introduction to biomedical optics

School of EngineeringDepartment of Biomedical Engineering

Fall 2014-2015EENG624 – Biomedical Optics

Instructor: Jad AYOUB

Chapters

1. Introduction to biomedical optics

2. Single scattering: Rayleigh theory and Mie theory

3. Monte Carlo modeling of photon transport

4. Convolution for broad-beam responses

5. Radiative transfer equation and diffusion theory

6. Hybrid model of Monte Carlo method and diffusion theory

7. Sensing of optical properties and spectroscopy

8. Ballistic imaging and microscopy

9. Optical coherence tomography

10.Mueller optical coherence tomography

11.Diffuse optical tomography

12.Photoacoustic tomography

13.Ultrasound-modulated optical tomography

Chapter 1 - Introduction

• Motivation for Optical Imaging

• General Behavior of Light in Biological Tissue

• Basic Physics of Light-Matter Interaction

Motivation for Optical Imaging

1. Optical photons provide nonionizing and safe radiation for medical applications.

2. Optical spectra -based on absorption, fluorescence, or Raman scattering- provide biochemical information because they are related to molecular conformation.

3. Optical absorption, in particular, reveals angiogenesis and hypermetabolism, both of which are hallmarks of cancer; the former is related to the concentration of hemoglobin and the latter to the oxygen saturation of hemoglobin. Therefore, optical absorption provides contrast for functional imaging.

4. Optical scattering spectra provide information about the size distribution of optical scatterers, such as cell nuclei.

5. Optical polarization provides information about structurally anisotropic tissue components, such as collagen and muscle fiber.

Motivation for Optical Imaging (cont’d)

6. Optical frequency shifts due to the optical Doppler effect provide information about blood flow.

7. Optical properties of targeted contrast agents provide contrast for the molecular imaging of

biomarkers.

8. Optical properties or bioluminescence of products from gene expression provide contrast for

the molecular imaging of gene activities.

9. Optical spectroscopy permits simultaneous detection of multiple contrast agents.

10. Optical transparency in the eye provides a unique opportunity for high-resolution imaging of

the retina.

Behavior of light in Biological Tissue

Optical properties of biological tissue

Basic properties

• n [–]: index of refraction; e.g., 1.37

• μa [cm–1]: absorption coefficient; e.g., 0.1

• μs [cm–1]: scattering coefficient; e.g., 100

• g [–]: scattering anisotropy, <cosθ>; e.g., 0.9

Derived properties

• μt [cm–1]: total interaction (extinction) coefficient, μa + μs

• lt [cm]: mean free path, 1/ μt; e.g., 0.1 mm

• μs’ [cm–1]: reduced scattering coefficient, μs(1 – g)

• μt’ [cm–1]: transport interaction coefficient, μa + μs’

• lt’ [cm]: transport mean free path, 1/ μt’; e.g., 1 mm

• μeff [cm–1]: effective attenuation coefficient, (3μa μt’)1/2

• δ [cm]: penetration depth, 1/(3μa μt’)1/2; e.g., 5 mm

Light- Matter Interaction

Beer’s Law

• −𝑑𝐼/𝐼

𝑑𝑥= 𝜇𝑡

• 𝐼 𝑥 = 𝐼 0 𝑒−𝜇𝑡𝑥 = 𝐼(0)𝑒−𝑥/𝑙𝑡

I : Ballistic intensity

x : Pathlength

𝜇𝑡: Total interaction (extinction) coefficient

Spectra of major Biological Absorbers

Absorption and its biological origins

• Absorption cross section: 𝜎𝑎• Number of density: Na

• Absorption coefficient: total cross-sectional area for absorption per unit volume:

𝜇𝑎 = 𝑁𝑎𝜎𝑎• Light attenuates as it propagates in an absorbing medium:

𝑑𝐼

𝐼= −𝜇𝑎𝑑𝑥

𝐼 𝑥 = 𝐼0𝑒−𝜇𝑎𝑥 : Beer’s law

• Transmittance: 𝑇 =𝐼(𝑥)

𝐼0: Probability of survival after propagation over 𝑥.

