Pneumoperitoneum simulation based on mass-spring-damper models for laparoscopic surgical planning

Abstract

Laparoscopic surgery, which is one minimally invasive surgical technique that is now widely performed, is done by making a working space (pneumoperitoneum) by infusing carbon dioxide ([Formula: see text]) gas into the abdominal cavity. A virtual pneumoperitoneum method that simulates the abdominal wall and viscera motion by the pneumoperitoneum based on mass-spring-damper models (MSDMs) with mechanical properties is proposed. Our proposed method simulates the pneumoperitoneum based on MSDMs and Newton's equations of motion. The parameters of MSDMs are determined by the anatomical knowledge of the mechanical properties of human tissues. Virtual [Formula: see text] gas pressure is applied to the boundary surface of the abdominal cavity. The abdominal shapes after creation of the pneumoperitoneum are computed by solving the equations of motion. The mean position errors of our proposed method using 10 mmHg virtual gas pressure were [Formula: see text], and the position error of the previous method proposed by Kitasaka et al. was 35.6 mm. The differences in the errors were statistically significant ([Formula: see text], Student's [Formula: see text]-test). The position error of the proposed method was reduced from [Formula: see text] to [Formula: see text] using 30 mmHg virtual gas pressure. The proposed method simulated abdominal wall motion by infused gas pressure and generated deformed volumetric images from a preoperative volumetric image. Our method predicted abdominal wall deformation by just giving the [Formula: see text] gas pressure and the tissue properties. Measurement of the visceral displacement will be required to validate the visceral motion.

Keywords: dynamics; mass-spring-damper models; pneumoperitoneum; surgical planning.

Figures

Fig. 1

Mass-spring-damper system: Mass m attached to a spring with spring stiffness k and damper with damping coefficient c. f denotes an external force.

Fig. 2

Example of abdominal wall segmentation: (a) abdominal wall and viscera. Yellow (Y) and blue (B) regions indicate abdominal wall and viscera, respectively. (b) Some major organs are included in abdominal wall and viscera.

Fig. 3

Example of cube allocation: Yellow (Y) and blue (B) cubes include abdominal wall and viscera, respectively. Green (G) cubes include boundary surface of abdominal cavity. Therefore, they are doubly allocated. We created fixed cubes colored purple (P). No nodes included in purple cubes move.

Fig. 4

Mass, spring, and damper allocation: there are two types of allocation patterns (a) and (b) since the diagonals are shared by adjacent cubes.

Fig. 5

Thirteen corresponding points measured in the evaluation: Points of a real patient are measured by optical position sensor. Corresponding points of a preoperative volumetric image are measured by in-house application.

Fig. 6

Measurements of real pneumoperitoneum in the operating room. (a) Surgeon measures 13 points corresponding on abdominal surface using an optical positioning sensor. (b) and (c) Measurement before and after pneumoperitoneum.

Fig. 7

Boxplot of errors of previous and proposed methods. (a) Mean position errors of previous and proposed methods are 35.6 and 26.9 mm, respectively. These two error results are significantly different (p=6.0×10−8, Student’s t-test). (b) Displacement errors of ventrodorsal direction of previous and proposed methods were −32.6 and −23.2  mm, respectively. Displacement errors of ventrodorsal direction are significantly different (p=1.3×10−29, Student’s t-test).

Fig. 8

Relationship of errors and strength of virtual gas pressure: (a) position and (b) displacement errors.

Fig. 9

Relationship of errors and strength of Young’s modulus: (a) position and (b) displacement errors.

Fig. 10

Examples of volumetric images generated by proposed method: Left side of each subfigure shows a preoperative volumetric image. Right side shows a volumetric image generated by proposed method.

Fig. 11

Visceral deformation: Surface of visceral region moves to back direction by virtual gas pressure.

Fig. 12

Examples of visualization of volumetric images generated by proposed method: (a) left half of body from right side. (b) Virtual laparoscopic view. Subfigures in middle and right columns show that visualized images are obtained by superimposing organ labels within the volumetric image.