An experimental and theoretical approach to the study of the photoacoustic signal produced by cancer cells

The distinctive spectral absorption characteristics of cancer cells make photoacoustic techniques useful for detection in vitro and in vivo. Here we report on our evaluation of the photoacoustic signal produced by a series of monolayers of different cell lines in vitro. Only the melanoma cell line HS936 produced a detectable photoacoustic signal in which amplitude was dependent on the number of cells. This finding appears to be related to the amount of melanin available in these cells. Other cell lines (i.e. HL60, SK-Mel-1, T47D, Hela, HT29 and PC12) exhibited values similar to a precursor of melanin (tyrosinase), but failed to produce sufficient melanin to generate a photoacoustic signal that could be distinguished from background noise. To better understand this phenomenon, we determined a formula for the time-domain photoacoustic wave equation for a monolayer of cells in a non-viscous fluid on the thermoelastic regime. The theoretical results showed that the amplitude and profile of the photoacoustic s...


I. INTRODUCTION
Cancer is the number one health problem in the U.S.; it accounts for approximately 7.6 million deaths each year (around 13% of all deaths). 1 Reducing and controlling cancer requires early detection.Current detection techniques involve radiographic methods that utilize ionizing radiation.At present, six imaging modalities are available to clinicians who diagnose, stage, and treat human cancer: x-ray (plain film and computed tomography (CT)), ultrasound (US), magnetic resonance imaging (MRI), single-photon emission computed tomography (SPECT), positron emission tomography (PET), and optical imaging.Of these, only CT, MRI, SPECT, and PET are capable of three-dimensional detection of cancer anywhere in the human body.These imaging modalities are a Author to whom correspondence should be addressed to poloparadal@missouri.edu for LPP or ggutj@fisica.ugto.mxfor GGJ.Rafael Pérez Solano and Francisco I. Ramírez-Pérez contributed equally to this work.
2158-3226/2012/2(1)/011102/15 C Author(s) 2012 2, 011102-1 limited by deficiencies in sensitivity and/or resolution; they simply were not designed to image small numbers of cancer cells. 2 The problem is one of scale.A typical human cell is approximately 10 μm in diameter, with a volume of only 1 pL.Every 1 cm 3 (1g) of solid tissue contains approximately 10 9 cells. 3Because a malignant clone develops from a single cell, early detection requires us to be able to detect a few cancer cells in 10 6 cells per mm, 3 an inconceivably small number.Solid tumors typically display Gompertzian kinetics, 4 with a first lag phase starting at the single cell stage, a lag phase heralded by angiogenesis and escape from diffusion-limited nutrition at approximately the 10 5 cell stage, and a second lag phase that culminates in death of the patient at approximately the 10 12 (1 kg) cell stage.The goal of cancer imaging is to detect and/or image the smallest possible number of tumor cells, ideally before the angiogenic switch (<10 5 ).][7] This level of uncertainty is unacceptable to both patient and caregiver. 2,5,8 Psed Photoacoustic (PPA) diagnostic techniques for cancer detection in vivo and in vitro have been developed in the last several years.Photoacoustic techniques combine the high optical contrast of optical tomography with the high resolution of ultrasound techniques.PPA has been used in two main areas: the detection of breast cancer (BC) [9][10][11][12][13] and the detection of circulating cancer cells (CTC's) in vitro. 14,15 n BC detection, optical contrast is produced by the vascularization that develops with the cancer (a well-known process called angiogenesis).The detection of CTC makes use of the natural chromophore concentration (i.][16] Recent technical advances in the use of PPA suggest that it may be possible to identify clusters of a few cancer cells in vitro and in vivo.5][16] Our goal has been to characterize the photoacoustic signal (PAS) profile of a single absorbent element or material (e.g.][19][20][21] Several groups have worked exhaustively for many years developing mathematical models to describe the process of photoacoustic signal generation.Recent efforts have focused on the PA signal generated by tissues and organs; however, little has been done to study the PA signal generated by one or more simulated cells in different regions of the stimulation field.][21][22][23] Recently, a two-dimensional model of the PA signal of non-aggregated and aggregated erythrocytes has been described. 24In their research, the energy density absorbed by the cells was described by using a delta-pulse for illumination via a Fourier transform of the frequency-domain response, 19 founding that for the non-aggregating case PA signals demonstrated a monotonic rise with hematocrit and for the aggregating case it was found that spectral (<20 MHz) intensity increased (11 dB at 15.6 MHz) when the aggregate size increased.
To better understand the factors involved in the generation of a PA signal in the time domain, we have used an absorption model, involving an absorbent single cell in which we can measure the density of energy per unit of time. 23When this variable is inserted into the PA wave equation, we can determine an analytical PA pressure profile.The resulting PA pressure can be used to simulate a signal from a single cell throughout a monolayer made of a different number of cells.We found that the expected PA amplitude was correlated to the number of cells in the monolayer.The contribution of the position of the cells in the stimulation field to the PA signal was negligible.The findings of this study may help us understand the challenges ahead in the use of PPA techniques for the identification of cancer cells in vivo and in vitro and can help us to develop new strategies for designing and manufacturing sensors and algorithms to identify and characterize the information encoded in a PA signal.

