Robust optimization for the placement of and current through electrodes for neurostimulation

Meeting of the Minds 2023 CIT Honors Thesis Presentation

Shivank Joshi

Dr. Pulkit Grover

Chaitanya Goswami

1. Background and Motivation
2. Robust Optimization Formulation
3. Results
4. Next Steps

Agenda

Background

• Researchers use electrodes on the scalp to stimulate different regions of the brain
• Computational tools increasingly used to design electrode schemes

3

[1]

This brain model uses concentric spheres for each layer

• Radii of different brain layers
• Conductivities of the layers
• Relationship between physical parameters, current, and resulting electric field in brain

4

The relationship between current passed through electrodes and the expected current density in the brain can be represented by a transfer matrix

We select two subsets of the points inside the brain:

F - Focus points

C - Cancel points

5

The design of electrodes focuses on achieving activation in a ‘focus’ region and having minimal current in a ‘cancel’ region

A_F - Transfer matrix for focus points

A_C - Transfer matrix for cancel points

I - Current injected into each electrode

6

The optimization problem to get the best design for some A_F and A_C is convex

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7

The reverse problem aims to get the transfer matrices, A_F and A_C, for designed I

c’ - original conductivities

c - conductivity variable

g - tolerance on how much

c can deviate from c’

8

The robust optimization approach sequentially

1

Solve for I using original approach.

I’ = I

2

Solve for worst case c yielding A’_F and A’_C using I’

3

Resolve for I’ using original approach

9

How does the robust optimization compare to the original formulation?

Using particle swarm optimization to get worst-case solution

• This robust formulation yielded
• 12.5% worst-case improvement
• Slightly worst average-case performance

10

Conclusions and Next Steps

• A robust approach could help researchers design safer experiments
• Future work
• Validating work on larger variety of parameters
• Extend to include other uncertainties
• Design other robust formulations

14

Thank you to Dr. Pulkit Grover and Chaitanya Goswami!