RAMS Laboratory: Surgical Simulation - Modeling Tissue Cutting

Surgical Simulation - Modeling Tissue Cutting

Motivation: Modeling the response of a deformable soft tissue during cutting or probing is a fundamental scientific problem, an understanding of which can be used to develop realistic surgical simulators for providing accurate force feedback to the surgeon during surgical training for soft-tissue cutting and probing procedures (such as palpation, skin incision and biopsies). Before surgeon trainees actually operate on patients, it is desirable to practice basic surgical skills on simulators to familiarize themselves with the real responses of the soft tissue encountered in a surgical procedure. To enable realistic simulation, it is necessary to develop models based on actual experimental data.

Experimental setup for measuring the cutting forces and the depth of cut during liver cutting. A typical force versus displacement profile during scalpel cutting.

Experimental Platform for Tissue Cutting: The equipment was designed to use a scalpel to cut soft tissue with a sliding motion at controlled cutting (only one degree-of-freedom: horizontal motion) speed while monitoring the force and torque that the tissue exerted on the blade during the cutting process. The equipment consists of a scalpel-blade cutting sub-system, a computer control subsystem, a digital data-acquisition subsystem, stereo camera, and a data post-processing subsystem (see Figure). The test equipment to measure the liver cutting forces has been designed so that the cutting blade can move with variable speed, to measure the effect of cutting speed on cutting forces and strain rates within the specimen (speeds can be varied from 0 to 3.81cm/second). The entire cutting mechanism consists of two vertical supports, a lead screw assembly with a geared DC motor and an incremental encoder (manufactured by Maxon Motors, model A-max32 with planetary gearhead GP 32C and digital encoder HEDL 55 with line driver RS 422), and a JR3 precision 6-axis force/torque sensor model 20E12A-I25, with resolution of 0.002 N in Fx, Fy, Fz, and 0.000025 Nm in Tx, Ty and Tz to which a surgeon’s scalpel is attached. We used #10 Bard-Parker stainless steel surgical blade in our experimental studies, consistent with what is used by surgeons in scalpel cutting. To enable estimation of the depth of the blade embedded in the tissue, a B umblebee stereo camera system (manufactured by Point Grey Research) utilizing two Sony ICX204 1/3” CCDs with 1024x768 pixels, 10 bit A/D, and maximum of 15 frames per second was used.

Determination of deformation resistance of the tissue to cutting: It is desirable to construct a predictive computational model that can simulate the cutting process and predict the mechanical response (cutting force versus cutting-blade displacement characteristics) of liver cutting. The purpose of the finite element model is to extract the necessary characterizing parameters such as the local effective modulus that provides a quantitative estimate of the tissue deformation resistance immediately preceding the extension of the cut. Such parameters can be used to develop haptics simulation of surgical cutting. During the deformation phase, the deformation resistance that a scalpel senses is caused by many different simultaneous deformation modes, including modes that are affected by strain-rate. These deformation modes include local finite-strain elastic deformation and plastic deformation near the scalpel-tissue interaction edge, compliance change due to local kinematics re-arrangement, frictional sliding of the scalpel blade, and dragging of the top-layer tissue by the elastic and viscoelastic foundation, and small-strain global elastic deformation. For the deformation phase, we seek to quantify this deformation resistance by integrating the experimental force-displacement data with finite element modeling. We iteratively solve an inverse problem with finite element models to determine an operational parameter defined as the local effective modulus (LEM). The finite element models use the observed force versus displacement characteristics measured during the deformation phase of cutting to determine the local effective modulus. The local effective modulus so determined can be used in a discretized continuum approach (such as finite element method, boundary element method etc) to simulate surgery cutting. Using finite element modeling, a simulator can incorporate all the governing physical laws in the entire continuum that represent the tissue and the scalpel. With the physical laws incorporated, such approach has advantage over the empirical look-up table approach that does not incorporate principles of continuum mechanics. A price that the finite element approach has to pay is computational cost. Hence, it is important to perform model order reduction as discussed below.

Three levels of model order reduction: To have faster simulation with realistic force feedback, our goal is to use model order reduction to simplify the internal complexity of the model and simultaneously preserve the overall input-output (displacement-force) behavior. The realistic force feedback part is attained via using LEM. The speed of the simulation depends on how much order reduction the model can attain. We have studied three levels of model order reduction, namely: 1) 3D quadratic-element model with unit thickness, 2) 2D quadratic-element model, and 3) 2D linear-element model.

