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