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TECHNICAL PAPERS: Cell

# Axon Kinematics Change During Growth and Development

[+] Author and Article Information
Hailing Hao

Department of Biomedical Engineering, Rutgers,  The State University of New Jersey, 617 Bowser Road, Piscataway, NJ 08854

David I. Shreiber

Department of Biomedical Engineering, Rutgers,  The State University of New Jersey, 617 Bowser Road, Piscataway, NJ 08854shreiber@rci.rutgers.edu

J Biomech Eng 129(4), 511-522 (Feb 14, 2007) (12 pages) doi:10.1115/1.2746372 History: Received March 28, 2006; Revised February 14, 2007

## Abstract

The microkinematic response of axons to mechanical stretch was examined in the developing chick embryo spinal cord during a period of rapid growth and myelination. Spinal cords were isolated at different days of embryonic (E) development post-fertilization (E12, E14, E16, and E18) and stretched 0%, 5%, 10%, 15%, and 20%, respectively. During this period, the spinal cord grew $∼$55% in length, and white matter tracts were myelinated significantly. The spinal cords were fixed with paraformaldehyde at the stretched length, sectioned, stained immunohistochemically for neurofilament proteins, and imaged with epifluorescence microscopy. Axons in unstretched spinal cords were undulated, or tortuous, to varying degrees, and appeared to straighten with stretch. The degree of tortuosity (ratio of the segment’s pathlength to its end-to-end length) was quantified in each spinal cord by tracing several hundred randomly selected axons. The change in tortuosity distributions with stretch indicated that axons switched from non-affine, uncoupled behavior at low stretch levels to affine, coupled behavior at high stretch levels, which was consistent with previous reports of axon behavior in the adult guinea pig optic nerve (Bain, Shreiber, and Meaney, J. Biomech. Eng., 125(6), pp. 798–804). A mathematical model previously proposed by Bain was applied to quantify the transition in kinematic behavior. The results indicated that significant percentages of axons demonstrated purely non-affine behavior at each stage, but that this percentage decreased from 64% at E12 to 30% at E18. The decrease correlated negatively to increases in both length and myelination with development, but the change in axon kinematics could not be explained by stretch applied during physical growth of the spinal cord. The relationship between tissue-level and axonal-level deformation changes with development, which can have important implications in the response to physiological forces experienced during growth and trauma.

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## Figures

Figure 1

Chick embryo spinal cord growth in ovo from E12 to E18. During this period of development, the length between the third to thirteenth nerve root increased almost 55%. Significant increases in length were observed from stage-to-stage (ANOVA with repeated measures, followed by Scheffé’s post hoc tests, max p<0.001). Growth during this period was linear (R2=0.99), with a slope (± std err) of 1.38±0.02mm∕day.

Figure 2

Progression of myelination in the chick embryo spinal cord. (A–D) Neurofilament immunohistochemistry indicating presence of axons. (E–H) Myelin basic protein immunohistochemistry indicating myelination. Low magnification images of whole cross sections and higher magnification images of the lateral funiculus (LF) were taken following immunohistochemical double-labeling of the chick embryo spinal cord. Little myelin was observed in E12 spinal cords (E versus A). At E14 (F versus B), myelination is pronounced in the ventral funiculus (VF), but less so in the lateral funiculus. By E16 (G versus C), myelination has begun in nearly all white matter tracts, and by E18 (H versus D) myelin is pronounced throughout the white matter, including the lateral funiculus. Scale bars=200μm.

Figure 3

Quantitative comparison of changes in myelination with development. The degree of myelination was determined from images of immunohistochemically double-labeled spinal cord tissue as the ratio of myelin-positive staining to neurofilament-positive staining in white matter. The degree of myelination (average ± standard deviation) increased significantly from E12 to E18 (ANOVA, followed by Scheffé’s post hoc test, max p=0.008).

Figure 4

Immunohistochemistry and tortuosity characterization for E12 spinal cords. Fixed spinal cords were sectioned horizontally and immunhistochemically stained for neurofilament proteins. (A) Many axially oriented, wavy axons were observed in unstretched spinal cords. The distribution of axonal tortuosity followed a normal distribution. As stretch increased ((B)=5%, (C)=10%, (D)=15%) axons became progressively straighter, and a significant number of axons had tortuosity equal or near one. At the highest stretch ratio ((E)=20%), almost all axons appeared to be straight or nearly straight. (Scale bars=200μm.)

