Abstract

In photoacoustic imaging, the intensity of photoacoustic signal induced by optical absorption in biological tissue is proportional to light energy deposition, which is the product of the absorption coefficient and the local light fluence. Because tissue optical properties are highly dependent on the wavelength, the spectrum of the local light fluence at a target tissue beneath the sample surface is different than the spectrum of the incident light fluence. Therefore, quantifying the tissue optical absorption spectrum by using a photoacoustic technique is not feasible without the knowledge of the local light fluence. In this work, a highly accurate photoacoustic measurement of the subsurface tissue optical absorption spectrum has been achieved for the first time by introducing an extrinsic optical contrast agent with known optical properties. From the photoacoustic measurements with and without the contrast agent, a quantified measurement of the chromophore absorption spectrum can be realized in a strongly scattering medium. Experiments on micro-flow vessels containing fresh canine blood buried in phantoms and chicken breast tissues were carried out in a wavelength range from 680 nm to 950 nm. Spectroscopic photoacoustic measurements of both oxygenated and deoxygenated blood specimens presented an improved match with the references when employing this technique.

©2009 Optical Society of America

1. Introduction

Photoacoustic tomography (PAT), also referred to as thermoacoustic or optoacoustic tomography, is an emerging biomedical imaging technique which has drawn considerable interest in the past decade [1–16]. In PAT, a short-pulsed laser source is used to illuminate a biological sample. The laser-generated photoacoustic signals that are excited by thermoelastic expansion resulting from a transient temperature rise on the order of 10 mK can be measured by a wide-band ultrasonic transducer. The acquired signals can then be used to rebuild the distribution of optical energy deposition within the sample. The amplitude and the time of arrival of the photoacoustic (PA) signal provide respectively the information about the intensity and the spatial distribution of tissue optical absorption [17–19]. PAT images have the advantages of the inherent high contrast of diffuse optical imaging and the high spatial resolution of ultrasonography.

It is known that all chromophores (e.g. water, oxy-hemoglobin, deoxy-hemoglobin, lipid, cytochrome oxidase and melanin) in biological tissues have characteristic spectroscopic optical absorption features. These are essentially the fingerprints which allow these chromophores to be uniquely identified. Various tissues, containing different concentrations of chromophores, also show different optical absorption spectra. The spectroscopic form of PAT (i.e. SPAT), which employs multiple wavelengths to image a sample, provides a potentially new method for quantifying various chromophores and monitoring physiological properties in the target tissue with high sensitivity and high spatial resolution. In other words, SPAT enables not only morphological imaging based on tissue optical contrast but also quantitative evaluation of molecular conformation of biological tissues. As an example, based on the differences between the absorption spectra of oxygenated hemoglobin (HbO2) and deoxygenated hemoglobin (Hb), imaging of blood oxygen saturation and blood volume has been explored using the SPAT technique [6–11]. Moreover, SPAT also shows prominent sensitivity to a variety of optical contrast agents, including both organic dyes and metallic nanocolloids, and holds promise in revealing physiological and biochemical information of living tissues by imaging exogenous bioactive contrast agents [20,21].

The intensity of PA signals induced by light pulses is proportional to the optical energy deposition at the target tissue which is the product of the tissue optical absorption coefficient and the local light fluence. The optical properties including the absorption coefficients, scattering coefficients, refractive indices and anisotropy factors of the target and the background tissues are all highly dependent on the wavelength. Thus the spectrum of the local light fluence at the target tissue is different from the spectrum of the incident light on the sample surface. Therefore, the knowledge of the spectrum as well as the spatial distribution of light fluence in the sample is essential to achieve quantitative spectroscopic measurement or imaging with high accuracy [22–24]. Previous SPAT experiments either did not take into account the local light fluence in image reconstruction procedures [8,25] or included a correction factor from the measurement on ex vivo tissue of the same type to compensate the wavelength-dependent light attenuation during in vivo imaging [6]. Mathematical model has also been used to extract the chromophore distribution from the measured PA signals [23]. However, due to the high complexity and heterogeneity of biological tissue structure, composition, optical properties and physiological parameters (e.g. oxygen saturation) that all affect the distribution and the spectrum of light fluence in the sample, all of the above methods have limited accuracy and cannot provide satisfactory compensation for quantitative photoacoustic measurement of subsurface tissues.

