Supplement 1

Supplement 1, Table 1–Summary of the different models to compensate motion and deformation with their respective mathematical equation.

Model / Compensation of motion and deformation / Explanation / equation
A / No compensation
B / Rigidmotion compensation / The targets are moved exactly as theorgan sensor was moved /
C1 / Compensation of elongation of the organ / Stepwise scaling of sensor motion according to target position in relation to the sensor /
C2 / Linear compensation of elongation of the organ / Same as C1 but with scaling factor based on linear regression on sensor height /
C3 / Compensation of elongation and motion / Same as C2 but with an additional constant to correct for motion of the whole organ /
C4 / Compensation of deformation and motion / Same as C3, but with additional quadratic regression based on sensor position to account for bending of the organ /
C5 / Target specific compensation / Regression on single targets. The organ was considered as a collection of independent single elements. /

Here is the calculated vector for the motion of the target, whereas is the vector for the motion of the sensor and are the parameters of the respective linear regression models. For the different positions of the targets is accounted for by representing their “sensor height” (h) on an ordinal scale from 1 to 11 where the targets at height of the sensor are all considered to have h= 6.

Supplement 1, picture 1 - The picture shows a schematic representation of the differences between the models, emphasizing their specific limitations by visualizing the calculated form of the rectum (middle) for the respective model between the initial form of the rectum (left) and the form after deformation (right).