A portable photoacoustic device has been designed for individual self-checking in order to help early detection and prevention of breast cancer. In this first year, we have focused on the design, fundamental investigation, setting-up, preliminary testing, data collection and process and development of associated computer programs and software (See our Software page for more information).

Photoacoustic effect refers to the generation of acoustic waves by light irradiation induced thermal expansion.^1-3 It provides deeper images than light-based techniques because of the detection of acoustic waves that avoids light scattering.⁴ In addition, the utilization of light-generated acoustic waves enables the dissection of diverse soft tissue structures that are difficult for ultrasound emission-based imaging.⁵ Currently, mammography, ultrasound and MRI are the major techniques for breast cancer screening.^6-10 In order to ensure early detection and prevention of breast cancer, the development of portable and individually affordable devices is demanded for self-checking. We take the advantages of photoacoustic effects for the development of such devices.¹¹

Several photoacoustic systems have been developed and show promises in clinical applications. It has been reported that a single photoacoustic system may reach a penetration depth up to 53 mm with the resolution down to 0.3 mm.^12-15 By using light emitting diodes and pulsed laser diodes, different photoacoustic imaging systems that can reach down to 0.95 m lateral resolution have been reported.^16-21 Various applications of photoacoustic devices to not only biomedical but also other disciplines have been reported.^22-25 In order to dissect the complex process of the generation of acoustic waves and elaborate photoacoustic systems, lots of rigorous mathematic models, algorithms, and tools have been developed, including models for photoacoustic tomography and imaging, universal back projection algorithms, simulation, reconstruction of initial pressures, sampling and signal processes.^26-34 We have designed a dual mode portable photoacoustic device that is based on the interferences of photoacoustic waves and reflected ultrasound pulses. It is designed for improved spatial resolution and enhanced ability for the detection of early symptoms.

The proposed photoacoustic imaging includes 3 major processes: (1) emission of the light source and thermoelastic expansion. (2) acoustic wave propagation. (3) sampling and image generation. Major parameters are listed and described in Table 1.

The key to obtaining a high contrast of the image is the amplification of differences among tissues. It has been reported that different wavelengths correspond to different absorption of chromophores.^35-37 Considering the blood components in tumor tissues, the absorption rate can be described as the following equation.³⁵

Thresholds for thermal and the stress confinement have been considered, which represent the thermal diffusion and the volume expansion in response to light illumination as shown in equation 2 and 3.^27,38

When the pulse duration of the light satisfies the 2 and 3equations, the effect introduced by thermal diffusion and volume expansion can be ignored in equation 4 that can be converted as equation 5.

Equation 5 can be simplified as equation 6 and 7 with the optical absorption.

These equations are combined as equation 8 and 9 with the definition of the Grueneisen parameter that represents the efficiency of energy conversion.³⁹

In order to reveal physical difference present in different tissues such as normal and cancerous tissues, we are seeking the initial changes in local pressure that is denote by 0 in the subscript. When these equations are applied to the illuminated tissues that are acoustic wave source, then equation 10 is defined.

Considering safety issues associated with the usages of laser,⁴⁰ parameters of the light source must satisfy equation 11 and 12.

As for raster scanning photoacoustic microscopy in the range of 400-700 nm, the parameters should satisfy equation 13.²⁷

The wavelength (λ), pulse duration (τ), the single pulse energy of the light source (E), and the repetition rate (f_P) should be considered for the selection of light sources.

Two problems are addressed in this section. (1) the optical inverse problem is how the excitation light propagate within the tissue. (2) the acoustic inverse problem is how does the acoustic wave propagate and interact with the transducers. The two problems are interconnected by p₀ () and μ_a () in equation 10.

In order to find the initial local pressure change distribution p₀ (), we can only sample the propagated acoustic wave p(,t) due to the transmitting time of the signal and limited sampling positions. The following procedure is aimed to find p₀ () using p(,t) in inverse order. Then the problem of image reconstruction is categorized as an inverse acoustic problem.³⁰ Transducers will be used to collect the propagated wave. For simplification, we proposed a few assumptions.

Assumption 1.

The tissue is acoustically homogeneous that can be represented equation 14.

