A simulated worst case scenario of a SOS distribution variation between SIM and TX in a prostate cancer case: the variation (plotted as a change in tissue thicknesses, indicated by the arrows showing how the organs and the whole patient shrink between SIM and TX) changes the SOS average value along the LOV (thin arrow) to the target (indicated by the cross). The worst case scenario assumption is that this value switches from higher to lower than 1540 m/s. US-TX reports the position of the target (the prostate) at depth A. Due to SOS aberration at TX, the real position is B, shallower than A; but the shift applied to the patient is from A to C, which is the position of the prostate as seen by the reference image at SIM. Its real position at SIM was D (which we are trying to reproduce at TX), now deeper than C because of the change in SOS mean value along the LOV on the opposite side of 1540 m/s. So the real target will be after the shift at E, whose distance from the TX position A is the sum of the real shift (A to C) and the SOS aberration at TX (A to B), while it should be in D. So the final error would be the shift E to D. The arrow connecting line A-C shows the performed apparent shift; the arrow connecting line B-E shows the real shift.
The scenarios with possible changes between SIM and TX are plotted. The dashed line drawings refer to SIM, the solid ones to TX. (a) The patient undergoes a rotation and a translation. (b) The patient position does not change, but the transducer scans the tissues from a different entry angle on the skin. (c) Internal motion and changes in tissue thickness occur, so internal structures are not in the same relative position anymore.
Experimental setup: (a) the PMMA phantom filled with approximately 4 cm of sunflower oil overlying 1 cm of 20% saline solution; (b) the layer thicknesses are increased to approximately 5 cm and 2 cm, respectively (the exact values are reported in Table I); (c) the measurement is performed using a Clarity linear probe on the PMMA support: the transducer is positioned and rocked around the contact points to span the US volume. The shape of the support is drawn to show the aperture through which the probe, positioned on the support, scanned the liquids.
INTER (a) and INTRA (b) approaches applied to PMMA phantom measurements. On the left are the SIM images to which the TX images, on the right, are compared. For INTER the comparison is performed by aligning the bottom surface of the phantom on TX-US and on SIM-CT. For INTRA the comparison is performed with the SIM-US. Apparent errors are exaggerated for clarity.
An example of how a simulated extreme change in transducer position can result in a possible wrong patient shift, due to SOS corrections in opposite directions. The real position of the target is RP (15 cm along the SIM LOV), but at SIM it is shown at SP (15.46 cm, along SIM LOV) due to SOS aberration. At TX the SOS aberration is accumulated along a different LOV, because the probe is in a different location, so the target is at TP (14.93 cm along the TX LOV, shallower due to the increased amount of muscle tissue along the LOV) on the TX US scan. A shift of the structure between SP and TP seems then required (dashed arrow) to restore the SIM position, but this apparent shift in reality displaces the target by about 5 mm (indicated by the solid arrow) from RP to RP′. The shift is exaggerated for display purposes in the image.
Measurements of thicknesses of the two liquid layers in the PMMA phantom according to CT and US scans. The phantom is initially filled with approximately 4 cm of sunflower oil on top and 1 cm of water or 20% saline solution below it to simulate the SIM situation; then the thicknesses are increased to approximately 5 cm and 2 cm, respectively (TX1) to simulate a change in the patient between SIM and TX. Both measurements performed on co-registered CT scans and US scans are reported. The measured differences in depths between CT and US scans match the expected values according to the calculated distance error in US, where SOS aberration is present, proportional to the ratio between the assumed SOS value of 1540 and the real value (Ref. 22). Also an extreme variation where the sunflower oil layer is increased to approximately 6 cm (TX2) was performed for the combination with water. On the right side is drawn a schematic plot of the layer thicknesses in the phantom.
For all the workflows considered, noncorrected (INTER and INTRA) and corrected (INTERc and INTRAc), the effect of density change between SIM and TX in the different scenarios is reported with respect to SOS aberration: SOSTX is a pure SOS aberration error due to the SOS distribution at TX; δSOS is the effect of SOS distribution change in its most general definition, in particular here it takes into account the change of LOV of the US transducer between SIM and TX; ΔSOS is as δSOS with the assumption that the LOV does not change. SOSTX, δSOS, and ΔSOS are the different types of errors and do not indicate their magnitude.
In the third column of the table, “apparent shift,” the differences are presented between the positions of the bottom surface of the phantom from the TX-US and the positions according to the SIM-CT (for INTER) and to the SIM-US (for INTRA). The same differences are also shown for the corrected workflows, INTERc and INTRAc; in the fourth column the real shifts are given due to the change in layer thickness (resulting from the comparison between TX-CT and SIM-CT); in the fifth column the differences between real and apparent position are given; and in the sixth column the expected calculated errors according to the thickness of liquids and their SOS values are reported for a direct comparison: the values are always in good agreement and within the experimental error (the CT scan resolution of 1 mm).
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