A. Numerical solution
The numerical analysis was performed on a 2.4 GHz Intel Core 2 Duo MacBook Pro with 4 Gb of RAM running on Mac OS X 10.6.7 (Apple Inc., Cupertino, CA); the code implemented was C-code compiled with ROOT 5.28 (CERN, The European Organization for Nuclear Research).The data was exported as an ASCII file and graphics were created using Origin 8.5 (OriginLab, Northampton, MA).

B. Cancer cells
The human malignant cancer cell lines HS93, HL60, SK-Mel-1, T47D, Hela, HT29, and PC12 were obtained from the ATCC and maintained as indicated by the supplier.Cells were cultured and propagated in a 250 ml flask following the ATCC recommendation for each cell type.

C. Optical properties of the different cell lines
We evaluated the optical properties of the different cell lines with two different approaches.First, we took pictures with a B&W camera (Q-IMAGING) at 10 ms exposure; for all the pictures, the gain was set at 1.The camera was attached to the side port of an inverted microscope Olympus IX-71 (Olympus).The lamp intensity of the microscope was kept constant.A 40x lens bright field lens trans-illumination was used.In all the pictures only the focus was adjusted.
The cells were cultured in the recommended cell culture media and replaced with a clear Tyrodes buffer (in mM: 120 NaCl, 10 Glucose, 10 NaHCO 3 , 5 KCl, 2 CaCl 2 , 1 MgCl 2 , 1.8 NaHPO3, pH 7.4 with NaOH, 320 ± 5 mosm).This eliminated any alteration in the intensity of the pictures due to the different composition media and amount of phenol red.Ten random pictures were taken of each cell culture.
To determine the mean pixel intensity of each cell culture, a region of interest (ROI) was drawn around the perimeter of each cell and evaluated using imageJ software (NIH).The mean pixel intensity of 1000 cells was calculated and the mean ± SE was reported.To confirm our findings, the spectra absorption analysis of a 1x 10 6 cells/ml was obtained using a Helios Zeta UV-Vis spectrophotometer (Thermo-Scienfic-Fisher Sci, USA).

D. Photoacoustic signal of cancer cells monolayer
For photoacoustic experiments, cells were plated on a 10 μm transparent saran polyvinylidene chloride (PVDC) wrapping film glued to the drill-out bottom of 35 mm culture dishes and cultured for 24-48 hrs in a standard cultured medium.This allowed the cells to attach to the film and to form a dense, side-to-side monolayer of melanoma cells.For the evaluation of the PA signal, the cell culture medium was removed and substituted with Tyrode's buffer.

E. Photoacoustic detection
A schematic representation of the experimental set-up is shown in Fig. 1.A Sheshou-8 type Q-switched laser of Nd: Ce: YAG solid-state laser was used.We used a 532 nm adapter with a fluency of 213.5 mJ/cm 2 with pulse duration of ∼6 ns and frequency of repetition up to 6Hz.An optical fiber of 1 mm diameter (ThorLabs) was used to deliver the laser pulse into the dish with the preparation.A calibrated QE12 energy detector from Gentec-EO was used to monitor the energy delivered to the cells.A digital oscilloscope RIGOL DS1302CA was used to acquire and store the PAS and the energy profile of the laser.The PAS generated by the cells was isolated from the ultrasonic detector by a 40 mm long cylinder made of 2% agar and 10% lipids.The photoacoustic detector was created in house, based on a Piezo ceramic transducer of 500 MHz, 20x0. 4   This arrangement allowed for the isolation of the photothermal signal produced by the laser in the detector, allowing the acquisition of only the PAS.The signal detected by the ultrasonic detector was digitized at 2.5Gs/s and stored in one of the channels of the oscilloscope and transferred to a computer for further analysis and processing, using Origin 8.5 (OriginLab, Northampton, MA).When the signal-to-noise ratio could not be easily distinguished from the background noise, we employed one or two ZFL-500 (Mini-Circuits, Brooklyn, New York) amplifiers in series.Each amplifier has a 21.36 dB gain.
To evaluate the PA signal generated from a few cells, a stock solution of 10 6 cells/ml was prepared in a Tyrodes solution.A droplet of 5 μl was placed in the center of a culture dish and tested for PA signal in the setup previously described.If a PA signal (signal-to-noise ratio >3) was observed, the stock solution was diluted by half with a Tyrodes solution.The process was repeated until an indistinguishable PA signal was obtained.At that point the cells in the droplet were labeled with the nuclear stain 4 ,6-diamidino-2-phenylindole (DAPI) and the number of cells counted under transmission and fluorescent (nuclear staining) microscopy.The process was triplicated.