Equation 15 is obtained by the substitution equation 10 with equation 14.

By using Newton’s 2^nd law, the acoustic wave can be represented as equation 16.⁴¹

Where □ is the d’Alembert operator, which can be expanded as equation 17.

It is noted the relationship between specific heat capacity at constant volume and isobaric specific heat abides by the equation 18.⁴¹

All the operators involved in differential equations are integrated into a d’Alembert operator, which satisfies the linearity requirement. With Green’s function, the solution to equation 16 is shown below.⁴²

Because the differential equation is linear, the superposition principle can be applied. By superposing all possible locations of the tissue, equation 20 can be obtained.

As we mentioned in the previous section, the pulse duration of the light source satisfies the thermal and the stress confinement threshold. It’s proven that the term μ_a ( )∙F( ) can be approximated.

Thus, by substituting equation 21 into equation 15 and equation 20, we get equation 22 and 23.

Now the pressure distribution over the spatial domain and time domain can be solved theoretically. From now on, there are multiple ways to obtain the initial pressure distribution p₀ (). Here we adopt the categorization proposed by Amir et al. that the acoustic inversion problem can be solved by 4 approaches, namely time-domain algorithms, frequency-domain algorithms, time-reversal algorithms, and model-based algorithms.⁴³ We have studied the back-projection algorithm in detail for its wide application and excellent reconstruction quality.⁴⁴

Assume at a specific time t_0, the collected data form a set {p_n (,t₀ )│n=1,2,…,N}. Recalling Assumption 1, becasue v_s is homogeneous, the possible wave source of the collected wave signal is on a spherical shell with a radius equal to v_s∙t₀. The sphere shell corresponding to the n-th transducer is denoted as S_n. For all transducers, we project the signal onto the corresponding sphere shell. The intersection among sphere shells is the wave source.

Assumption 2.

The distance between the tissue and the transducer is significantly larger than the size of the tissue(far-field).^49,50 Mathematically speaking, we have equation 25.

Then

Where S, and Ω denote the detection surface, the normal vector pointing out the surface, and the solid angle, respectively. The solid angle varies with different detection surfaces. For example, when the detection surface is spherical or cylindrical, the solid angle is 4π. Additionally, the solution to the inverse acoustic problem is the superposition of each transducer’s projection.

In summary, the projection surface and transducer should be examined when designing a photoacoustic imaging system. More specifically, the spatial distribution () and the sensitivity distribution function of the transducers (S). Additionally, deconvolution should also be considered in image processing.^51,52

Since the absorption coefficient is a function of wavelength as shown earlier, we explicitly include wavelength in future discussions. The local absorption coefficient of tissues can be expressed as the linear combination of the absorption coefficient of the interested chromophores weighted by their concentration.

Considering the scattering effects and decay effects taking place within the tissue, we conclude that the local optical influence is affected by the absorption coefficient and scattering coefficient.

Considering the scattering effects and decay effects taking place within the tissue, we conclude that the local optical influence is affected by the absorption coefficient and scattering coefficient.

This equation reveals how the rate of changes in the light radiance changes in response to spatial position, direction, and time. In the equation, term (a) and (b) represent the total changes in the number of photons, and the net flux of the photons, respectively. Term (c) consists of three items, in which s ̂∙∇ represents the photons flowing out due to the gradient, μ_a () represents the photons absorbed by the tissue, and μ_s ( ) represents the photons scattered to other directions. The Θ(,' ) in term (d) is called the scattering phase function. It modulates the probability of a scattered photon that switches the traveling direction from to '.⁵⁴ This term can be interpreted as the scattered photons that switches back to the original traveling direction. It contributes to the increase of radiance.

By replacing the time-dependent terms on both sides in equation 30 with the corresponding time-independent terms, we obtain the time-independent radiative transfer equation. The left-hand term is erased since photoacoustic imaging utilizes pulsed light sources. Because the pulse duration of the light source is compressed, thus for most of the time, and equation 31 is obtained.

Considering light illumination as the combined effect of the radiance in all directions, equation 32 is obtained.

