Light Electromagnetic Radiation

Transcription

1 Biomedicinsk Optik Ljusutbredning i vävnad STEFAN ANDERSSON-ENGELS 1 Light Electromagnetic Radiation Soto Thompson, PhD Thesis,

2 Ionizing versus optical radiation Ionizing Radiation Optical Radiation Electron shell model Electron shell model h 1 h 2 Energy h 1 Molecular energy level diagram h 2 Energy Molecular energy level diagram 3 Light transport in tissue Tissue Light source s >> a Diffusion Absorption, a [m -1 ] Scattering, s [m -1 ] Scattering phase function 2

3 Absorption i vävnad Absorptionskoefficient (cm -1 ) Absorption Blod Vatten 5 Absorption i vävnad Absorptionskoefficient (cm -1 ) Spridning Absorption Blod Vatten 6 3

4 Mie Scattering Size of particles comparable or larger than the wavelength, Mie scattering predominates Because of the relative particle size, Mie scattering is not strongly wavelength dependent Forward directional scattering 7 Reduced Scattering Coefficient Useful for description of photon propagation in diffuse regime Example: g cos o ' (1 g) s mfp 1 1 mfp' s s ' s 0.10 s Each step involves isotropic scattering. Such a description is equivalent to description of photon movement using many small steps 1/µ s that each involve only a partial deflection angle 1 iso-scattering step = 1/(1-g) aniso-scattering steps 8 4

5 Light propagation in turbid media Incident Light Absorption Tissue Chromophores (absorbing molecules) Scattering elements (cells, organelles fibers, etc.) Scattering Light interaction volume UV Visible Red - NIR IR 5

6 Diffuse and specular reflectance Parallel polarisation Perpendicular polarisation Biomedicinsk Optik STEFAN ANDERSSON-ENGELS 12 6

7 Biomedicinsk Optik INNEHÅLL Introduktion och definitioner Ljusutredning i vävnad Diagnostiska Tillämpningar Behandlingstillämpningar 13 Nina Reistad Biomedicinsk Optik LJUSUTBREDNING I VÄVNAD BIOPHOTONICS@LUNDUNIVERSITY 14 7

8 Biomedical Optics 15 From clear liquid to diffuse media Cuvette filled with water. HeNe laser beam coming in from left Increase scattering by adding droplets of milk-like material. 16 8

9 Wavelength matters! 17 Hand exposed with red and green laser light 18 9

10 Ljuspropagering genom vävnad Röntgen Ljus (NIR) Markerad skugga Diffus skugga 19 Prediction and measurement of the light dose Aim: Understand the importance of optical measurements and dosimetry Provide a brief outline of light modelling Diffusion Monte Carlo simulations 20 10

11 Tissue Optics success Pulse oximetri Examples from internet 21 Interstitial illumination with a cylindrical light distributor ' 22 11

12 "Backscattering-balloon-based" Light distributor for PDT in the bronchi (Ranges; Length: mm. Diameter: 2-15 mm) Photo courtesy of Medlight SA 23 "Backscattering-balloon-based" Light distributor for PDT in the bronchi Photo courtesy of Medlight SA 24 12

13 Light modelling - simplifications necessary 25 Medical Laser Treatments Laser surgery Eye (Ar-ion, Nd:YAG, Excimer lasers) Dermatological (CO2, Dye, Ruby, Ar-ion lasers) General surgery (Nd:YAG, diode, CO2 lasers) Thermotherapy Photodynamic therapy Dosimetry is essential!! 26 13

14 Dosimetry Diagnostics 27 The transport equation a, s Radiance in Radiance absorbed Radiance out L e ( r, sˆ, t) t csˆ L c ( r) L s c ( r) s e 4 ( r, sˆ, t) e ( r, sˆ, t) c ( r) L p( sˆ' sˆ) L e a dv Radiance scattered from another direction to direction of interest e ( r, sˆ, t) Scattered to another direction ( r, sˆ', t) dsˆ' q( r, sˆ, t) 28 14

15 The Diffusion Equation! One can derive the Diffusion Eq. for 1. Many scattering event occur so the light becomes diffuse 2. A homogenous medium, that means that the diffusion coefficient D is constant 1 2 ( r, t) D c t ( r, t) ( r, t) a S ( r, t) Analytical or numerical (FEM) solutions Steady State Diffusion ( r ) 2 eff 2 ( r ) S ( r ) With the solution in a homogenous medium with a point source at S(r) =P δ(r=0) ( r) P 2 eff 4 a 1 r exp( eff r ) where eff 3 a ( a s (1 s s (1 g ) 1 D 3( a s (1 g )) g )) a 2 eff 30 15

