Influence of the number of severed axons on axonal regeneration.

a) Growth rate of regenerating axons, b) success rate of axonal regeneration, c) effective growth rate, d) concentration of CRMs-1, and e) concentration ratio of CRMs-3 to CRMs-2, plotted as functions of log10 NA, where NA is the number of severed axons. The curves in each panel were obtained on scaffold No. 1 (0.15 × 0.3), No. 2 (0.3 × 0.3), and No. 3 (0.45 × 0.3), respectively. f) Longitudinal coordinates in panel b averaged over the number of horizontal coordinates on scaffolds No. 1, No. 2, and No. 3 (left to right). Error bars indicate the standard deviations.</p

Influence of CRMs1-3 point-source density on axonal regeneration.

a) Growth rate of regenerating axons, b) success rate of axonal regeneration, and c) effective growth rate of axons as functions of CRMs-3 point-source densityfor different densities (η2) of the CRMs-2 point source. The test scaffold is sized as ra×rb = 0.15×0.3, the CRMs-1 point-source density is η1 = 1, and the number of severed axons is NA = 1200. d) Success rate of axonal regeneration averaged over η3 = 0−100 for each η2.</p

Three test scaffolds of different lateral sizes and some products.

a)–c)The scaffolds and attached regenerated axons are separated and extracted from the models after calculation. In scaffolds No. 1, No. 2, and No. 3, the lateral semi-axis is ra = 0.15, 0.3, and 0.45 (or 0.75, 1.50, and 2.25 mm), respectively. The longitudinal semi-axis is rb = 0.3(or 1.5 mm) in all cases, and the number of severed axons is NA = 300 in each calculation. The green bubbles with number NT = 300 and density γ1 = 0.1 μm−2 embedded in the upper part (or the caudal/off-ramp) of each scaffold represent the coarsening point sources (or target cells) for CRMs-1 (two other seed types with densities γ2 = γ3 = 0.1 μm−2 also cover the whole surface of each scaffold but are not shown). The green longitudinal lines (slightly fascicled) stemming from the lower part (the rostral/on-ramp) of each scaffold represent the regenerated axons (numbering 0.78 NA, 0.7 NA, and 0.58 NA in a, b, and c, respectively, corresponding to axonal regeneration success rates of 0.78, 0.7, and 0.58, respectively). d)–g) Results related to a typical regenerating axon taken from the calculation of scaffold No. 1 (qualitatively similar results are obtained for the other two scaffolds). At the beginning, when the axon is at the on-ramp, its growth is unstable and some retraction is observed (d and e) because the concentrations of the positive factors CRMs-1 (f) and CRMs-3 are low (g; green), while those of the inhibitoryfactors are high (g; red). This situation is reversed as the axon approached the off-ramp.</p

Influence of CRM1-1 point-source density on axonal regeneration.

a) Growth rate of regenerated axons, b) success rate of axonal regeneration, and c) effective growth rate of axons as functions of the density (η1) of the CRMs-1 point source. Results are plotted for different densities (η2) of the CRMs-2 point source. The test scaffold is sized as ra×rb = 0.15×0.3, the CRMs-3 point source density is η3 = 1, and the number of severed axons is NA = 1200. d) Success rate of axonal regeneration averaged over η1 = 0−100 for each η2.</p

Parameters used in simulations.

Parameters used in simulations.</p

Schematics of an injured spinal cord bridged by a spherical scaffold.

a) A complete transection of spinal cord with a gap bridged by a spherical scaffold between the rostral and caudal stumps. b) The scaffold architecture, coordinate system, and symbols employed in the mathematical models. The fabricated scaffold is assumed to be coated with hydroxylapatite (HA)/extracellular matrix (ECM) components (collagen I, fibronectin, and laminin I) and HA/LV-chondroitinase ABC (ChABC) over the whole surface (green). Additional HA/LV-NT-3/LV-brain-derived neurotrophic factor (BDNF) was coated on the off-ramp area (yellow).</p