Urinary Bladder Volume Monitoring Using Magnetic Induction Tomography: A Rotational Simulation Model for Anatomical Slices Within the Pelvic Region

Urinary bladder volume monitoring can benefit from contactless measurements, as alternative to the traditional medical methods of transurethral catheterization or ultrasound examination. The emerging modality of Magnetic Induction Tomography (MIT) offers the possibility for estimation of the intravesical volume in the physiological and pathological states using conductivity map reconstructions of the tissues present in the pelvic region. Within MIT, eddy currents originating from the conductive urine can produce their own magnetic field in response to an external magnetic source that is susceptible of being detected outside the body by means of a static ring of sensing coils. However, the ill-conditioned and ill-posed nature of the MIT Inverse Problem make the numerical implementation and conductivity estimation highly laborious. In this paper, we present a rotational frame model based on the MIT principles with application in urodynamic studies, which allows to extend the number of contactless measurements without increasing the overall dimension of the simulation domain, at the expense of solving multiple MIT Forward Problems. On the inversion process, the single-step Gauss-Newton method with Laplacian regularizer is recruited to estimate the bladder volume non-invasively and remotely (estimation error of 19%) using a simplified (quasi 2D) approximation to the distribution of eddy currents in the examined region, therefore paving the way for this technique to surpass the current limitations found in intravesical volume monitoring.