16 Interstitial PDT geometry Question: How long is the treatment time to accomplish the treatment threshold of an absorbed dose of 20 Jcm -1 at a distance r = 0.8 cm? Tissue a = 0.1 cm -1 s = 10 cm -1 Optical fibre 160 mw r 1 Treated volume Guidelines for solution First, consider the solution to the steadystate diffusion equation as valid for this problem. P eff ( r) 4 a 2 1 exp( r eff r) with eff 3 a a s ( ') 16

17 Guidelines cont d (II) Secondly, consider the absorbed power density a(r) (mw/mm 3 ) to be: a( r) a ( r) Thirdly, the absorbed energy density A(r) depends on the treatment time T as A( r) T a( r) Insert all values in the equation: Computer Lab in MatLab 34 17

18 Absorption spectra Absorption of light in tissue is due to chromophores (= molecules absorbing light). The absorption probability is a material property that varies with the wavelength of light. tissue_abs.m (5% blood, 75% water and 15% fat) Absorption Coefficient (m -1 ) Tissue absorption vs oxygen saturation Sat=65% Sat=75% Sat=85% Absorption Coefficient (m -1 ) Tissue absorption vs water concentration Sat=65% Sat=75% Sat=85% Scattering spectra Scattering of light in tissue is due to changes in the refractive index on the microscopic scale. The scattering probability is a material property that varies with the wavelength of light. tissue_sca.m (a_rayleigh = 400, a_mie = 1900) 3000 Tissue scattering for Rayleigh and Mie scattering 2500 Tissue scattering for different sizes of scatterers Reduced Scattering Coefficient (m -1 ) Total scattering Rayleigh scattering Mie scattering Reduced Scattering Coefficient (m -1 ) b_mie=1 b_mie=1.5 b_mie=

19 Effective attenuation spectra The effective attenuation of light in tissue is due to both absorption and scattering properties, and thus is a material property that varies with the wavelength of light. tissue_mueff.m 2500 Tissue absorption Blood Conc=5% 2500 Tissue scattering Rayleigh strength = Tissue scattering Blood Sat=65% Mie strength = Water Conc=70% 2000 b-parameter = Absorption Coefficient (m -1 ) Lipid Conc=15% Reduced Scattering Coefficient (m -1 ) Effective Attenuation Coefficient (m -1 ) Fluence rate in an infinite medium The fluence rate at a distance from a source depends on the optical properties (= wavelength-dependent) and the distance from the source. CWinfinite.m (5% blood, 60% oxygen saturation, 65% water and 15% fat, a_rayleigh = 500, a_mie = 1000, b_mie = 1) Fluence rate as a function of wavelength and radial distance from point source 25 Fluence rate at various distances Radial distance (cm) Fluence Rate (Wm -2 ) mm 15 mm 20 mm

20 Source term in Diffusion 1. Where to place an isotropic source? 2. How to manage the boundary condition? 1. If we consider a pencil beam incident perpendicular on a semi-infinite volume of tissue, a useful source term in the diffusion equation would be en exponential decay from the surface. Incident light Intensity 1. Source term for narrow beam incident light To simplify the problem, we first assume that all the incident photons are initially scattered at a single depth of z (1 g 1 0 1/ s ' ) The reduced scattering coefficient s can be regarded as an effective isotropic scattering coefficient that represents the cumulative effect of several forward-scattering events. Thus, z o corresponds to an isotropic source at the depth of one reduced scattering coefficient s 20

21 Point source geometry 2. How to manage the boundary condition? Incident light z = -z o - z = 0 z = z o + (,z) z Fluence rate in a semi-infinite medium The fluence rate at a distance from a source depends on the optical properties (= wavelength-dependent), the distance from the source and the tissue boundary. CWsemi.m (5% blood, 65% oxygen saturation and 15% fat, a_rayleigh = 500, a_mie = 1000, b_mie = 1) Fluence rate spectrum as a function of wavelength at position (rho,z) 12 60% H2O Fluence Rate (Wm -2 ) % H2O 80% H2O Incident light - + (,z) z 42 21

22 Diffuse Reflectance from a semi-infinite medium Fluence Rate (Wm -2 ) The diffuse reflectance at a distance from a source depends on the optical properties (= wavelength-dependent), the distance from the source and the tissue boundary. CWsemi.m (5% blood, 65% oxygen saturation and 15% fat, a_rayleigh = 500, a_mie = 1000, b_mie = 1) Fluence rate spectrum as a function of wavelength at position (rho,z) 12 60% H2O 10 70% H2O % H2O Monte Carlo Simulations It is as the name implies a method that relies on random sampling of propagation variables from well defined probability distributions - throwing the dice The path length before a scattering or an absorption event occur The scattering angle length angle 44 22

23 Light transport in tissue Light source Path length Scattering direction Absorption Tissue Start MatLab Simulation 45 How each step is randomised W=W a s a y x W=W-W z s= -ln(1-r[0-1]) s =2R[0-1] 1-g p(cos)= 2(1+g -2gcos) a 2 2 3/

24 Thanks for the attention, Questions? 24