F. Western blot analysis
Cells were cultured as suggested by the ATCC to 80-90% confluence and homogenized in a HEPES extraction buffer (in mM): 25 HEPES, 150 NaCl, 1 EDTA) containing a 1% NP-40 and protease inhibitor mixture (Roche Diagnostics, Mannheim, Germany).The solubilized protein concentrations were determined (BCA method; Pierce, Rockford, IL) and adjusted to 2 μg/ml.The SDS sample buffer containing dithiotheritol was added to each sample and the proteins separated by SDS-PAGE, according to the Lamellae method, on a 4-15% Tris-HCL Criterion Precast Gel (Bio-Rad, Hercules CA).The proteins were transferred onto polyvinylidene fluoride membranes pre-absorbed with a solution of PBS and 4% milk.The membranes were then probed with primary antibodies in PBS and 4% milk overnight at 4 • C. The Tyrosinase and β − actin antibodies were obtained from Santa Cruz Biotechnology, Inc (Santa Cruz, CA).The membranes were then washed in PBX, 0.1% Triton X-100, and HRP-conjugated secondary antibody for 2hrs.The membranes were washed five times, 15 min each, in PBS.An enhanced chemical luminescence kit (Promega, Madison WI) was used to expose the blots onto film.Quantification of the bans was performed using ImageJ (NIH) quantification software.

III. RESULTS
The goal of this line of work is the detection of the smallest possible number of cells by PA.PA signal systems employ a "hydrophone" in the detection of the signal.The sensitivity is limited by the properties of the transducer and the electronics to amplify and record the signal.We have described an optical-based PA system that allows the detection of 2-3 cells in vitro. 14,15 owever, intrinsic factors in the design exclude its use for in vivo applications.We used a common PA detector and experimental arrangement to evaluate the PA signals generated by different cell lines (see figure 1).We cultured some of the most commonly used cell lines for in vitro studies (i.e.HS936, HL60, SK-Mel-1, T47D, Hela, HT29 and PC12).

A. Optical and cellular properties of the cell lines
To evaluate the absorption properties of the cells, we performed two different sets of experiments (Figure 2). Figure 2(A) shows that the HS936 cells are darker than any of the other cells tested.The absorption spectra and the pixel-intensity profile reflect similar results (Figure 2(C)).
In order to confirm the best cancer cell line to produce a measurable PA signal, we examined ways to determine the melanin content in different cancer cell lines.Because it is not possible to directly evaluate the amount of melanin in any cell(s), we chose to evaluate the concentration of the rate-limiting enzyme for melanin synthesis, tyrosinase. 22,25,26 T[28][29][30] Tyrosinase is synthesized in melanosomal ribosomes found on the rough endoplasmic reticulum.After synthesis, tyrosinase is glycosylated within the Golgi, then delivered to melanosomes via coated vesicles. 29,30 sing standard Western Blot analysis we found that, from all the cell lines tested (HS936, HL60, SK-Mel-1, T47-D, MCF-7, Hela, HT29, PC12), the HS936 had the highest levels of tyrosinase and therefore, presumably, of melanin (see Fig. 3(A)).The HS936 in culture or in suspension seems to be largely opaque (Fig. 3(B) and 3(C)).Furthermore, HS936 cells cultured in a monolayer exhibited elongated shapes and diverse color intensities (Fig. 3(B)).However, HS936 in solution exhibited a more rounded, uniform size, but retained a diverse color intensity (Fig. 3(C)).

