A computational framework for investigating the feasibility of focusing light in biological tissue via photoacoustic wavefront shaping

A manuscript and the acompanying presentation for one of two talks given SPIE Photonics West in San Fransico.

Simulation of Gaussian beam propagation — Figure: 2D cross-section of a Gaussian beam propagating through the tissue-like medium. The location of a target location for focusing light to via PAWS is shown by the white circle. A 30 by 30 μm plane of interest at this target is shown by dashed line, onto which we will focus light.

Biological tissue scatters light, limiting the penetration depth of various biomedical optics techniques. A technique that that could compensate for the deleterious effects of scattering is wavefront shaping (WFS). WFS involves spatially structuring the light field incident upon a scattering medium, so as to control the interference patterns produced in the medium. In principle, this allows creating a bright optical focus deep in scattering media, including biological tissue. By focusing light in tissue, WFS could enable increasing the penetration depth of a range of biomedical optics techniques.

The ability of focusing light through scattering layers such as optical diffusers using WFS is now well established. However, focusing inside tissue is significantly more challenging. One challenge is it requires monitoring the light field inside the tissue order to provide a feedback signal to guide the optimization, i.e. a so-called internal “guidestar”. One possible “guidestar” involves measuring photoacoustic (PA) signals – ultrasound waves generated when light is absorbed by tissue. Using PA signals to guide WFS gives rise to “photoacoustic wavefront shaping” (PAWS).

Like WFS in general, PAWS has enabled focusing light through diffusers, but focusing in tissue presents challenges. One relates to the sensitivity and spatial resolution of PAWS systems. Specifically, the theoretical maximum focal enhancement (achievable increase in light intensity at the “focus”) is expected to scale with 𝑁/𝑀 . Where: 𝑁 is the number of independently controlled “input modes” (commonly: the number of elements on the spatial light modulator (SLM) used to structure the incident light), and; 𝑀 is the number of independently observable “output modes” (independently resolvable speckle grains in the interference (speckle) pattern producing the PA signals). In static benchtop PAWS experiments, 𝑁 can be made large using high-resolution SLMs. Concurrently, 𝑀 can be made small because the speckle field generating the PA signals can be physically expanded (to ultrasonic length scales) to enable isolating the PA signals generated by a small number of speckles. By contrast, when focusing in tissue, factors such as the tissue decorrelation time and finite PA detection sensitivity will limit the number of controllable input modes. Moreover, the speckle size is expected to tend towards half the optical wavelength; much smaller than the ultrasonically defined spatial resolution of PA detectors. For these reasons and others, focusing in tissue is expected to be highly demanding.

While tissue-based PAWS will be demanding, it is difficult to make firm predictions to guide experimental design and explore the expected capabilities of PAWS. One reason is it is hard to model the characteristics of coherent PA excitation light fields deep in tissue with available computational tools. Specifically, existing models based on, e.g. diffusion theory, Monte Carlo, Finite-Difference Time-Domain, or random phase screens, are typically either too simplistic to represent the required physics (e.g. contain no deterministic phase information), or else too computationally expensive (e.g. requiring a <λ/2 discretisation of the medium) to simulate propagation through large enough volumes of tissue.

To address this challenge, a scalable computational framework for accurately simulating coherent light propagation through tissue-like media was developed and applied to simulate the evolution of light fields during PAWS. The framework is based on a discrete particle model, in which tissue is treated as a collection of spheres (of higher refractive index) embedded in a homogeneous medium (of lower index). This model has two key features. First, using appropriately chosen spheres enables designing synthetic media that have certain desired tissue-like properties. For example, one can use Mie theory to design a collection of spheres providing a desired scattering coefficient and anisotropy. The second key feature of the model is it allows for the use of computationally efficient yet physically rigorous light field simulations. Specifically, here, the established T-matrix method is used to perform such simulations. The T-matrix method directly solves Maxwell’s equations and, in this way, is sufficiently physically rigorous. As such, accepting the discrete particle approximation, the solutions of the model are physically exact.

To demonstrate the model, it was applied to simulate the focusing of light in an 800 μm thick tissue-like medium. To show the potential utility of the model in studying PAWS, the focusing was repeated in different conditions illustrative of PAWS experiments involving different spatial resolutions. As expected, higher spatial resolutions led to brighter foci. By providing a simulation platform for studying PAWS, ongoing work involving this model could pave the way to developing systems that can focus light in tissue.