In this study, we present a fast analytical approach for laser induced temperature increase in biological tissue. The whole problem consists of two main steps. These steps are the light propagation and heat transfer in tissue. We first obtain a detailed analytical solution for the diffusion equation based on an integral approach for specific boundary conditions. Secondly, we also solve the Pennes' bio-heat transfer equation analytically using the separation of variables technique and obtain the temperature induced by optical absorption of tissue. Here, heat source term consists of the local absorption and photon density, which will be determined from the diffusion equation. We find a very comprehensive solution for the diffusion equation by using an integral method for the Robin boundary condition. In other words, we obtain a particular Green's function in a different way. Next, we use this solution as a source term in the Pennes’ bio-heat equation by utilizing the heat convection boundary condition. It is important to note that these boundary conditions are good approximations for imaging of biological tissue. As a result, we obtain spatio-temporal temperature distribution inside the medium. First, our approach is validated by a numerical approach using a Finite Element Method (FEM). Next, we also validate our method by performing phantom and tissue experiments. Experimental data corresponding to spatio-temporal temperature distribution are recorded using magnetic resonance thermometry. The analytical results obtained by our method are in a very good agreement with ones obtained by the FEM and experiment.
This work presents an analytical approach for the solution of the tissue diffusion equation based on the bound- ary measurements. We consider a bioluminescent point source in both homogeneous and heterogeneous circular turbid media. The point source is described by the Dirac delta function. Analytical expressions for the strength and position of the point source are obtained introducing boundary measurements and then applying appropriate boundary conditions. In addition, numerical simulations are performed for the position of the source. Calculations show that that the analytical results are in a good accordance with the numerical results.
The representation theorems of the convolution type and the correlation type are used to obtain the superposition of the Green's function and its time reversal counterpart for the photoacoustic wave equation. Based on the representation theorems, an interferometry relation providing the Green's function between sources and receivers is obtained. The reciprocity theorems for a spherical geometrical system consisting of sources located on the boundary of the inner spherical region and transducers located on the outer boundary are utilized. Therefore, the measurement would be observed at one of the detectors if there were a photoacoustic point source at the other one.
Photoacoustic microscopy, as an imaging modality, has shown promising results in imaging angiogenesis and
cutaneous malignancies like melanoma, revealing systemic diseases including diabetes, hypertension, tracing drug
efficiency and assessment of therapy, monitoring healing processes such as wound cicatrization, brain imaging and
mapping. Clinically, photoacoustic microscopy is emerging as a capable diagnostic tool. Parameters of lasers used
in photoacoustic microscopy, particularly, pulse duration, energy, pulse repetition frequency, and pulse-to-pulse
stability affect signal amplitude and quality, data acquisition speed and indirectly, spatial resolution. Lasers used
in photoacoustic microscopy are typically Q-switched lasers, low-power laser diodes, and recently, fiber lasers.
Significantly, the key parameters cannot be adjusted independently of each other, whereas microvasculature and
cellular imaging, e.g., have different requirements. Here, we report an integrated fiber laser system producing
nanosecond pulses, covering the spectrum from 600 nm to 1100 nm, developed specifically for photoacoustic
excitation. The system comprises of Yb-doped fiber oscillator and amplifier, an acousto-optic modulator and a
photonic-crystal fiber to generate supercontinuum. Complete control over the pulse train, including generation
of non-uniform pulse trains, is achieved via the AOM through custom-developed field-programmable gate-array
electronics. The system is unique in that all the important parameters are adjustable: pulse duration in the range
of 1-3 ns, pulse energy up to 10 μJ, repetition rate from 50 kHz to 3 MHz. Different photocoustic imaging probes
can be excited with the ultrabroad spectrum. The entire system is fiber-integrated; guided-beam-propagation
rendersit misalignment free and largely immune to mechanical perturbations. The laser is robust, low-cost and
built using readily available components.
In this work, Fourier transform based analytical solution to photoacoustic wave equation is obtained for an optically absorbing spherical object warmed up by a pulsed laser for rectangular and Gaussian radial profiles by treating the temporal profile of the laser as Gaussian. The photoacoustic signal is investigated as a function of time for different locations outside the spherical object. An expression including the dependency of the laser parameters on the photoacoustic signal is presented.