B. Experimental photoacoustic signal of a cell layer
We cultured all the different cell lines to 90-95% confluence in the PVDF bottom culture dishes and evaluated the PA signal from the cultures, using the system described in the Materials and Methods (Fig. 1).We exposed the cell cultures to an area of 1 mm 2 with an energy of 10 mJ.Using a 4 -6-Diamidino-2-phenylindole (DAPI) nuclear counterstain, we estimated that, in an area of 1 mm, 2 there were ∼ 1548 ± 107 cells (n = 22).Also we found that when the cells were exposed to more than one single laser pulse, the intensity of the PA signal decreased exponentially, reaching a plateau value, as previously reported for other biological materials. 31To eliminate this potential artifact in our evaluations, we used the PA signal generated by the cells in the culture exposed to a single laser pulse for each experiment.
We were able to detect only a PA signal from the HS936 cultured cells.In cultures in which we had a lower cell density, the PA signal amplitude was dramatically reduced (S/N > 3).The signal-to-noise-ratio of the PA generated by other cells (i.e.HL 60, SK-MEL-01, T47-D, MCF-7, HELA, HT29, PC12) was so small that it could not be distinguished from background noise, including at high confluence densities (data not shown, S/N<3).Other groups have found similar results and overcome this problem by using a photoacoustic enhancer or contrast materials such as gold and/or carbon nanoparticles.We did not pursue this route, mainly because a PA enhancer would override the normal properties of the cells tested.Furthermore, when HS936 cells were cultured over 50 passes, they began to lose their ability to produce melanin and became transparent with the decrease in their associated PA signal.
The experiments were performed under well-controlled laboratory conditions.For the HS936 cells, the amplitude of the PA signal seems to be related to the number of cells irradiated.However, blind experiments in which we evaluated the magnitude of the PA signal showed no relation to the number, quality, position, or optical properties of the cells in the stimulation field.To better understand this phenomenon, we developed a mathematical study of our experimental arrangement.

C. Theoretical background
Although others have demonstrated the detection of single cells via the PA signal, there is no study in which the PA model has been applied to understand the PA signal produced by a single cell or group of cells.In the thermoelastic model of the PA effect, the wave equation can be simplified by using the relationship between pressure and velocity potential, expressed as: obtaining an inhomogeneous wave equation in terms of velocity potential, where p is the PA pressure, r is the position, t is the time, ρ is the density, ϕ is the velocity potential, c s is the speed of sound of the sample, β is the thermal expansion coefficient, C p is the heat capacity at constant pressure, and H is the energy per unit volume and time deposited by the optical source.For our particular application, we assumed that the absorbers were diluted in an optically non-absorbent media, with boundary conditions at infinity.

Energy per unit volume and time
In a system with n absorber samples, each sample has an absorption coefficient of α s j in an optically non-absorbent media with absorption coefficient α f , (α f << α s j ).Cells and media are assumed to be homogeneous, isotropic, and linear.Because the cell sizes were around 10 μm, they can been assumed to have spherical shape with radius R j centered at the point r j , j = 1, 2, • • • , n. (Figure 4).The direction of the light hitting the cell is labeled z.The energy per unit time on the j − th cell on an area da at the r 0 , is given by: where Q( r) is the laser fluence, f (t) describes the deposition rate of energy, and θ 0 and ϕ 0 are angular coordinates of r 0 .The transmitting energy is determined by the Lambert-Beer law, given by (Fig. 2) From Eq. ( 4), it follows that the energy per unit time absorbed by the sample can be expressed as: Integrating Eq. ( 5) over the sphere leads to a formula for the energy absorbed per unit time in the cell: Because the dimensions of the PA cell are in the order of millimeters, we can assume that the energy absorbed by one cell is concentrated in a point located in its position.The point density of energy per unit time of the j − th cell is defined as: where δ( r − r j ) is the Dirac delta distribution.The density of energy per unit time for n cells is: Experimentally, it is possible to obtain a constant spatial profile of the fluence.In this case Q( r 0 ) becomes constant and, from Eq. ( 6), Eq. ( 8) is given by: Where is the absorbed energy by the j − th sample and E j0 = 2π R 2 j Q 0 is the delivered energy by laser over the spherical cell, and Q 0 is the laser fluence.