In this paper, we present a new technique that can directly measure the spectrum of local light fluence at a target tissue in a highly scattering medium by introducing an extrinsic optical contrast agent with known optical absorption spectrum. By using the measured PA spectra of the target tissue with and without the contrast agent, a differentiation measurement can be conducted and the spectrum of local light fluence can be determined with high accuracy. With the spectroscopic local light fluence determined, quantitative photoacoustic measurement of the optical absorption spectrum in the target tissue can be achieved without being affected by the morphological features and physiological parameters in the imaged sample. To examine the feasibility of this method, experiments on oxygenated and deoxygenated fresh canine blood specimens in vessels buried in optical scattering phantoms and chicken breast tissues were conducted, and SPAT outcomes were validated with the references of the intrinsic optical absorption spectra of the measured blood specimens.

2. Methods

In whole human or canine blood, the two forms of hemoglobin (i.e. HbO2 and Hb) are the dominant chromophores in the visible and near-infrared (NIR) spectral region. If ε is the molar extinction coefficient of the whole blood and εHbO2 and εHb are those corresponding to HbO2 and Hb respectively, the spectroscopic photoacoustic signal intensity from a blood specimen can be written as

P1(λ)=(λ)CTϕ(λ),

where

ε(λ)=εHbO2(λ)SO2+εHb(λ)(1SO2).

CT = CHbO2+CHb is the total molar concentration of hemoglobin, SO2 = CHbO2/CT is the oxygen saturation of hemoglobin, ϕ is the spectroscopic light fluence at the target blood specimen, and K is a constant that is independent of laser wavelength. The values of εHbO2 and εHb in a wide wavelength range from the visible to the NIR regions are available in the literature [26]. As indicated in Eq. (1), SO2 of a blood specimen can be estimated if the values of P1 and ϕ are known at two or more different wavelengths.

It is not difficult to measure the spectrum of the incident light fluence on the sample surface. However, because the optical properties of biological tissues are wavelength dependent, the spectrum of the local light fluence ϕ at the target blood specimen will not be the same as the spectrum of the incident light. We have developed a new strategy of photoacoustic spectroscopy that can obtain the local light spectrum by introducing an extrinsic contrast agent that is an IR dye in this study (FHI 9001 1S, Fabricolor Holding Inc, New Jersey). If εdye is the molar extinction coefficient of the contrast agent that is introduced to the blood sample, then the spectroscopic PA signal from the mixture can be written as

P2(λ)=(λ)CTϕ(λ)+KεdyeCdye(λ)ϕ(λ),

where Cdye is the molar concentration of the contrast agent. From Eqs. (1) and (3) we can obtain the local light spectrum at the target tissue by

ϕ(λ)=P2(λ)P1(λ)Kεdye(λ)Cdye.

Substitution of Eq. (4) in Eq. (1) yields the spectroscopic absorption coefficient of the blood sample that is given by

ε(λ)=P1εdye(λ)CdyeCT[P2(λ)P1(λ)].

This equation gives the absorption spectrum of the blood specimen localized inside a biological sample that is free from the optical properties such as the scattering and absorption in the background tissue. This method is based on an assumption that the introducing of the optical contrast agent should not affect the spectroscopic local light fluence. This assumption should hold when the concentration of the introduced contrast agent is low and the size of the imaged object is small in comparison with the penetration depth of the light in the imaged object. Second assumption is that the chromophores (e.g. hemoglobin) in the target tissue should not have chemical or physical reactions to the introduced contrast agent which may change the intrinsic optical absorption spectra of these chromophores as well as the contrast agent. Other assumptions include that the introduction of the contrast agent should not change the hemoglobin concentration and the thermal parameters (e.g. specific heat and coefficient of volume thermal expansion) of the studied blood specimen. These assumptions should also hold when the amount of the introduced contrast agent is low.

After the systemic injection of a contrast agent in the circulatory system, different tissues or vessels may have different concentrations of the agent. Moreover, the contrast agent may be continuously removed from the circulation by the liver and spleen. Therefore, it could be difficult to estimate the contrast agent concentration in a target tissue or vessel. In this case, the Cdye in Eq. (5) is unknown. If we take all the parameters which depend on the wavelength together as a function Q(λ), then Eq. (5) can be rewritten as,

ε(λ)=Q(λ)CdyeCT,

where Q(λ)=P1εdye(λ)[P2(λ)P1(λ)] is quantified with the two spectroscopic measurements before and after the administration of the contrast agent. If PA measurements at two different wavelengths, λ1 and λ2, are conducted, we will have

εHbO2(λ1)SO2+εHb(λ1)(1SO2)=Q(λ1)CdyeCT,
ndεHbO2(λ2)SO2+εHb(λ2)(1SO2)=Q(λ2)CdyeCT.

