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Theoretical simulation of the selective stimulation of axons in different areas of a nerve bundle by multichannel near-infrared lasers

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Abstract

Damaged nerve function can be repaired by applying external stimuli, and the selective stimulation of nerve fibers is the highest goal of nerve functional repair. This paper proposes a method of using multichannel near-infrared lasers to achieve the selective stimulation of axons in different areas in a mixed nerve bundle. An exposed bullfrog sciatic nerve was considered the object of study to realize the selective stimulation. A model was established by using COMSOL Multiphysics to simulate the temperature distribution of nerves under multichannel near-infrared laser stimulation. The results of this model showed that by changing the distance between the laser fiber and the nerve (d) or the power of the 4 lasers (P), the axons at different parts of the nerve bundle may be selectively stimulated. If only the axons located in the center are selected to be activated, it is necessary to set the d and P value in the four directions to the same value. If only axons on the nerve edge are selected for activation, we can reduce the d value of the nearest laser (or increase P) and increase the d value of lasers in other directions (or decrease P). If only axons in the shallow area below the surface between the two lasers are selected for activation, it is necessary to reduce the d value of the laser in two directions close there (or increase P) and increase the d value of the laser in the other two directions (or decrease P). If only the axons of the superficial region on the coordinate axis are activated, the d value of the laser in the farthest direction can be increased (or decrease P) and the d value of the other three lasers can be reduced (or increase P). Moreover, the results of animal experiments further verify the feasibility of our method to realize selective activation of the axons.

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Funding

This work was supported by the Nature Science Foundation of China Grant (No. 31500796).

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Authors and Affiliations

  1. Key Laboratory of Biomaterials of Guangdong Higher Education Institutes, Institution of Biomedical Engineering, Jinan University, Guangzhou, 510632, Guangdong, China

    Rui Zhou & Zongxia Mou

  2. Hubei Key Laboratory of Medical Information Analysis and Tumor Diagnosis and Treatment, South-Central University for Nationalities, Wuhan, 430074, China

    Dandan Yang

  3. Key Laboratory of Biorheological Science and Technology of Ministry of Education, Chongqing University, Chongqing, 400044, China

    Xing Wang

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  1. Rui Zhou
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  2. Zongxia Mou
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  4. Xing Wang
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Correspondence to Zongxia Mou or Xing Wang.

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Appendix

Appendix

According to Beer-Lambert Law,

$$AU=\mathrm{lg}(1/T)=KCl,$$
(8)

Where,

T:

the transmittance (the ratio of transmitted light intensity to incident light intensity).

K :

the extinction coefficient of the solution (L/g/cm).

C :

the concentration of the solution (g/L).

l :

the optical path of the solution (cm).

In this paper, μα = 1/lα.

μα:

the absorption coefficient (1/cm).

l α :

the absorption length (cm).

l α :

is also the optical path when T = 1/e, where AUα = lg(1/T) = lge = 0.43429448. According to Formula (8), AUα = KClα, then

$${\mu }_{\alpha }=1/{l}_{\alpha }=KC/{AU}_{\alpha }.$$
(9)

From the measurement results we can see that AU is about 2 at λ = 808 nm, where C = 3e-5 g/l, and l = 1 cm. So according to Formula (8),

$$AU=KCl=2.$$
(10)

Where,

K and C is equal to those in Formula (9) and l is the equal the thickness of the cuvette (l = 1 cm). Then solve formulas (9) and (10), μα = 4.6 (1/cm) = 460 (1/m).

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Zhou, R., Mou, Z., Yang, D. et al. Theoretical simulation of the selective stimulation of axons in different areas of a nerve bundle by multichannel near-infrared lasers. Med Biol Eng Comput 60, 205–220 (2022). https://doi.org/10.1007/s11517-021-02475-y

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