Solution for the PA wave equation
A short pulse can be modeled by f (t) = δ(t − t ), with t as the time when the pulse occurs.Substituting Eq. ( 9) in Eq. ( 2), we have a differential Green equation for the inhomogeneous wave equation.Its solution is given by the retarded potentials. 32From Eq. (1), the expression for PA pressure is: We assumed that all samples were excited by the pulse at t = 0.For a pulsed beam with Gaussian temporal profile of width 1/e equal to τ , the pressure is given by 33 Substituting equation ( 11) in (12), and taking into account Eq. ( 10), we arrive at;

Numerical solution
We used Eq. ( 13) for one and two cells and a monolayer of simulated cells for the numerical solution.In all of these simulated cells, it was assumed that α j = 552.4cm −1 , 34 c s = 1.5 mm/μs, and R j = 5 μm.The pulse duration was τ = 10 ns.We considered a point-like detector localized in r = 0.The cells were localized in the plane z = 40 mm, centered with the stimulation zone, generated by a laser fiber 1 mm in diameter.These conditions resemble our experimental design (see Materials and Methods and Figure 1 for more detail).

Photoacoustic signal from a simulated cell monolayer
To evaluate the PA signal generated by a simulated cell monolayer, we examined a hexagonal arrangement of the simulated cells (Fig. 5(A)).We selected this configuration because it is the only cell distribution that allows the maximal number of cells per unit of area.We calculated that the number of cells in a hexagonal array was given by: where n represents the number of hexagons employed in the layout (n ≥ 1).We evaluated the PA signal produced by a monolayer of 7, 331, 1261, . . .7651 contiguous cells organized in a hexagonal assembly (Figure 5(B)).When the PA signal of the different monolayer cells was normalized with respect to the PA signal from a single cell, we observed that the increase was directly proportionally to the number of cells in the arrangement (Figure 5(C)).In this figure, the grey line represents the best linear fit to the data (slope 0.97457, Adj.R-Square 0.9999).As shown in Figure 5, this likely is due to both a predominantly constructive interference produced by the tight organization of the cells in the array and the distance (40 mm) between the cells and point of measurement.Figure 5(D) shows the PA time shift plot generated by different numbers of cells.
The highly-organized, hexagonal distribution of cells (Figure 5) is a special case that may be difficult to reproduce experimentally or in existing in vivo conditions.To more adequately evaluate our model's applicability to real conditions, we evaluated the PA signal characteristics generated by different numbers of cells randomly distributed in the stimulation field.Also we evaluated the PA signal profile generated by these cells as a function of the distance to the sensor.Figure 6 shows the effect on the PA amplitude, peak to peak, of a different random distribution of cells (from 7 to 4921) in the stimulation field (in 7651 possible positions), as a function of the distance to the point of observation.The PA amplitude, peak to peak, was calculated as the difference between the maximal and minimal value and averaged over 1100 simulations.To allow a better understanding of the random distributions, the PA mean value was compared with the respective PA amplitude of the tight hexagonal arrangements (Figure 5(A)).
As shown in Figures 6(A)-6(E), in all cases the PA signal generated by the randomly distributed cells (dark circles) is smaller than those generated by the same number of cells in a highly organized configuration (grey circles).Moreover, the PA signal generated by the randomly distributed cells always show a linear behavior as a function of the number of cells.By contrast, the highly organized cells at the point of observation close to the stimulation zone lose the linearity.A monotonic increase of PA signal is observed with increased concentration of cells.Gutierrez et al. 14 obtained a similar variation of measured PA signals with latex microspheres and Karpiouk et al. 35 with hematocrits.In both random and high organized arrangement, as the point of detection was moved closer to the cells, the amplitude of the PA signal increased, more notably for the organized cells.The PA signal for the cells closer to the sensor exhibited a more complex PA profile (Figure 6(F)).For example, as shown in Figure 6(G)-6(I), the PA amplitude of seven cells in an organized arrangement is larger than when they are randomly distributed.In the random distribution, the distance between cells is increased, favoring PA interference.
Another feature that must be noted is that, because the randomly distributed cells have several possible positions, the distance between can increase and the PA amplitude can appear to delay (Figure 6(H) and 6(I)) encoding the structure of the cell distribution.Figure 6(H) and 6(I) show the behavior of the PA signal for the same number of cells (7) at two different distances (8 and 15 mm) from the point of detection.
In order to explore the bandwidth of the PA signal, we made the Fast Fourier Transform of the theoretical data for the highly organized arrangement of cells.Variations of PA amplitude spectra for all amounts of cells are shown in Figure 7(A) over a range of frequencies (from 1 MHz to 200 MHz).The spectral intensity increased as the number of cells within the region of stimulation increased.The same plots of Figure 7(B) are shown on a log-log scale.

