Needle insertion on soft tissue using set of dedicated complementarily constraints.
Needles, electrode or biopsy tools are some examples of thin and flexible medical tools used in a clinical routine. Several medical applications are concerned by the use of these tools, such as biopsy, brachytherapy or deep brain stimulation. As these objects are often thin and flexible, the accuracy of their insertion into soft tissues can be affected. Moreover, different physical phenomena, such as puncture, friction or cutting through heterogeneous tissues could alter the procedure. The simulation of the insertion of thin and flexible medical tools into various tissues can enable useful clinical feedback, such as training but also planning. We chose the example of a needle to explain our methodology but our method can be generalized to thin and flexible instruments.
Pioneering works concerning needle insertion were presented by Di Maio et al.  and Alterovitz et al. . They proposed modeling methods based on FEM for the interaction between a needle and soft tissues. A recent survey proposed by Abolhassani et al.  summarizes the different characteristics of the existing methods in the literature. Remeshing process of tissue models remains an obstacle to obtain interactive simulations. In , the authors simulate the insertion of several rigid needles in a single soft tissue (such as during brachytherapy procedures). The interaction model between needle and tissue is the most challenging part as it combines different physical phenomena. Different shidies based on experimental data are proposed in the literature to identify the forces occurring during the needle insertion . Three different types of force are often underlined: puncture force, cutting force and friction force. Recent studies use experimental data to perform an identification of the model parameters [6-8].
In this paper, a new generic method based on the formulation of several constraints is proposed in order to simulate the insertion of thin and flexible medical devices into soft tissues. Any classical deformation models of both tissue and needle can be used with our approach. For this study, we obtain interactive frame rate while modeling the geometrical non-linearities of the tissue and needle deformations. Contraiy to existing methods, no remeshing process is needed, even if Finite Element Method (FEM) is used for the tissue simulation. Our method can handle complex scenarios where needle steering, non-homogeneous tissues and interactions between different needles can be combined.
Constraint-based Modeling of Needle Insertion:
In this work, we propose a new model for the interactions that take place at the surface of a needle during its insertion in soft tissues. The formulation relies on a constraint formulation which is independent of both needle and tissue models that are used to simulate deformations. We highlight two different aspects: Firstly, for the constraint positioning, no remeshing is necessary. Secondly, we present several new constraint laws, based on complementarily theory. These laws capture in a unified formalism all the non-smooth mechanical phenomena that occur during insertion.
Flow to avoid remeshing ?:
The constraint positioning is defined by two points: one on the tissue volume P and one on the needle curve Q. For each constraint, [delta] measures the distance between these two points along a defined constraint direction n. The points can be placed anywhere in the volume of the soft tissue and anywhere on the needle curve. The displacements of these points are mapped with the same interpolation than the deformable models (see Fig. 1). The variation of [delta] can be mapped on the displacements of deformable model nodes.
A linear interpolation is used on tetrahedra for the soft tissue model, the displacement ut of a tissue constraint point placed inside a tetrahedron is given by the barycentric coordinates and the displacement [DELTA]qt of the 4 nodes ut = Jt[DELTA]qt. The displacement of the needle point un is mapped using the interpolation of the needle deformation model un = Jn[DELTA]qn.
Puncturing Soft Tissue:
Puncturing illustrates the interest of using complementarily theory to model the constraint: three successive steps of the interaction can be defined with a set of inequalities, as illustrated in Fig. 2. Here, Q is the tip of the needle and p is the contacting point (or the penetration point) on the tissue surface. n is the surface normal vector at point p. The puncture constraint can be applied several times during the simulation if the needle passes through different tissue layers: different values for the threshold fp can be defined in order to simulate different tissue behaviors. If the tip of the needle hits a
During step 1, Q is only approaching the tissue surface. The gap [delta] is positive (Sp > 0) and the interaction force must be null ([lambda]p = 0). During step 2, Q is touching without puncturing the tissue surface. The gap between p and Q is null ([delta]p = 0) and the interaction force is necessarily positive in the direction of the surface normal ([lambda]p [greater than or equal to] 0). The value of this force is strictly less than a punchiring force threshold [lambda]p [less than or equal to] fp. During step 3, the needle tip enters in the tissue, the gap along the constraint direction is negative ([delta]p [less than or equal to] 0) and the constraint force is equal to the threshold ([lambda]p = fp).
Cutting through Different Layers:
The cutting force fc is the force needed to traverse a tissue structure. As for fv, it can be tuned to different values from a layer to another. This force disappears if the needle is re-inserted at the same location. The constraint used to simulate cutting is similar to the one used for puncturing, except that [delta]c measures the relative displacement between the needle tip and the extremity of a curve created by a previous cutting path. [lambda]c is still the force that solves the constraint.
