MRI-compatible Haptics: Deflection and Force Sensing of Biopsy Needle using FBG sensors

ISMRM 2008

• Y-L. Park, S. Elayaperumal, B.L. Daniel, E. Kaye, K.B. Pauly, R.J. Black, and M.R. Cutkosky, "MRI-compatible Haptics: Feasibility of using optical fiber Bragg grating strain-sensors to detect deflection of needles in an MRI environment", International Society for Magnetic Resonance in Medicine (ISMRM) 2008, 16th Scientific Meeting and Exhibition, Toronto, Canada, May 2008

• Power Point Presentation Slides

Background

The manipulation of catheters, needles and other minimally invasive devices to reach tumors and other targets is the initial step of nearly all MRI-guided interventions. To date, most research on MRI targeting has focused on using MR to image the target, and to plan the trajectory of interventional devices. During the subsequent manipulation, however, it is useful to track any deviation from the planned trajectory to minimize positioning error and procedural complications. Previous techniques for tracking devices include rapid MRI, MR-tracking [1] and gradient-based tracking (“Endoscout®”, Robin Medical Inc). These methods are all limited because they require use of the MRI system during manipulation, require the device to be within the homogeneous volume of the gradient fields used for imaging, and because susceptibility artifacts from MRI-compatible metallic devices may cause distortions that lead to poor signal and/or inaccurate position information. The latter two tracking methods also require integration of an electronic apparatus into the interventional devices, which further increases device complexity including adding the need for appropriate patient isolation electronics.

Sensorized Tooling

New project(s) on estimating the curvature and/or loading on sensorized, elastic tooling used in surgical applications.

Biopsy Needle

note: May 6th is the conference in Toronto.

Assume a long, slender biospy needle that has strain gages (e.g. fiber optic bragg cell gages) bonded to it. The needle deflects as it is inserted. We would like to estimate the actual profile taken by the needle and/or the forces imposed on it.

Starting points:

• assume long, slender beam; beam theory applies
• sensors measure the curvature at discrete points along the beam
• assume needle either passes through a couple of fixed locations (e.g. over bones) or else has some forces imposed on it. Boundary conditions apply:
  • zero deflection and slope at base, without loss of generality
  • possibly zero moment and hence zero curvature at tip
  • main force may be at the tip (this force might dominate the loading)

Q: how many sensors do we need and where should we put them?

Forward force and displacement problem

Force: Given a set of N loads at known locations along the beam, the deflection of the beam can be computed using the moment/curvature equation.

Displacement: Given that the beam passes through a set of fixed points (e.g. over one peg and under another) the curvature and profile of the beam is again uniquely determined. This is a version of the classic elastic spline problem. It is usually solved by energy minimization.

• Glass 1966: - elastic spline as energy minimization BV problem. This paper provides a simple formulation of the energy minimization problem for an elastic spline that goes through N fixed points. The result is a nonlinear 4th order differential equation. The solution method is probably more complicated than what we want to do (suboptimal discretization would be fine).
• http://people.csail.mit.edu/bkph/papers/Least_Energy.pdf
• A Criterion for the Optimal Design of Multiaxis Force Sensors
• An approach to optimise the critical sensor locations in one-dimensional novel distributive tactile surface to maximise performance
• Multi-component force sensor based on multiplexed fibre Bragg grating strain sensors

-- MarkCutkosky - 09 Apr 2008

MRI-Compatible Robotics Article Summaries

July 16, 2008

The articles summarized include review studies about MR-compatible materials, actuators, sensors, and other limitations. Also, state-of-the art technologies and manipulators are presented. The current favorite actuation method is ultrasonic motors. However MR-compatible, they still produce significant image artifact when ON.

• MagneticResonanceArticles_July16.doc: articles include review studies, fluidic actuation comparison, and a new USM for use inside the MR scanner

• PaperSummary.doc: articles describe MR-compatible manipulators (PZT, pneumatic), and a 3-DOF joystick

July 23, 2008

These articles describe a fiber optic force sensor which based on Hirose's 4-segmented photo-diode method (1993). Recently, they have been used in fMRI devices.

• OpticalForceSensor_Articles.doc:

Sensor Placement

So far, two models were used to determine the best locations for two sensors along the length of the needle. The first model describes a force-based approach, in which the actual curvature and deflection is calculated from two known forces applied at known locations. The next model uses a known deflection profile of a bent needle. The mathematics that describe both methods are found in "Sensor Placement Estimation.ppt".

Also attached is the Matlab code for both models.

• Needle Modeling, Simulation and Experiments: Detailed notes on modeling the deflection of the needle based on beam theory, MATLAB simulation results, and experimental results.

• SensorPlacementEstimation.ppt: Mathematics & results of force-based and deflection based models.

• Needle3.m: Force based model, MATLAB code.

• Needle4.m: Deflection based model, MATLAB code.

Next: Modeling using parametric curves and minimum energy splines.

Parametric representation allows for more degrees of freedom to describe a curve in space. In this approach, the (x,y,z) position of any point along the length of the needle is described as a function of u. x,y, and z are not given as functions of each other. The example attached shows how by knowing the curvature at given sensor positions, a multiple-part profile of the needle curvature can be determined.

• ParametricFormofCurves.ppt: Description of interpolating a deflection profile given curvature information at specific locations along the needle.

• Parameterization_pg1.pdf: lab notes

• Parameterization_pg2.pdf: lab notes

The following slides show how the math to find the unknown parametric equations can be simplified due to the assumptions in the needle bending case.

• Bendingin2Planes.ppt: Math to solve parametric coefficients assuming small deflections and no torsion.

These results show that in the case of a load only at the tip of the needle, sensor location of two sensors does not effect deflection error. The magnitude of possible deflection errors increase with increased loads. The tip deflection error is decreased the closer the sensors are to inflection points.

• SmallDeflectionsModel.ppt: Results for simplified math simulations.

-- SanthiElayaperumal - 11 Aug 2008

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