Statistical corrections for the precise estimation of cyanoacrylate microbubble concentration in targeted imaging

The precise quantification of microbubble concentration is crucial for ultrasound molecular imaging. However, for high concentrations direct quantification approaches fail to precisely estimate the concentration of aggregated microbubbles (MB). Thus Sensitive Particle Acoustic Quantification (SPAQ) was proposed by Reinhardt et al. by destroying all MBs in an image and then moving the transducer in sub-millimeter increments in elevation direction the destruction volume is reduced. Individual destruction events become visible in Doppler imaging and are quantified by measuring the color pixel density. To calculate MB concentration from color pixel density, in only an approximation was derived. Now we derive a statistical model of SPAQ allowing the precise count of MBs even if the individual destruction events are not distinguishable. For this, only the average color pixel area of a single destruction event has to be known. The resulting correction was applied to SPAQ images of 8 gelatine phantoms with concentrations of MB ranging from 0.6*10⁶ - 2.1*10⁷ MBs / ml. A high frequency ultrasound system using the 3D Power Doppler mode was employed to obtain the images. The exact concentrations were determined optically. The corrected acoustic quantification showed the expected linear dependence on the MB concentration. The filling factor of colored pixels in the ROI ranged from 12% to 93% for the highest concentration. The optical analysis showed that only 46% of the bubbles were counted in the acoustic analysis. However, since a linear relationship was found between optical and acoustical counts, one can derive the total concentration from the acoustic measurement. This is not possible without a correction where the highest concentration is underestimated by 74%. Thus, the proposed correction improves quantification considerably.