The possible features of photo acoustic tomography (PAT) in medical research and practice, including applications in orthopedics and cardiovascular areas, among others, have motivated the emphasis of this study towards human bone applications. PAT modality is an emerging approach that features safety and greater penetration depth compared to other modalities such as X-ray and microwave. The high-resolution images and safety related to PAT modality are attributed to the scattering properties of ultrasound as compared to light within a human tissue. PAT brought considerable attention from the medical research community to target optimum parameters for practical models. It includes source frequency penetration depth, dynamic temperature responses, and acoustic pressure throughout the multilayer structure of the human tissues. In this work, the acoustic pressure and the bio-heat equations were analyzed for power distribution and penetration depth, covering the basic principles of PAT within the human body. Three sources with three dif-ferent heat energy pulses; 1 s, 3 s, and 5 s, were considered in order to study the rise time and fall time dynamic responses inside the bone material. The computer simulation was designed to simu-late the human tissue at 1 MHz with an acoustic pressure of 1 MPa. A penetration depth for all sources was estimated to be near 4 cm with a temperature change from 0.5 K to near 1 K over a pe-riod of 10 s. The simulation data provide promising results when taken to the next level of practical implementation. The 4 cm penetration depth range may enable the researchers to investigate mul-tiple layers within the human body, leading to non-invasive deterministic approach. The simulation presented here will serve as a pilot study towards photoacoustic applications in orthopedic applica-tions.
The constraints associated with the safety in microwave and X-ray imaging, the high resolution inquired in medical imaging and limitation of the penetration depth for the energy inside human body, have raised concerns by medical researchers in achieving and accommodating high performance modality that provides the patient with safety and accepted resolution. The reliability of the modality is quite important in the diagnostic process; therefore, the image quality is of high demand in the practical model of the diagnostic system. In the past decade, the PA tomography has offered acceptable modality that overcomes such challenges [
The acoustic wave equation used by COMSOL is given by:
where Pt = P + Pb, and Pb is bio thermal pressure, P is the acoustic pressure, and
Boundary conditions
where m is the mass density, r is the location in space, and ω is the radian frequency. The sound hard boundary equation, matching normal where n is the unit vector normal to the surface. P is the acoustic pressure, c is the speed of sound, ρ is the material density, and k is the wave number.
The Bioheat equations are given as:
where q is the progressing source via the various layers of the materials,
The effect of the thermo acoustic takes place at the interface between the catheter and the bone material. Therefore, it is important to consider the penetration depth throughout the materials. The drop over the interface is related to the mismatch of the acoustic impedance. The thermal penetration depth is the distance that the heat may travel through. The phonons in the sound possess same characteristics as in heat, therefore, the characteristic length for the thermal interaction between two media may be characterized by δ given as:
where k is the thermal conductivity, Vm the molar volume, and C is the molar heat capacity, given at constant pressure. In the simulation, the heat source 1 is given a constant number of Q0 centered at 2.46 cm, at a starting temperature T0 (was given 293.6 K) with a tissue of 2.46 cm.
The mathematical models presented in Section 2 above were combined by COMSOL software to present the thermal distribution and the acoustic wave spread out within the bone layer. The parameters of the human bones used in the simulation are presented in
The data presented here was based on comparative study for three different sources providing energy providing energy for 1 s, 3 s, and 5 s. The amount of energy is then released into the bone material, providing the dynamic fall time response for different energies. The sound pressure level is presented in
Permittivity | Elec. Cond. (S/m) | Density (kg/m³) | Heat Capacity (J/kg/˚C) | Therm. Cond. W/m/˚C | Heat Transfer Rate (ml/min/kg) | Heat Generation Rate (W/kg) |
---|---|---|---|---|---|---|
2.49E+2 | 9.04E−2 | 1178 | 2274 | 0.31 | 30 | 0.46 |
found well proportional with the acoustic pressure. The theory supports power transmission for temperature and acoustic energy near 2.5 cm from both sides.
The data presented here indicates the feasibility to have photo acoustic imaging that may penetrate to the cm range and diagnose multiple layers within the human body. The safety factor of this novel modality will bring research attention to future practical models. The work presented here serves as a first phase of a project that simulates multiple layers from the body skin, bone, and human arteries where fat cholesterol can be diagnosed. The properties of the acoustic reflected and transmitted powers in addition to the thermal expansion of the layers may be detected for the practical model, and this is reserved for future considerations. The various sources of energy emphasized the thermal response with a wide range of temperature difference from 0.5 K to 1 K. This data give promising approach to detect the temperature distribution across the bone materials. A typical practical model then can be followed using infrared scanner to detect the temperature distribution within the materials and their boundaries. In the future, this approach may be expanded to cover multiple layers including fat material inside the human arteries. The application towards cardiovascular is reserved for future consideration.
The authors and co-authors offer their great appreciation for the INDI Center at IUPUI for their support during the work of this study.
James Rizkalla,Vinay Kumar Suryadevara,Ashok Kumar Thella,Ahdy Helmy,Paul Salama,Maher E. Rizkalla, (2016) Photo Acoustic Thermal for Human Bone Characterization: A Feasibility Study. Journal of Biomedical Science and Engineering,09,445-449. doi: 10.4236/jbise.2016.99040