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Research Paper

# A Multivariate Logistical Model for Identifying the Compressive Sensitivity of Single Rat Tactile Receptors as Nanobiosensors

[+] Author and Article Information
Sean S. Kohles1

Reparative Bioengineering Laboratory, Department of Mechanical and Materials Engineering, Portland State University, Portland, OR 97201; Department of Surgery, Oregon Health and Science University, Portland, OR 97239kohles@cecs.pdx.edu

Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, MA 01609

Shelley S. Mason

Reparative Bioengineering Laboratory, Department of Mechanical and Materials Engineering, Department of Biology, Portland State University, Portland, OR 97201

Fred J. Looft

Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, MA 01609fjlooft@wpi.edu

1

Corresponding author.

2

Presently with PMC-Sierra, Roseville, CA.

J. Nanotechnol. Eng. Med 2(1), 011002 (Dec 13, 2010) (7 pages) doi:10.1115/1.4002750 History: Received August 25, 2010; Revised September 14, 2010; Published December 13, 2010

## Abstract

Tactile sensation is a complex manifestation of mechanical stimuli applied to the skin. At the most fundamental level of the somatosensory system is the cutaneous mechanoreceptor. The objective here was to establish a framework for modeling afferent mechanoreceptor behavior as a nanoscale biosensor under dynamic compressive loads using multivariate regression techniques. A multivariate logistical model was chosen because the system contains continuous input variables and a singular binary-output variable corresponding to the nerve action potential. Subsequently, this method was used to quantify the sensitivity of ten rapidly adapting afferents from rat hairy skin due to the stimulus metrics of compressive stress, strain, their respective time derivatives, and interactions. In vitro experiments involving compressive stimulation of isolated afferents using pseudorandom and nonrepeating noise sequences were completed. An analysis of the data was performed using multivariate logistical regression producing odds ratios (ORs) as a metric associated with mechanotransduction. It was determined that cutaneous mechanoreceptors are preferentially sensitive to stress (mean $ORmax=26.10$), stress rate (mean $ORmax=15.03$), strain (mean $ORmax=12.01$), and strain rate (mean $ORmax=7.29$) typically occurring within 7.3 ms of the nerve response. As a novel approach to receptor characterization, this analytical framework was validated for the multiple-input, binary-output neural system.

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## Figures

Figure 1

Schematic of the mechanical and statistical modeling approach as functionally interrelated through single nerve mechanotransduction. Individual components of the rapidly adapting nerve are noted with the oval corpuscles having longitudinal and transverse dimensions ranging from 156 μm to 2025 μm and 88 μm to 1249 μm (in monkeys), respectively, as dependent upon location and distribution (23).

Figure 2

Illustration of the experimental setup, control loop scheme, and data acquisition arrangement. The applied time-dependent mechanical stimulus was established in either force or displacement control.

Figure 3

Representative normalized plots of the applied dynamic mechanical stimulus (stress and strain) as well as their time derivatives. The input waveform was a nonrepeating, pseudorandom noise function. Here, normalization was conducted by subtracting the means and dividing by the standard deviations. This allowed for all input variables to be represented nondimensionally within the model.

Figure 4

95% confidence intervals of ORs as an aggregate influence of all experimental variables represented over the offset times leading to a nerve signal response. ORs>1.0 indicate a probabilistic likelihood of predicting the nerve signal based on the direct mechanical stimulus, its time-derivative, or a stimulus interaction.

Figure 5

The response frequency of a maximum OR occurring at a specific offset time leading to a nerve signal based on the direct mechanical stimulus, its time-derivative, or a stimulus interaction

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