Division of Eq. (7) by Eq. (8) will cancel both the contrast agent concentration Cdye and the total hemoglobin concentration CT. We can then have the absolutely quantified blood oxygen saturation SO2 as

SO2=Q(λ2)εHb(λ1)Q(λ1)εHbO2(λ2)Q(λ1)[εHbO2(λ2)εHb(λ2)]Q(λ2)[εHbO2(λ1)εHb(λ1)].

Even without knowing the concentration of the introduced contrast agent in a target tissue or vessel, we can still quantify the blood oxygen concentration by using this SPAT technique. It is important to note that the concentration of the contrast agent in the target tissue or vessel should not change during the second SPAT measurements at different wavelengths.

In another case, we may employ an optical blood pool agent similar to those used in contrast enhanced perfusion MRI. The blood pool agent will normally remain confined to the intravascular space with an extended retention time in the blood. Hence the concentration Cdye in the blood after systemic administration is homogenous and stable and can also be estimated from the applied dose and the total amount of blood in the subject body. In this case, Eq. (5) can be rewritten as

εHbO2(λ)CHbO2+εHb(λ)CHb=Q(λ)Cdye.

With the spectroscopic measurements at two or more wavelengths, the concentrations of the two types of hemoglobin, CHbO2 and CHb, can then be quantified. We can further quantify the hemodynamic parameters in the target tissue or vessel including both the blood oxygen saturation and the blood volume.

3. Experimental procedure

The schematic of the photoacoustic setup is shown in Fig. 1. An optical parametric oscillator (OPO) system (Vibrant B, Opotek) pumped by an Nd:YAG laser (Brilliant B, Bigsky) was used as the laser source. The laser generated 5.5-ns duration pulses at 10-Hz pulse repetition rate with wavelength tunable from 680 nm to 950 nm. A laser beam along the Z-axis illuminated the sample with an incident energy density less than the ANSI safety limit. Micro-flow vessels were created by injecting fresh canine blood into a soft polyethylene (PE) tube (Intramedic, Clay Adams Brand) which is optically transparent and has an inner diameter of 0.58 mm. The vessel was aligned along the Y-axis with the center part exposed to the laser beam. Before reaching the sample surface, a small portion of the laser beam was extracted by putting a glass plate just before the sample and the reflected light was measured with a photodiode to monitor the incident light energy and the laser fluctuation. Neutral density filters (NDF) were used to reduce the power of the laser reaching the photodiode. A focused wideband transducer (V312, Panametrics) with a focal length of 19 mm, diameter of 6.35 mm, -6 dB bandwidth of 133 %, and a center frequency of 10 MHz was used to collect the PA signals propagating along the X–axis. Both the sample and the transducer were immersed in water for acoustic coupling. The PA signals received by the transducer were amplified (PR5072, Panametrics) and fed into a channel of a 500-MHz digital oscilloscope (TDS 540B, Tektronics). Output of the photodiode was fed into another channel of the oscilloscope. The oscilloscope was triggered by the laser pulse and a computer was used to collect and store the data from the oscilloscope. Photoacoustic measurements were carried out in the spectral range from 680 nm to 950 nm with a constant interval of 5 nm for a total of 55 samples. At each wavelength, PA signals generated by 20 laser pulses were averaged to achieve a better signal-to-noise ratio. A complete set of spectroscopic photoacoustic measurements at the 55 wavelengths took about 40 min using the current system.

 

Fig. 1. Schematic of the experimental setup for SPAT measurement of tissue optical absorption spectrum. NDF: neutral density filter.

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Fresh whole blood collected from dogs was used. Oxygenated blood was taken from the left atrium of the heart when the dog was alive, while the deoxygenated blood was collected from the venous-caudal vena cava, 5–10 min after the dog was sacrificed. A blood gas analyzer (ABL 5, Radiometer Copenhagen) was used to measure the oxygen level of each blood specimen. The infrared dye used as the contrast agent has strong absorption over the entire wavelength range from 680 nm to 950 nm (see Fig. 2). To keep the hemoglobin concentration constant before and after introducing the dye, only a small amount of highly concentrated dye solution (5 μL in 1 mL of blood) was added to the blood. This amount led to the concentration of the dye in the blood of 2.2 mM/L. With the measured PA spectra from the same blood specimen with and without the dye, the local light fluence was obtained by using Eq. (4). The PA spectrum of the blood sample without the dye was then divided by the local light spectrum to obtain the corrected spectrum of optical absorption of the blood specimen, as indicated by Eq. (5).

 

Fig. 2. Optical absorption spectrum of the contrast agent (IR dye FHI90011S) measured by SPAT.