IV. DISCUSSION
Despite technical advances in many areas of diagnostic radiology, the early detection of human cancer remains a challenge.Improved cancer screening, staging, and treatment requires an improvement in the tumor-to-background detection ratio of three to four orders of magnitude, which will require proportional improvements in sensitivity and contrast agent targeting.Here we explore the potential of the pulsed PA signal for clinical care.
The generation of the PA signal in intact cells has been primarily based on the ability of the cell melanin to absorb the stimulation-pulsed laser radiation and produce a PA signal.However, not all the cells produce an equal amount of melanin.We demonstrated here that the HS936 exhibited the largest amount of tyrosinase (a precursor of melanin) in all the cells tested, followed by the HL-60 FIG. 7. Plot of the PA amplitude spectra for different amounts of cells in a highly organized configuration.The bandwidth was centered at 50MHz with a band of 100 MHZ for any given number of cells.and Sk-Mel-1.Other cancer cell types such as T47-D, MCF-7, Hela, HT29, and PC12 exhibited negligible levels of tyrosinase and presumably of melanin.This observation is in accordance with our optical evaluation of the degree of cell darkness and the absorption spectra of these cells (Figure 2 and 3).We and other groups have been able to detect a PA signal from intact HS936 cells, but not from other cell types.To overcome this problem, others have attached PA enhancers such as gold nanoparticles and carbon tubes covered with gold.
Our selection of the HS936 cells for our studies allowed us to identify the PA signal from these cells without the need of PA enhancers.However the use of the cells in culture attached to a substrate allowed for the extension of the cells with a consequent reduction in intensity compared with the same cells in solution (see Fig. 3(B) and 3(C)).These dramatic differences can be attributed to the well-known fact that when cells are not attached to a substrate, they have a tendency to become spherical, increasing the absorption by unit of volume, resulting in an increase in absorption.The mean amplitude of the PA signal generated by the same number of cells in solution in the same area is larger when the cells are floating in the recording media attached to the cultured dish (data not shown).Moreover, the amplitude of the PA signal generated by a monolayer of HS936 cells depends upon the number of the cells and its distribution in the stimulation field.This observation aligns with our physical model.
A careful inspection of the PA signal generated by a monolayer composed of large numbers (∼1500) of HS936 cells reveals a more complicated PA signal than the one obtained in our model (Figure 2 and 3 vs 5 and 6).This finding could be attributed in part to several factors, including reflection in our experimental arrangement and ringing in our detector.Our model design relies on the assumption of homogenous cell characteristics (size and absorption.) The model presented in this work represents an approximation in time domain of a better understanding of the parameters involved in the generation of a PA signal from a cell monolayer.Some of our findings are in accordance with our observations here and the ones reported in the literature. 24,36 owever, further analysis and improvements in the model are necessary to fully understand the PA signals obtained from intact cells in culture.This particular planar distribution represents a very special case that could be useful for the detection of few cells in vitro.For example, a system using microfluidics should respond much like that of a monolayer.Clinical applications, where cells are distributed in a 3-D structure, will require more analysis.Ongoing studies from our group and others will help to understand this phenomenon in the near future.The results presented in this study will be of great assistance to these future developments.
The cancer cell lines HL60 and SK-Mel1 produced Tyrosinase slightly lower than the HS936 cell levels.This small decrease in the levels of Tyrosinase resulted in a decrease in the intracellular levels of melanin; therefore they were more transparent than the HS936 cells.This low level of melanin resulted in a low level of radiation absorption and consequently a dramatic decrease in the PA signal; the resulting signal was negligible at detection levels with current transducer technologies.This problem is well known, but can be resolved with the use of highly absorbent materials that produce a detectable PA signal (i.e.gold and/or carbon nanoparticles) attached to the cells.Another alternative is the development a more sensitive PA transducer that could identify these small signals.
Little progress has been made on this front, however.
The physical model adopted in the present study made use of an effective spherical model of the cells laser radiation absorption, used to predict the PA thermoelastic pressure produced by a group of cells as a function of its optical and geometric properties.Given homogeneous properties, the theoretical results show that, for a given number of cells distributed in the stimulation field, the magnitude and shape of the PA signal depends strongly upon the number of cells, the distribution, and the distance to the detector.As the point of detection moves closer to the cells, the PA amplitude signal increases its magnitude, up to a maximal value; then it will became smaller (peak-peak amplitude) but the profile will be more complex.The complexity of the PA signal may encode some information about the distribution and location of the source (in this case, the cells).
However, our model and results show that more than one distribution could produce a similar PA profile.This represents a limitation of our experimental design and the PA techniques.This limitation should take in consideration in blind experiments and in clinical settings, in which the source of the PA signal is unknown.Our simulations predict that, for real experiments in which the source and abundance of the material generating the PA signal, there is a distance in which the magnitude of the PA signal will be maximal.Outside this range the PA morphology may provide information about the characteristics of the source.Furthermore, our model predicts that the bandwidth of the PA signal generated by any given number of cells is almost constant.This fact is due to the assumption of the point source.In order to give important information for the design and construction of new PA detector and electronics associated, we need to improve the model, taking into account the size of the cells.
This study represents an advance in the understanding of the characteristics of the PA signal and its correlation with real data.In the near future we will continue our studies to evaluate the corresponding PA signal for a group of cells with properties (size, absorbance, etc.) randomly distributed in 2D and 3D, which may resemble a more realistic condition observed in the clinical settings.It may provide a better understanding of the PA signal produced by cells in these conditions and potentially reveal strategies to design better algorithms for a PA tomography system that could aid in the early detection of cancer in vivo.idea, contribute to the design implementation, analysis and execution of the experiments, supervising of the entire project and collaborate and supervise the writing of the project and sponsor the costs of the project.Supported partially by grants from the American Heart Association (AHA-SDG 0530140N), the National Science Foundation (ECCS-0901566) and CONACyT-Mexico (83945).

