain rate curves was done prior to averaging over the different heart cycles.

Averaging + integration Drift compensation No drift compensation εN εL εN εL Max Diff Max Diff Max Diff Max Diff 7.2 3.2 8.7 3.2 8.2 2.5 9.7 4.0 5.3 1.9 6.2 1.9 6.1 1.5 6.9 2.6 6.2 2.5 7.4 2.5 7.1 2.0 8.3 3.3 Table 4: Cf. Table 3. However, averaging of the strain rate curves was done prior to integration.

εN 57 ± 16 40 ± 20

εL 75 ± 27 48 ± 26

εM axM in 61 ± 15 45 ± 20

εM ax 52 ± 16 34 ± 17

Table 5: Mean value and standard deviation (SD) of the natural and Lagrangian strain indices, obtained by averaging the values obtained with all extraction methods for all animals at the highest frame rate (left). Mean value and SD for all extracted natural strain values at the highest frame rate, using either the maximal or the maximal minus the minimal strain as an index (right).

εdrif t 57 ± 17 41 ± 22

εnodrif t 57 ± 15 39 ± 18

εav−int 57 ± 16 40 ± 20

ACKNOWLEDGEMENTS This work was supported by the Fund for Scientific Research – Flanders (FWO – Vlaanderen). R EFERENCES [1] Heimdal A., Stoylen A., Torp H. and Skjaerpe T. “Real-time strain rate imaging of the left ventricle by ultrasound”, Journal of the American Society of Echocardiography, 11(11), p.1013–1019, 1998.

εint−av 57 ± 16 40 ± 20

[2] Mirsky I., Ghista, D.N. and Sandler H. “Cardiac mechanics: physiological, clinical, and mathematical considerations”, John Wiley & Sons Inc., New York, 1974. [3] D’hooge J., Heimdal A., Jamal F., Kukulski T., Bijnens B., Rademakers F., Hatle L., Suetens P. and Sutherland G.R. “Regional strain and strain rate measurements by cardiac ultrasound: principles, implementation and limitations.”, European Journal of Echocardiography, 2000 (In Press).

Table 6: Cf. Table 5 using natural strain values to assess the influence of drift compensation (left) and averaging/integration order (right). 4