Figure 5

Normalized axonal tortuosity distributions following controlled stretch for (A) E12, (B) E14, (C) E16, and (D) E18 chick embryo spinal cords. Each embryonic stage demonstrated similar distributions in unstretched spinal cords and as stretch was increased. The peak of the distributions for unstretched cords (circles, λ=1) shifted left from E12 to E18, indicating a progressive straightening of axons with growth and development. With increasing stretch, E12 axon tortuosity demonstrated a pronounced shift to the left (in a left-censored fashion), such that at 20% stretch, over 60% of the axons had a tortuosity ∼1, and a sharp drop-off in the distribution followed (inverted triangles, λ=1.20). With growth and development, distributions shifted to the left to lesser degrees, such that at E18, just over 30% of the axons had a tortuosity ∼1, and the subsequent fall-off was less steep.

Figure 6

Effects of changing T1 on predicted tortuosity distributions of E14 control axons exposed to 10% stretch. T1, which represents the lower bound of the uniform distribution that defines the switching parameters, was varied from 0.8 to 1.2, while holding T2 constant at 1.4. T1 influences the left-hand side of the tortuosity distribution. Increasing T1 shifts the behavior from non-affine to affine.

Figure 7

Effects of changing T2 on predicted tortuosity distributions of E14 control axons exposed to 10% stretch. T2, which represents the upper bound of the uniform distribution that defines the switching parameters, was varied from 1.1 to 1.3, while holding T1 constant at 1.0. T2 influences the right-hand side of the tortuosity distribution. Increasing T2 shifts the behavior from non-affine to affine.

Figure 8

Comparison of E12 results to affine, non-affine, and switching kinematic models. Neither the affine nor non-affine model (solid lines) suitably matched the experimental data (open squares) describing tortuosity changes with tissue level-stretch ((A)–5%. (B)–10%. (C)–15%, (D)–20%), though the general trend was better predicted by the non-affine model. The experimental data across all stretch levels was used as the objective function to optimize the switching model. The non-linear regression was executed 50 times (diamonds). The optimized switching model provided a much improved prediction of tortuosity (average R2=0.94±0.0015 for the 50 simulations).

Figure 9

Comparison of E18 results to affine, non-affine, and switching kinematic models. Neither the affine nor non-affine model (solid lines) suitably matched the experimental data (open squares) describing tortuosity changes with tissue level-stretch ((A)–5%. (B)–10%. (C)–15%, (D)–20%), though, like E16, the shift from non-affine to affine kinematics with stretch was more obvious. The experimental data across all stretch levels was used as the objective function to optimize the switching model. The non-linear regression was executed 50 times (diamonds). The optimized switching model provided a much improved prediction of tortuosity (average R2=0.86±0.01 for the 50 simulations).

Figure 10

Upper and lower bounds of the uniform distribution defining the best-fit switching models for all developmental stages (average ± standard deviation of the 50 simulations per stage). For all stages, T1<1 and T2>1, indicating that a percentage of the axons [(1−T1)∕(T2−T1)×100] demonstrates solely non-affine kinematics. Though statistical differences were detected among T2 values (diamonds), (ANOVA, p<0.01), no consistent trend was observed with developmental stage. Conversely, T1 (circles) increased with developmental stage, and showed the greatest increase between E14 and E16. A second set of simulations were run to find the values of T1 while holding T2 fixed across developmental stages at the average value from the two-parameter fits (T2=1.087). T1 values from the one-parameter fit (open squares) were not significantly different than T1 values from the two-parameter fit (p=0.37).

Figure 11

Predicted tortuosity cumulative distributions when applying incremental stretch to E12 control axons to simulate growth-induced stretch of the spinal cord. The percentage increases in length from E12 to E14, E12 to E16, and E12 to E18 were used as the applied stretch in the kinematic models, and the results were compared to unstretched distributions from E14, E16, and E18, respectively. All three kinematic models grossly over-estimated the degree of straightening that would be produced by growth of the spinal cord. (The switching model falls naturally between the non-affine and affine models and is not shown.) Similar results were observed following simulation of growth from E14 to E16, E14 to E18, and E16 to E18.

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