Session: 17-01-01: Research Posters

Paper Number: 143689

143689 - Developing Novel Coherence Measures for Systems With Multiple Correlated Inputs: Theory and Application to the Study of Pathological Tremor 

Coherence is a common tool used for analyzing relationships between measured inputs and outputs of an unknown system. In a single-input linear system, ordinary coherence describes the portion of the output power that can be attributed to the input (i.e., caused by the input). However, in a system with multiple inputs, input/output relationships become more complicated, so much so that standard coherence measures only allow for robust analysis of the simple case where inputs are uncorrelated. Using existing coherence measures, four primary paths exist for analysis of a multiple input system with correlated inputs:

1. If inputs can be controlled, design a set of uncorrelated inputs (then ordinary coherence quantifies the contribution of each input).

2. Transform the actual, correlated inputs into a new set of uncorrelated inputs (this new set may not have any physical meaning).

3. Use ordinary coherence to establish an upper bound on the contribution of each input.

4. Use multiple coherence to quantify the contribution of the set of inputs collectively (this provides no insight into the contributions of individual inputs).

In some applications, such as pathological tremor (see below), we desire to estimate the exact contribution of each individual input, but inputs cannot be controlled, and transformed, uncorrelated inputs have no physical meaning. In such cases, existing coherence measures are unable to comprehensively quantify the input/output relationships of the system in a satisfactory manner. Therefore, we have expanded the concept of coherence and proposed two novel coherence measures: component coherence and adjusted coherence.

Component coherence is derived as a decomposition of multiple coherence into individual components associated with power from each input individually (ordinary components) and cross-power between each pair of inputs (cross components). Ordinary components describe the portion of output power that a given input would optimally contribute to the measured output if no other inputs were present, and cross components describe the portion of the measured output power optimally caused by interference between inputs. Formulaically, component coherence is a generalization of ordinary coherence to multiple-input systems.

Adjusted coherence describes the portion of the output power that would be removed if the given input (or group of inputs) were removed (i.e., set to zero). Adjusted coherence is calculated as the sum of all component coherence terms associated with the specified input (or group of inputs). This measure represents the optimal linear estimate of the portion of output power contributed by a given input or group of inputs. Formulaically, adjusted coherence represents a generalization of multiple coherence from the full set of inputs to allow for any subset of inputs.

Application of this method is illustrated by analyzing the problem of peripheral tremor suppression. Many peripheral methods for tremor suppression have shown promise but currently fall short of their full potential due to uncertainty about where to intervene most efficiently (which joints or muscles). To improve the effectiveness of these methods we aim to identify how much each muscle contributes to tremor.

Tremor can be modeled as a multiple-input system, with muscle activity as the inputs and physical tremor at the output. However, muscle activity tends to be highly correlated at the frequency of tremor and none of the existing analysis paths (options 1-4 listed above) provide a suitable answer to the question of which muscles contribute most to tremor. We have successfully implemented the new coherence measures, yielding estimates of the contribution of each wrist muscle to tremor at the hand. A statistical analysis of adjusted coherence values has revealed significant trends in which muscles contribute most to tremor both within individuals and across subjects.

Presenting Author: Nolan Howes Brigham Young University

Presenting Author Biography: Nolan Howes is currently a doctoral researcher with the Neuromechanics Research Group at Brigham Young University. His research focuses on the application of principles from system dynamics, controls, and signal processing to the problem of pathological upper limb tremor.

Authors:

Nolan Howes Brigham Young University
Matthew Allen Brigham Young University
Dario Farina Imperial College London
Steven Charles Brigham Young University