Quantitative techniques for diagnostic and interventional

applications – a decision support based approach.

- Cartik S. Sharma

Structure of presentation

An introduction to the clinical decision support problem.

Decision making in a multimodal environment with multiple tradeoffs.

Applications in the field of diagnostic prediction for conformal voxel spectroscopy.

Some math theory for imaging analytics..

Applications for neurodiagnostics in magnetoencaphalography.

Applied computation for surgical robotics.

Conclusions

References

Motivation

Characteristics of multimodal clinical OR environments.• Clinical environments tend towards high

information content.• Have multiple tradeoffs in decision making.• Focused around optimal patient rehabilitation and

clinical efficacy.

Hence..Ideal candidates for elegant quantitative techniques and advanced computational heuristics!

A cognitive task framework for multimodal decision making….some initial work

We consider a NP complete decision scenario where there are multiple local optima and global optimal choice.Designers and decision makers have to make optimal choices based on multiattribute parameters and variations .We conducted studies at the VR Laboratory at SUNY at Buffalo for the layout problemto interpret choice and decision making in an NP complete facility layout problem.

Studies indicate virtual reality with haptics and graphics enhances decision making (66.67% of subjects) and wrt time to arrive to optimal choice, note: initial solution obtain by implementing simulated annealing.

Figure 1. A combined haptic and graphics decision layout model for optimal decision making. [1,2]

Implications in the clinical world..

Adding haptic and other reality augmenting cues will simplify complex decision making in the OR.

Model clinical/surgical problems quantitatively.

Then augment models with VR aids based on initial conclusions..

Interpret choice and behavior with post processing.

Arrive at clinical solutions with greater efficacy.

Hence improve patient outcomes..

Z-KAT Inc., (now Mako Surgical) Makers of image guided surgery software

Benefits of Image Guided Surgery:

oMinimally invasive surgical procedures.

oImproved accuracy and shorter Operation Room times.

oEnhanced decision support system for the surgeon.Figure 1: IGS Workstation

Figure 2: Active probe array and fiducial spheres

Centre of rotation of the elbow

Fluoro image of the external fixation device placed over the elbow

External fixator, EBI Medical.

Z-KAT Inc. (now Mako Surgical) Makers of image guided surgery software (contd)

External fixation of the elbow using image guided and imageless techniques

Calculation of center of rotation of the elbow using optical trackers with submillimetric accuracy.

Estimate the center of the circle formed by movement of elbow by minimizing norm of least squares of radius, ||r-r0||^2

Provide a means to position and orient the external fixator on the elbow.

Compute postoperative range of motion for the elbow after the fixatorhas been placed.

Conformal voxel spectroscopy

Approach:

Intensity based segmentation of brain tumours.

3D representation of tumor surface using quad strips.

Mesh decimation to progressively reduce number of planes for optimal saturation planes around the tumor.

Clinical post processing of resultant saturation planes around the tissue of interest.

Problem statement:

Optimize placement of saturation planes around the tumor to obtain maximum spectral response from tumor tissue as compared to surrounding healthy tissue.

Diagnostic indicators for tumor prediction in spectroscopy.

Mathematical problem:

Given an unstructured grid, create a condensed form of mesh like structures for maximum spectroscopic signal discerning tumor and healthy tissue.

Existing methods had a simple cuboid around tumor, improved approach [3], (Ryner et al.) focusses on a convex planar set to collect and display signal.

Our collective approach [4]

Segmentation

Spatial specification, meshing for topology preservation [4], [5]

Rendering

Post processing & mesh redistribution.

Optimize signal recovery on scanner.

Image segmentation, ROI Generation

Conformal Voxel Spectroscopy Cancer program at

National Research Council of Canada, Institute of Bio diagnostics

Figure 3. Progressive mesh decimation at 10% (1159 planes), 1% (122 planes) and 0.15%. (18 planes)

Tumor rendering (courtsey, nrc, ibd)

Surf rendering,..1159 planes, 10%

Tumor surrounded by voxel. 0.15% at 18 planes

SR. NO. TUMOR VOLUME

(MM3)

TUMOR /CUBOID

TUMOR / NON ORTHOGONAL

CUBOID

TUMOR /CONFORMAL

VOXEL

TIME TAKEN

(S)

NUMBER OF PLANES

1. 7664.6 0.55 0.57 0.84 12.82 18

2. 5602.17 0.405 0.55 0.99 3.1 18

3. 7414.63 0.538 0.538 0.96 1.22 18

4. 7739.93 0.56 0.58 0.73 1.2 16

5. 7980.68 0.577 0.6 0.88 1.22 18

6. 7020.47 0.508 0.74 0.83 10.2 18

Average 7237.08 0.52 0.6 0.87 4.96 18

VSM Medtech Ltd (Magnetoencephalography manufacturers)

Cortical surface segmentation and extraction based on Brain Extraction Technique. (fMRI laboratory FSL)

Interpolation of the cortical surface using spherical harmonics and

Improved source localization accuracy for MEG devices.