FIG. 1 .
FIG. 1. Experimental setup.In the close up: schematic representation of the PA cell.This representation was the same used to calculate the PA pressure numerically.

FIG. 2 .
FIG. 2. Optical properties of the cell lines.A) Black and white pictures of the different cells lines.B) PA signal generated by the different cell lines in suspension C) Absorption spectra of the different cell lines.D) Mean pixel intensity of the cells in culture.Calibration A) 15 μm.B) 5 msec -20 mV.

FIG. 3 .
FIG. 3. Characteristics of HS936 melanoma cells and its photoacoustic signal at different cell concentrations.A) Top: Bar graphs quantifying the level of tyrosinase via the ratio of immune staining with an antibody that recognized tyrosinase compared with the control (b-actin).Bottom: A representative Western blot showing the bands of tyrosinase loaded under the same conditions.Quantification of data is expressed as the mean ± SEM.Picture of HS936 in culture attached to the culture dish at 95% confluences (B) and in solution (C).PAS produced by a monolayer of HS936 cultured cells ∼ 1540 cell (D) and amplified PA (see material and methods for details) from 7 cells (E).

011102- 8 PFIG. 4 .
FIG. 4. Spherical geometry of cells.Here r , is the point where the energy merges from sphere.

011102- 9 P
FIG. 5. PA signal generated by a different number of artificial cells in a hexagonal configuration.A) Cell arrangement.B) PA signal generated by different numbers of cells.Note that the amplitude of the PA signal is proportional to the number of cells in the hexagonal arrangements.Also the PA signal generated by 7 artificial cells is very small (insert).C) Relationship of the PA signal (PAi i≥ 1, i = number of cells) normalized by the PA amplitude of one single cell (PA0), as a function of the number of cells in the arrangement.D) Plot of the shift of time for PA generated by different numbers of cells.

FIG. 6 .
FIG.6.Changes in PA signal amplitude as a function of the distance between the cells and the sensor for a random and organized group of cells.A) 40 mm, B) 30 mm, C) 20 mm, D) 8 mm, E) 1 mm between the point of sensing and the plane where the cells were irradiated.Each point represents highly organized cells in an ideal hexagonal arrangement (gray circles) and randomly distributed (dark circles) in 7651 possible positions.F) PA signal profiles generated from different amounts of highly organized cells, where the point of sensing was localized at 1 mm from the plane in which the cells were localized.G-I) PA signal amplitude produced by seven cells spread randomly at three different distances from the point of observation.G) 1 mm, H) 8 mm, and I) 15 mm, between the point of observation and the plane where the cells were irradiated.A-E) Mean ± standard deviation.