Monte Carlo simulation of photon propagation is a flexible but accurate approach to simulating photon migration. In this method, the local rules for the migration of photons are presented as probability distributions that describe the step size of the photon between the points of interaction with the tissue and the angles at which the photon's trajectory during scattering deviates. This method is equivalent to modeling photon migration using the analytical radiation transfer equation (UPI), which describes the motion of photons using differential equations. However, UPI analytical decisions are often impossible to obtain; for some geometric shapes, the diffusion approximation can be used to simplify the UPI, although this, in turn, introduces many inaccuracies, especially near sources and boundaries. At the same time, Monte Carlo simulations can be made arbitrarily accurate by increasing the number of photons.
The Monte Carlo method is a statistical test method and, therefore, considerable computational time is required to achieve the required accuracy. In addition, Monte Carlo simulation allows you to take into account several physical quantities simultaneously with any spatial and temporal resolution. This flexibility makes the Monte Carlo method a powerful tool. Thus, Monte Carlo methods require a lot of time for calculations, but are usually considered the standard for modeling photon migration for many biomedical applications.
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Monte Carlo Biomedical Applications
Biomedical Tomography
The optical properties of biological tissues make it possible to solve the problems of biomedical tomography. There are many endogenous optical contrasts, including absorption by blood and melanin, scattering by nerve cells and nuclei of cancer cells. In addition, fluorescence probes can be attached to various tissues. Microscopy methods (including confocal and two-photon microscopy , as well as optical coherence tomography ) can display these properties with high spatial resolution, but since they are based on the registration of ballistic photons, their penetration depth is limited to a few millimeters. Tomography of deeper tissue layers, where photons are scattered many times, requires a more detailed description of the behavior of a large number of photons in such an environment. The Monte Carlo method provides a flexible structure that has been used in various techniques to reconstruct the optical properties of deep tissue layers. Here is a brief introduction to some of these techniques.
- Photoacoustic tomography (FAT), absorbed laser light leads to a local increase in temperature. In turn, this change in temperature, due to thermal expansion, causes the propagation of ultrasonic waves, which are recorded using an ultrasonic transducer. In practice, various settings are changed (wavelength of light, numerical aperture of the sensor, ...). As a result, Monte Carlo simulation is a valuable tool for simulating scattering and predicting the behavior of photons in an experiment.
- Diffusion optical tomography (DOT) is an imaging technique that uses infrared sources and light detectors to measure the optical properties of biological tissues. Contrasts of light intensity can be measured by the difference in the absorption of oxy- and deoxy-hemoglobin (for functional diagnosis of the brain or the detection of cancer) or the difference in the concentration of fluorescent labels. In order to recreate the image, you need to know how the light migrated from a given source to a given detector and how the measurement depends on the distribution and change of optical properties (direct task). Due to the strong scattering of light in biological tissues, this method is quite complicated, the sensitivity functions are diffusive. The direct problem in DOT is often solved using Monte Carlo methods.
Radiation Therapy
The goal of radiation therapy is to deliver energy, usually in the form of ionizing radiation to a cancerous tumor, while surrounding tissues cannot be damaged. Monte Carlo simulation is commonly used in radiation therapy to determine the dose of radiation a patient will receive due to radiation scattering in tissues, as well as due to a collimated beam in a linear accelerator.
Photodynamic therapy
In photodynamic therapy (PDT), light is used to activate chemotherapeutic drugs. The principles of PDT determine the usefulness of using Monte Carlo methods to simulate scattering and absorption in tissues to provide the necessary level of light intensity for the activation of chemotherapeutic drugs.
Links
- Wang, LH and Wu Hsin-I. Biomedical Optics: Principles and Imaging. Wiley 2007.
- L.-H. Wang, SL Jacques, and L.-Q. Zheng, "Monte Carlo modeling of photon transport in multi-layered tissues," Computer Methods and Programs in Biomedicine 47, 131-146 (1995).