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Research Papers

Mechanics-Based Interactive Modeling for Medical Flexible Needle Insertion in Consideration of Nonlinear Factors

[+] Author and Article Information
Shan Jiang

Centre for Advanced Mechanisms and Robotics,
School of Mechanical Engineering,
Tianjin University,
Tianjin 300072, China
e-mail: shanjmri@tju.edu.cn

Xingji Wang

Centre for Advanced Mechanisms and Robotics,
School of Mechanical Engineering,
Tianjin University,
Tianjin 300072, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 18, 2013; final manuscript received May 30, 2015; published online June 30, 2015. Assoc. Editor: Carmen M. Lilley.

J. Comput. Nonlinear Dynam 11(1), 011004 (Jan 01, 2016) (11 pages) Paper No: CND-13-1290; doi: 10.1115/1.4030747 History: Received November 18, 2013; Revised May 30, 2015; Online June 30, 2015

A mechanics-based model of flexible needle insertion into soft tissue is presented in this paper. Different from the existing kinematic model, a new model has been established based on the quasi-static principle, which also incorporates the dynamics of needle motions. In order to increase the accuracy of the model, nonlinear characteristics of the flexible needle and the soft tissue are both taken into account. The nonlinear Winkler foundation model and the modified Euler–Bernoulli theory are applied in this study, providing a theoretical framework to study insertion and deformation of needles. Galerkin method and iteration cycle analysis are applied in solving a series of deformation control equations to obtain the needle deflection. The parameters used in the mechanics-based model are obtained from the needle force and needle insertion experiment. Sensitivity studies show that the model can respond reasonably to changes in response to variations in different parameters. A 50 mm needle insertion simulation and a 50 mm corresponding needle insertion experiment are conducted to prove the validity of the model. At last, a study on different needle tip bevel demonstrates that the mechanics-based model can precisely predict the needle deflection when more than one parameter is changed. The solution can also be used in optimizing trajectory of the needle tip, enabling the needle to reach the target without touching important physiological structures such as blood vessels with the help of dynamic trajectory planning.

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References

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Figures

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Fig. 1

The biomechanical model of the insertion system with forces acting on the whole needle as it interacts with the elastic medium, where linput is the applied needle base displacement working as the input of the system. The two dimensional model incorporates needle insertion forces (cutting force Ft, distribution forces fyfz), soft tissue Winkler foundation parameters k1k3 and flexible needle parameters (flexural rigidity EI, bevel angle α).

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Fig. 2

The needle movement during two steering phases, dotted line represents the initial needle position (a) the insertion phase and (b) the adjustment phase

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Fig. 3

Needle insertion using a robotic assisted needle insertion system to measure the insertion force

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Fig. 4

Insertion forces profile into PVA phantom at six different insertion velocities. The experiment data and simulation input used in this study are acquired at a fixed velocity. The whole insertion process is continuous without interruption.

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Fig. 5

The relationship between insertion force and insertion depth during puncture process. The averaged maximum puncture force (subtract friction force from total insertion force) is 0.1304 N.

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Fig. 6

The horizontal force along the needle measured by a six-axis force sensor and the simulation result obtained by the mechanics model

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Fig. 7

Depiction of the mechanics-based needle insertion model and methods to solve the reasonable numerical solution of needle deflection

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Fig. 8

Five sequential movements with 10 mm depth of insertion phase. Each movement corresponds to a deflection curve obtained by the simulation result.

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Fig. 9

Needle tip trajectories of needle–tissue interaction model with five movements. During each 10 mm insertion, only the tip position is marked out, so the horizontal axis contains the needle length.

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Fig. 10

Five insertion phases and one adjustment phase of the whole needle beam. The base of the needle is forced to insert into the soft tissue. It can be seen that the displacement of needle tip is reduced comparing to Fig. 8.

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Fig. 11

The needle deflection curves of different slenderness ratio λ in 200 mm insertion simulation. Other simulation parameters are the same as the needle insertion simulation shown in Fig. 8.

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Fig. 12

The needle deflection curves of different friction coefficient η in 200 mm insertion simulation. Other simulation parameters are the same as the needle insertion simulation shown in Fig. 8.

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Fig. 13

The needle deflection curves of different puncture force Ft, caused by different tissue stiffness in 30 mm insertion

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Fig. 14

Robotic assisted needle insertion system and image acquisition system setup, used for needle deformation measurement

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Fig. 15

Experimental data showing needle trajectories. In each 10 mm insertion, the needle tip position is measured to form a single curve. Then, the experimental data and simulation results for needle deflection are compared in one figure. The experimental image and dotted box indicate the needle insertion depth in the PVA phantom.

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Fig. 16

Needle insertion simulation error between the simulated model and the experiment result

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Fig. 17

Insertion force measured during the needle insertion into the PVA phantom. Except different bevel angles, other dimension parameters of the surgical needles are the same.

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Fig. 18

Needle insertion experiment result, needle insertion simulation result, and simulation error of two surgical needles with different bevel angles. The insertion depth is set as 50 mm.

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