(a)

(b)

Displacement profile from: a) 3D quadratic-element model, b) 2D quadratic-element plane-stress model.

Findings:

We performed a quasi-static analysis using ABAQUS finite element software. Since the force versus displacement profile during the deformation phase appeared to be linear, we conducted isotropic linear elastic analysis. With experimental force-displacement data from 0.15 inch/sec cutting speed, we performed analysis to determine LEM using the 3D-quadratic-element model (20-nodes element) with reduced integration, 2D-quadrtic-element model (8-node elements), and 2D-linear-element (4-node elements) plane-stress model. From the perspective of computational effort, there is a significant difference among these models, namely, the size (or order) of the model and the computational effort needed to solve it. The Table shows a comparison among these models in terms of total number of equations and the actual computation time.

Comparison of local effective modulus determined from 2D plane-stress model and 3D model (Poisson’s ratio = 0.5).

FE Model	3D quadratic elements	2D quadratic elements	2D linear elements
Number of elements	480	120	120
Number of nodes	2830	438	160
Number of equations	8490	876	320
Calculation time (seconds)	5.7	0.6	0.2

Distance from constrained edge (cm)	LEM from 3D quadratic FE model (N/m ²) reduce Integration	LEM from 2D quadratic FE models and Ratio of LEM from 2D to that from 3D model		LEM from 2D linear FE models and Ratio of LEM from 2D to that from 3D model
Distance from constrained edge (cm)	LEM from 3D quadratic FE model (N/m ²) reduce Integration	Plane- stress (N/m ²)	Plane-stress / 3D model	Plane- stress (N/m ²)	Plane-stress / 3D model
2.15	2300	3400	1.48	4100	1.79
2.90	5300	7900	1.50	7700	1.45
4.08	7800	10100	1.30	9400	1.20
4.75	30600	38200	1.25	35600	1.16
5.14	25200	30900	1.22	28800	1.14
5.64	32300	39100	1.21	36300	1.13
6.09	16000	18900	1.19	17700	1.11
6.61	53400	62400	1.17	58800	1.10
6.90	44700	51600	1.15	48800	1.09

Effect of cutting angle and cutting speed: Experimental results of parametric study shows that the LEM varies with cutting speed and the cutting angle. For a given cutting angle, the deformation resistance decreases with increase in cutting speed in a linear fashion. For a given cutting speed, the deformation resistance decreases as the cutting angle varies from 90 o to 45 o. This is consistent with visual observation that there was physically more tissue deformation encountered by the blade when the blade was perpendicular to the tissue surface (90 o cutting angle).The above trend is consistent with independent observations reported in Contact Mechanics literature. Since contact and frictional sliding are part of the multiple mechanisms that contribute to the deformation resistance in our case, it is not surprising that our results of deformation resistance are consistent with observations reported in the literature. This confirmation lends support to the mechanistic interpretation of the source of the deformation resistance.

Variation of local effective modulus with cutting speed for 90 o and 45 o cutting angle (2D plane-stress model, Poisson’s ratio = 0.5).

	Plane stress model (90° angle)		Plane stress model (45° angle)
Cutting speed cm/sec	Average LEM x10³ N/m²	Standard deviation x10³ N/m²	Average LEM x10³ N/m²	Standard deviation x10³ N/m²
0.1	82	17	49	27
0.38	67	18	46	9
0.89	59	19	42	22
1.27	69	12	26	16
1.65	39	9	34	12
2.16	36	8	26	16
2.54	38	9	20	18

Relevant archival publications:

Teeranoot Chanthasopeephan, Jaydev P. Desai, and Alan C. W. Lau, “Modeling Soft-Tissue Deformation Prior to Cutting for Surgical Simulation: Finite Element Analysis and Study of Cutting Parameters”, Accepted for publication to IEEE Transactions on Biomedical Engineering, 2006.
Teeranoot Chanthasopeephan, Jaydev P. Desai, and Alan C. W. Lau, “Measuring Forces in Liver Cutting: New Equipment and Experimental Results”, Annals of Biomedical Engineering, 31(11): 1372-1382, 2003.

For further information, please contact:

Prof. Jaydev P. Desai
Director, RAMS Laboratory
Department of Mechanical Engineering
Room 0160, Building 088
Glenn L. Martin Hall
University of Maryland
College Park, MD, 20742
Email: jaydev (at) umd.edu
Phone: 301-405-4427
Fax: 301-314-9477