<aside> 💡 Summary :

1. Hardware Design and Build: This involves creating an optical illuminating system for a handheld probe and managing the splitting of optical and ultrasonic waves.
2. Software Design and Programming: This part focuses on Rx Beamforming using a programming model called CUDA.
3. Applications: This section discusses the use of PAT in animal studies, specifically in ex-vivo imaging with cancer models on rabbits. </aside>

Clinical Background

Photoacoustic Tomography (PAT) represents an innovative breakthrough in the field of imaging techniques. It ingeniously marries the benefits that are intrinsic to both ultrasound and optical imaging systems, thereby making it an exceptionally effective modality for the angiogenesis detection in early-stage cancer. Ultrasound imaging, a well-established technique, is particularly recognized for its capacity for deep penetration into tissues and its ability to deliver high spatial resolution images. However, it falls short when it comes to contrast, thus making it a less effective tool for the detection of early-stage tumors.

Conversely, optical imaging, another key player in the imaging field, is celebrated for its outstanding contrast capabilities. This allows it to discern and delineate structures with great precision. Unfortunately, it is limited by its relatively shallow penetration depth, making it less effective for imaging deeper tissues.

PAT ingeniously circumvents these limitations by creating a powerful synergy between the high contrast capabilities of optical imaging and the deep penetration offered by ultrasound imaging. This unique combination enables PAT to detect and characterize tumors in their early stages by visualizing angiogenesis, a process that is critically associated with cancer development and growth. Angiogenesis, the formation of new blood vessels, is a hallmark of cancer, and its visualization can provide critical insights into the nature and progression of the disease. This highlights the indispensable role of PAT in the imaging of cancer and its potential to revolutionize the field by enabling early detection and characterization of tumors.

Theory

Mathematical Theory: The 3D Photoacoustic Tomography Model

Photoacoustic Tomography (PAT) is an imaging modality that operates on the principle of the photoacoustic effect. This effect is observed when a short pulse of light is absorbed by a medium, resulting in a rapid temperature increase. This sudden heat surge causes thermoelastic expansion, which in turn generates an ultrasound wave. The ultrasound wave is then picked up by a transducer, which converts it into an electrical signal that can be processed and used to reconstruct an image representing the initial pressure distribution.

In a 3D model, the mathematical representation of PAT is encapsulated by two interconnected partial differential equations (PDEs): the wave equation and the heat equation.

The wave equation serves to model the propagation of the ultrasound wave that has been generated. It can be expressed mathematically in the form:

$$ ∇²p(r, t) - (1/c²) ∂²p(r, t)/∂t² = -β ∂Q(r, t)/∂t $$

In this equation:

• p(r, t) represents the pressure field
• c is the speed of sound in the medium
• β is the thermal coefficient of volume expansion
• Q(r, t) is the heat source term

The wave equation essentially describes how the pressure wave, generated due to thermoelastic expansion, propagates through the medium.

On the other hand, the heat equation models the heat transfer process resulting from the absorption of the light pulse. It can be represented as: