Bulk modulus and volume variation measurement of the liver and the kidneys in vivo using abdominal kinetics during free breathing

Abstract

This article presents a method of predictive simulation, patient-dependant, in real time of the abdominal organ positions during free breathing. The method, that considers both influence of the abdominal breathing and thoracic breathing, needs a tracking of the patient skin and a model of the patient-specific modification of the diaphragm shape. From a measurement of the abdomen viscera kinematic during free breathing, we evaluate through a finite element analysis, the stress field sustained by the organs for a hyperelastic mechanical behaviour using large strain theory. From this analysis, we deduce an in vivo Poisson's ratio and a homogeneous bulk modulus of the liver and kidneys, and compare it to the ones in vitro available in the literature.

Introduction

Preoperative 3D CT images are used in many medical contexts. For some of them, the breathing motion is an issue that is taken into account but not compensated. For instance, in radiotherapy, the dosimetry computation is performed on a static preoperative CT image although the patient breathes freely during the irradiation. Then, the planned target volume is overestimated so as to totally irradiate the tumour. Consequently, healthy tissue irradiations are much more important than if the tumour position was perfectly known during the breathing.

Respiratory gating techniques [1], [2] are the first attempt to reduce the breathing influence. The patient is immobilized on the intervention table and his breathing is monitored to synchronize his lung volume to the one during the preoperative CT acquisition. These methods are however constraining: they lengthen the intervention, they are uncomfortable for the patient and the repositioning accuracy, of 1.5 mm on average, can sometimes exceed 5 mm [3] if the patient is not intubated.

Therefore, a predictive method to simulate the abdomen and thorax breathing motions would be a great improvement for the previous reported application. Internal motion during a quiet breathing being between 10 and 35 mm [4], and practitioners estimate that prediction accuracy within 4 mm would bring a significant improvement to the current protocol in radiotherapy.

Solutions to simulate organ deformations and interactions are numerous [5], [6], [7], [8], [9], however they require the rheological parameters of the patient organs to provide predictive results, which is currently difficult to evaluate in vivo. Furthermore, in most cases, the computation time is not compatible with a real time simulation. Consequently, the methods that were developed for realistic simulation of surgical interventions are not adapted to intra-operative applications in the operating room.

Meier et al. [10] present a list of deformable models for organs simulation with their advantages and disadvantages. Although these models present interests for medical applications such as surgery, they still need a fair amount of development for everyday use.

Sarrut et al. [11] propose to simulate an artificial 3D + t CT image during a breathing cycle from two CT images acquired at inhale and exhale breath-hold. Simulated 3D + t images are built by a vector field interpolation between both CT images. Although this interesting method provides a simulated CT image, it assumes that the breathing is perfectly reproducible and cyclical. Therefore, this method is limited to patients who are under general anaesthesia and intubated. Furthermore, the abdominal organs’ sliding against the peritonea or the pleura is not taken into account.

Our purpose is to compute a displacement field that take the motion of the abdominal organs (such as liver, kidneys, pancreas or spleen) into account in order to provide in real time simulated CT and mesh images during free breathing, using a tracking of the skin position and a modelling of the diaphragm motion.

In previous papers [12], [13], [14], we have highlighted the link between skin variations and abdominal organs positions and presented a method that only considered the cranio-caudal motion. In the new model presented in this paper, the lateral and anterior–posterior motions are integrated, due to a better analysis of the diaphragm motion. This upgrade [15] completely modifies the previous modelling.

In this paper, we present the whole method that describes qualitatively each key point and the major steps. We provide an evaluation on two human clinical data showing that our simulation can be computed at 50 Hz with a prediction accuracy between 2 and 3 mm. The complete maximum displacement field is then extracted from the real time analysis and used as an input in the finite element analysis. The local strain and stress fields are calculated through a large strain hyperelastic analysis. Finally, from the obtained Von Mises equivalent stress and using the experimental volume variation measurement, we evaluate a homogeneous equivalent Poisson's ratio and bulk modulus for the liver and the kidneys in vivo.