MEG scanner

Spherical harmonics in the cortical surface interpolation realm

The general solution to Laplace’s equation for a ball centered at the origin is a linear combination of spherical harmonic functions multiplied by appropriate scale factor r raise to l.

Where f is the objective function at degree m, power l with harmonic coefficients at polar coordinates (the, psi) defined over a sphere of radius r,

Solving …for expression of Yl, m will yield a spherical harmonic solution of value equivalent to:

Matrix mathematics for interpolation. (NR in C)

Imagine sampling the Y co-ordinate of a point is expressed as a function of x and higher orders of x for any curve.

Y = f(x) = c0+c1*x+c2*x^2+...+cn*x^nFor the matrix,

[A] [X] = [B]The elements of A are the full polynomial expansion expressing the y co-ordinate of a point y = f(x)

X is the matrix the column matrix indicating coefficients of various points in the point cloud.

The elements of B are the final value of the Y co-ordinate of the point.

So for various point pairs, we identify interpolation points as well as the co-ordinate values and solve the equation to obtain these interpolation coefficients. (Include CTF references)

Solving the Laplace equation for a ball, (based on a set of points from initial estimate) at various levels of l and orders of m, give us the spherical harmonic coefficients and hence an adaptive interpolation scheme for cortical surface points.

Applications to cortical surface interpolation for improvements in magnetoencaphalography signal reconstruction..

Generate neuroimages with an MRI scanner

Create a boundary mesh, rough approximations preserving topology.

Problem(s) : How do we interpolate for signal measurement in infinitesimally small patches?

Model with spherical harmonic expansions..interpolate with coefficients obtained in the previous sections..

Redefine cortical surface to adequately represent individual signal measurements.

Observations from MEG PIs: Higher source localization accuracy due to improved interpolation.

Cortical surface extraction. Courtesy Brainvisa

Run BET

Run Spherical harmonic interpolation

Open DICOM

Obtain interpolation and high density gridfor magnetoencaphalography

Interventional robotics as a decision support system.

Clinically, neurosurgical , orthopedics ,cardiovascular imaging and laparoscopy therapy are rich with examples requiring precision and automation. (include a reference)

Adopts and improves on various imaging measurements and modalities and provides an error free environment for intraoperative procedures.

Provides distinct advantages: minimal incision sizes, reduces OR times and faster rehabilitation.

* Include number of procedures, clinical improvements and clinical market needs and work ahead..

Summary

We have explored the world of applied computation to clinical practice.

The power of computing and improved communication through technology opens possibilities of a world that are Unbounded..

Challenges:

To bring to the foyer computationally elegant solutions with high clinical value to overcome complex routine challenges in the OR!

Provide the clinician with high quality precision images and computation.

Give the patient a low cost, reliable and accurate operative solution.

References

Kusiak, A. and Heragu, S.S. “The facility layout problem, European Journal of Operations Research, 29, 229-251, 1987

Sharma C. and Kesavadas, T. “ Investigation of haptic framework in quantitative decision making in a virtual environment” Virtual Systems and Multimedia, UC Berkeley 2001.

L. Ryner, G. Westmacott, N. Davidson, P. Latta . “Automated Positioning of MultipleSpatial Saturation Planes for Non-Cuboidal Voxel Prescription in MR Spectroscopy”, ISMRM 2005.

A hybrid mesh refinement paradigm for conformal voxel spectroscopy. Sharma C., Bolinger L., Ryner L. International Symposium for Biomedical Imaging, Bethesda, MD.

Garland M., Heckbert P. Surface simplification Using Quadric Error Metrics. Proceedings of SIGGRAPH 97, 1997

Spherical Harmonics from Wikipedia: http://en.wikipedia.org/wiki/Spherical_harmonics