Fig. 1. Moving diagram of spherical coordinate

Fig. 2. (a) 3D model of vein and perivenous tissues; (b) 360° radial light source

Fig. 3. Simplified model of vein. (a) xz plane(y=0); (b) yz plane(x=0)

Fig. 4. Light distributions of xz plane (y=0) at different wavelengths. (a) 810 nm; (b) 940 nm; (c) 980 nm; (d) 1320 nm; (e) 1500 nm

Fig. 5. Longitudinal distribution of fluence with different wavelengths

Fig. 6. Light distribution of xz plane (y=0) with different wavelengths and vessel diameters. (a) 1500 nm, 0.6d1,0.6d2; (b) 1500 nm, 1.2d1, 1.2d2; (c) 1500 nm, 1.8d1, 1.8d2; (d) 1500 nm, 2.4d1, 2.4d2; (e) 1320 nm,0.6d1, 0.6d2; (f) 1320 nm, 1.2d1, 1.2d2; (g) 1320 nm, 1.8d1, 1.8d2; (h) 1320 nm, 2.4d1, 2.4d2

Fig. 7. Longitudinal distribution of fluence with different wavelengths and vessel diameters. (a) 1500 nm; (b) 1320 nm

Fig. 8. Light distributions of xz plane (y=0) at different light source positions. (a) (0,0,0.30); (b) (0,0,0.28);(c) (0,0,0.26); (d) (0,0,0.24); (e) (0,0,0.22); (f) (0,0,0.20)

Fig. 9. (a) Longitudinal distribution of fluence at different light source positions; (b) catheter developed by Vuylsteke et al[25]

Fig. 10. Light distributions of xz plane (y=0) for different optical parameters of blood. (a) Blood 1; (b) blood 2; (c) blood 3

Fig. 11. Longitudinal distribution of fluence of different optical parameters of blood

Table 1. Change of photon weight, position, and directional cosines

Table 2. Optical parameters of blood, vessel wall, and perivenous tissues