Tip Path and Needle Steering:
A direction is associated to the needle tip in order to constrain its lateral motion. To obtain needle steering due to bevel-tip needle, a specific orientation of the cutting direction in the tip frame is defined (Fig. 3(a)) and the displacement of the tip is tangential to this direction ([delta]t = 0). In that case, whether the needle is being pushed or pulled, the constraint is not aligned on the same direction (Fig. 3(b)). During needle insertion, the path of the tip inside the soft tissues is followed by the rest of the needle. This behavior is modeled using additional constraints: we impose a null relative displacement [delta]t between the needle and the organ along the tangential directions of the needle curve rig. 3(c)). Here [lambda]t will provide the force necessary to solve this equality constraint.
Dry friction resists to the motion when the needle is inserted but also retracted. The complementarily constraint for the friction defines two states: adherence (stick) when there is no relative motion [delta]f = 0 due to static friction and dynamic friction (slip) when the relative motion is not null [delta]f # 0 (Fig. 4).
A threshold [mu]. p is used to limit adherence: [mu] is the coefficient of friction and p is the pressure exerted by the soft tissue on the needle. Currently, this pressure is estimated from the stiffness of the soft tissue and remains constant. To model it more accurately, we plan to use stress measures based on the soft tissue deformable model. The value of the friction resistance r, given by the graph (Fig. 4) is integrated along the inserted surface of the needle. Each constraint point owns a part of the needle curve and computes the friction force by using the length l of this curve part ([lambda]f = I[pi]d. r where d is the diameter of the cross-section).
The soft tissues of the human anatomy often have a visco-elastic anisotropic behavior which leads to complex FEM models if high precision is needed. However, to assess our constraint-based model of the interaction between the needle and the soft tissues during insertion, we use basic shapes and simple tissue model. The simulated soft tissue can only undergo large displacements with small deformations. We use Hooke's constitutive law: deformations are considered to be isotropic and elastic and the Poisson ratio is tuned to quasi incompressibility (v = 0.49). A viscous behavior is obtained using Rayleigh model. It provides an attenuation that is proportionally related to both elastic and inertial forces. Using this model, we can obtain a very fast estimation of the compliance matrix Wt  that leads to the ability of obtaining real-time simulation of the needle insertion. Once again, this tissue model is only used in a preliminary approach, to validate the constraints used for needle insertion. More complex model could be used.
Stippled line represents the motion imposed to the needle. At step  the needle puncture the tissue surface. During step  friction is increasing with the penetration distance and  is the relaxation. After being partially retracted  the needle is inserted again along the same path ; therefore no cutting force is applied. During the last and complete retraction , the friction force decreases.
Our first experiment consists in inserting and pulling back multiple times the needle in a 3D soft tissue. This experiment is similar to the measurements proposed in , and the results obtained with our simulation (presented in Fig. 5) match the previous work.
Then we propose a second experiment based on the 3D simulation of an obstacle avoidance using needle steering. Indeed, surgeons sometimes use thin and flexible needles with beveled tip to reach the target with a curved path. However, flexible needle insertion and navigation deep into the tissue complicate the procedure . The experiment is close to the one presented in , except that their tissue phantom was considered as rigid and here the tissue is deformable. The Fig. 6 shows a real-time simulation of needle steering in a deformable object (we obtain an average of 28 frames per second).
In-vivo tissues are inherently non-homogeneous and thin medical tools can be deflected by harder regions inside overall soft tissues. We simulate this phenomenon using a 3D volume mesh composed of two regions with different stiffness's. During its insertion, a needle collides with the surface of the stiff region: as the force at the tip is lower than the puncture threshold, the needle slides along the surface of this object. The soft region can also be rigidified by the insertion of other needles. It allows for a precise insertion of the flexible needle without increasing its stiffness. This technique is commonly used for brachytherapy.
In this paper, we demonstrate the interest of using complementarily constraints for the simulation of the insertion of flexible needles into soft tissue. The presented model can be parameterized using previous work experiments, and also allows for the simulation of more complex scenarios. We plan to complete our simulations using more realistic constitutive laws for the deformation of the anatomy. In the near future, we will perform some validations on experiments to assess the precision on scenarios that are closer to clinical procedures. We aim at using the simulation as a planning tool for some therapeutic protocols that rely on the insertion of slender medical instruments.
Received 5 August 2015
Accepted 20 September 2015
Available online 30 September 2015
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(1) C. Murugamani, (2) S. Saravanakumar, (3) S. Prabakaran and (4) S.A. Kalaiselvan
(1) Research Scholar, Department of Information Technology, St.Peter's University, Avadi, Chennai, Tamil nadu, India,
(2) Professor, Department of Information Technology, Panimalar Institute of Technology, Chennai, Tamil nadu, India,
(3) Department of Computer Science and Engineering, University College of Engineering, Panruti, Anna University, Chennai, India,
(4) Research Scholar, Department of Computer Science and Engineering, St.Peter's University, Avadi, Chennai, India.
Corresponding Author: C.Murugamani, Research Scholar, Department of Information Technology, St.Peter's University, Avadi, Chennai, Tamilnadu, India.
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|Author:||Murugamani, C.; Saravanakumar, S.; Prabakaran, S.; Kalaiselvan, S.A.|
|Publication:||Advances in Environmental Biology|
|Date:||Sep 1, 2015|
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