Absorption and its biological origins

• Origin of absorption:

oHemoglobin (Oxygenated & de-Oxygenated)

oMelanin

oWater

Melanin absorbs (UV) light stronglywater can be highly absorbing in some spectral regions

Scattering and its biological origins

• Scattering cross section: 𝜎𝑠• Number of density: Ns

• Scattering coefficient: total cross-sectional area for scattering per unit volume:

𝜇𝑠 = 𝑁𝑠𝜎𝑠• Light attenuates as it propagates in an Scattering medium:

𝑑𝐼

𝐼= −𝜇𝑠𝑑𝑥

𝐼 𝑥 = 𝐼0𝑒−𝜇𝑠𝑥 : Beer’s law

• Transmittance: 𝑇 =𝐼(s)

𝐼0= 𝑒−𝜇𝑠𝑥 : Probability of survival after propagation

over 𝑥.

Scattering and its biological origins

• extinction coefficient : 𝜇𝑡 = 𝜇𝑎+𝜇𝑠 (Total interaction coefficient)

• The reciprocal of 𝜇𝑡 is the mean free path between interaction events

Biological structures of various sizes for photon scattering

Exercise 1

• In a purely absorbing (non-scattering) medium with absorption coefficient 𝜇𝑎, what percentage of light is left after a lightbeampropagates a length of L?

Exercise 1

• In a purely absorbing (non-scattering) medium with absorption coefficient 𝜇𝑎, what percentage of light is left after a lightbeampropagates a length of L?

Exercise 2

• In a purely absorbing (non-scattering) medium with absorption coefficient 𝜇𝑎, Derive the average length of survival of a photon?

Exercise 2

• In a purely absorbing (non-scattering) medium with absorption coefficient 𝜇𝑎, Derive the average length of survival of a photon?

Exercise 3

• In a purely scattering (non-absorbing) medium with scattering coefficient 𝜇𝑠, what percentage of light has not been scattered after the original lightbeam propagates a length of L?

Exercise 3

• In a purely scattering (non-absorbing) medium with scattering coefficient 𝜇𝑠, what percentage of light has not been scattered after the original lightbeam propagates a length of L?

Exercise 4

• In a purely scattering (non-absorbing) medium with scattering coefficient 𝜇𝑠, Derive the average length of survival of a photon.

Exercise 4

• In a purely scattering (non-absorbing) medium with scattering coefficient 𝜇𝑠, Derive the average length of survival of a photon.

Exercise 5

• In a scattering medium with absorption coefficient 𝜇𝑎 and scattering coefficient 𝜇𝑠 , what percentage of light has survived scattering and absorption after the original lightbeam propagates a length of L? Of the percentage that has been absorbed and scattered, what is the percentage that has been absorbed?

Oxygen Saturation and Concentration

• Estimating concentration by absorption coefficients (@ 𝜆1 ≠ 𝜆2):

• 𝜆1 , 𝜆2 : the two wavelengths

• 𝜀𝑜𝑥 , 𝜀𝑑𝑒: Molar extinction coefficients of oxy- and deoxyhemoglobin

• 𝐶𝑜𝑥 , 𝐶𝑑𝑒: Molar concentrations of oxy- and deoxyhemoglobin.

Oxygen Saturation and Concentration

• Once 𝐶𝑜𝑥 and 𝐶𝑑𝑒 are obtained, the oxygen saturation (𝑆𝑂2) and the total concentration (𝐶𝐻𝐵) of hemoglobin can be computed as follows:

• This principle provides the basis for pulse oximetry and functional imaging. Angiogenesis can increase 𝐶𝐻𝐵, whereas tumor hypermetabolism can decrease 𝑆𝑂2.

Application: NIRS (Near IR spectroscopy)