Accuracy and reproducibility of a subpixel extended phase correlation method to determine micron level displacements in the heart

Future treatment of heart disease may involve local perturbations of mechanical function, such as intramyocardial injections of angiogenic growth factors or progenitor cells. This necessitates an accurate measurement technique to determine regional heart function. We have previously developed a method to determine regional heart function using a phase correlation algorithm. However, in determining regional function over a single heartbeat it is necessary to sum displacements between many images. We have therefore incorporated a subpixel algorithm that models the result of phase correlation as a sinc function in order to increase the accuracy of our technique. This method, which we have named high density mapping (HDM), determines the subpixel displacement of 64 × 64 pixel regions from images of the heart. To determine the accuracy and precision of the technique, a high contrast image of a heart was digitally shifted 1, 2 or 3 pixels. The original and shifted images were then downsampled four times resulting in 0.25, 0.50 or 0.75 pixel shifts between the original and shifted images. The average accuracy of HDM in the digitally shifted images was 0.06 pixels, with a precision of 0.08 pixels. Effectiveness of HDM in characterization of deformation was also assessed in digitally stretched images. Error in quantification of strain was found to be less than 3.5% of the calculated strain. In an additional set of experiments, in which accuracy was determined using physical motion instead of digital shifting and downsampling, a speckle pattern was displaced by known distances using a micromanipulator, such that the displacement between the captured images was 0.5 pixels. These data demonstrated an accuracy of 0.09 pixels and a precision of 0.02 pixels. Finally, as HDM is used to determine the regional stroke work index (RSW) in beating hearts, the repeatability of using this method to compute RSW was assessed. RSW, the integral of intraventricular pressure with respect to unitless regional area, where end diastolic area was normalized to unity, was assessed in consecutive beats from four different hearts. The average standard deviation of RSW was 0.098 mmHg. Uncertainty analysis determined the maximum error of RSW to be ±0.41 mmHg, approximately two-thirds of the measured biologic variability. These data demonstrate the ability of HDM to accurately and reproducibly measure displacement and regional function in the beating heart.