By solving equation (31), we can obtain the local light illumination.^55,56 Since it is difficult to solve most of the time, we introduce the P_N approximation to obtain the approximation to the radiative transfer function.⁵⁷ The definition of the reduced scattering coefficient (μ_s') and optical diffusion coefficient (D) are shown below.

When μ_s' ()≫μ_a (), the final analytical expression of F() using this approximation approach is represented in equation 35 in which the effective attenuation coefficient is shown in equation 35.

Then the absorption coefficient of tissue can be calculated. Several techniques have been developed for the determination of the concentration of each interested chromophore. Here we explore the well-developed least-square minimization method that can locate and minimize the errors. The error function in this context is defined as ε, and the method is shown below.

The subscript for [k] stands for optimization. P([k]) term on the right-hand side represents the penalty function, which is added for special cases. Then we can obtain the calculated values of [k]. It should be noted there are many applicable solutions to this problem besides lease-square.⁵⁸

After the transducers collects the acoustic signals, the raw data are transported to the data acquisition unit for further processing. It has been assumed that the tissue is acoustically homogeneous for calculation simplicity in our previous discussion. However, acoustical properties of the tissue vary with the speed of sound, and tissue density distribution, which induces acoustic aberration and imaging resolution.^59-61 The raw data are the combination of photoacoustic signals and noise. By removing the noise and enhancing the interested signals, we should be able to reconstruct the images.^{62, 63}

The most commonly applied method in pre-processing is averaging.⁶⁴ Under the consumption that the ambient noise is uncorrelated random noise, larger averaging times correspond to better convergence. The principle of pre-processing is shown below. Because of the presence of noise, the measured data of the n-th transducer p_n-me(,t) at time t can be described as equation 38 with assumption 3 and 4.

Assumption 3. p_n(,t) and z(,t) are uncorrelated, and z(,t) are uncorrelated.

Assumption 4.The noise is random.⁶⁵

Mathematically, they can be expressed as equation 39, 40 and 41.

The variance of the environmental noise can be expanded as equation 42.

For total sampling times J, we obtain equation 43.

For total sampling times J, we obtain equation 43.

As J approaches infinity, the last term in equation (45) approaches 0 and the noise is reduced.⁶⁶ Considering the conversion of the analog signals to digital signals, the accuracy and time step length should also be taken into consideration. This step is essential because the collected signals are submerged with the background noise on a large scale.⁵⁹

Another approach is based on the signal-filtering technique. Using Fourier transformation, the time-domain signals are converted into frequency-domain signals. By selecting cutoff frequencies, the signals whose frequency falls out of the domain can be eliminated. We adopt the Butterworth filter to reach the maximum approximation of uniform sensitivity.⁶⁷ The transfer function of an nth-order Butterworth filter is represented as equation 46.

There are multiple sources of noise besides environmental noise, in the form of electronic noise and system thermal noise.^{50, 62} Different components of the system generate noise with different frequencies. We implemented a virtual Butterworth filter in our algorithm. In summary, the key parameters of the data acquisition unit are sampling frequency, sampling accuracy, and time step length.

Our photoacoustic system is designed as a dual mode portable device. It is based on the interference of photoacoustic wave with reflected ultrasound pulse wave as shown in Figure 1.

Figure 1. The design of a photoacoustic portable device

We have completed two related computer programs for fast Fourier transformation (FFT) as well as wave detection and data storage with an oscilloscope (WDDS). We hope make some contributions to the IGEM community and those computer programs are open for download.

Please Click here to download FFT program.

Please Click here to download WDDS program.

In this year, we mainly focus on the principle demonstration and fundamental investigation. We have performed lots of literature searching, interpretation and brainstorming team discussions. Figure 2 shows our preliminary setting up of the home-built dual mode photoacoustic device that is designed for the testing. It mainly contains a near infrared laser, a ultrasound generator, a transducer, an oscilloscope, a computer and some other related parts.

Figure 2. The experimental setting up of a home-built dual mode photoacoustic portable device

Proof of principle testing has been performed with the home-built device. Although the current result is disappointing, it is the first step towards the future innovation. The acquisition, storage and displaying of data have been achieved. Figure 3 shows there are huge environmental noises. The deconvolution and amplification of signals are undergoing.

Figure 3. Detected noises with the home-built photoacoustic device.

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