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4. Results and discussion

 

Fig. 3. Typical photoacoustic signal measured from the vessel. Inset shows the typical photodiode signal of the laser pulse.

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A typical PA signal from a blood vessel received by our photoacoustic system is given in Fig. 3 along with the received photodiode signal of the laser pulse. The peak-to-peak amplitude of the bipolar PA signal is proportional to the local light energy deposition in the vessel. However, the total shaded area under the curve, which is indicated in Fig. 3 and was used in this study, can manifest the local light energy deposition with an improved signal-to-noise ratio. For the same reason, the shaded area marked on the photodiode signal was used to indicate the incident light energy on the sample surface. The ratio between the PA signal and the photodiode signal gave the photoacoustic measurement at each wavelength.

 

Fig. 4. Optical absorption spectra of an oxygenated (circle) and a deoxygenated (square) canine blood specimens obtained with the SPAT system in comparison with the references (solid curves). The blood oxygen saturation (SO2) were 1.00 for the oxygenated blood specimen and 0.33 for the deoxygenated blood specimen.

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To validate the accuracy of our SPAT system in describing the optical absorption spectrum of a tissue, spectroscopic measurement of blood specimens was first conducted in a non-scattering medium. The fresh canine blood contained in the vessel was kept at a depth of 1 cm beneath the water surface during the measurement at all the 55 wavelengths. The oxygen saturation level (SO2) for each blood specimen was measured with the blood gas analyzer. With the SO2 of each blood specimen measured, the reference spectroscopic absorption of the blood specimen can be determined with the known molar extinction coefficients of the oxygenated and the deoxygenated hemoglobin [26]. This reference, shown by the solid curve in each of the following figures, enables the verification of SPAT measurement. Figure 4 shows the spectroscopic photoacoustic measurements of an oxygenated (SO2 =1.00) and a deoxygenated (SO2 = 0.33) blood specimens. Because this experiment was conducted in a non-scattering medium, the incident light fluence on the sample surface (i.e. the surface of the water) was very close to that at the target blood vessel, and hence the SPAT results can present the blood absorption spectra well without need for any compensation. The PA outcomes match with the references with goodness of fit R2 of 0.999 for the oxygenated blood and 0.998 for the deoxygenated blood. R2 is the sum of the squares of the relative errors. With the PA spectra obtained, we can estimate the oxygen saturation levels of the oxygenated and the deoxygenated blood specimens which are 0.98 and 0.30 respectively, both matching well with the results from the blood gas analyzer. The good match between the PA outcomes and the references has proven the accuracy of this SPAT system. Here, the blood oxygen saturation values were obtained by fitting the photoacoustic spectrum with the function [SO2εHbO2(λ)+(1-SO2Hb(λ)] with SO2 as the fitting parameter by using linear least square procedure.

To mimic the situation in a highly scattering medium such as a biological tissue, we made a phantom using whole milk diluted with water at the ratio of 1:4 [27–29]. Photoacoustic spectra of an oxygenated (SO2 =0.97) and a deoxygenated (SO2 = 0.10) canine blood specimens immersed 7.5-mm deep in the diluted milk are given in Fig. 5 in comparison with the references. Figure 5(a) shows the PA spectrum of the oxygenated blood specimen without the compensation for the local light spectrum; while Fig. 5(b) is the PA spectrum of the same blood specimen after the compensation for the local light spectrum through the method described above. The spectrum of the local light fluence was obtained by using Eq. (5) with the PA spectra taken before and after introducing the contrast agent. By comparing Figs. 5(a) and 5(b), we can see that the SPAT spectrum after the compensation shows a better match with the reference. The goodness of fit R2 improved from 0.978 to 0.988 for the oxygenated blood specimen. Figs. 5(c) and 5(d) show the result for deoxygenated blood specimen. Again, after the compensation by considering the local light spectrum, the SPAT spectrum shows a better match with the reference. The goodness of fit R2 improved from 0.963 to 0.993 for the deoxygenated blood specimen. Moreover, we have computed the oxygen saturation levels of each blood specimen by using the PA spectra before and after the compensation respectively. For the oxygenated blood, the computed SO2 is 0.97 after the compensation and is equal to the reference value of 0.97 provided by the blood gas analyzer; while before compensation, the value is computed to be 0.86. Similarly, the computed oxygen saturation levels of the deoxygenated blood are 0.14 and 0.12 respectively before and after the compensation. By using our technique, the PA measurement has a better match with the reference value of 0.10.

 

Fig. 5. Photoacoustic spectra of an oxygenated (circle) and a deoxygenated (square) canine blood specimens embedded in a scattering medium made from diluted whole milk. The blood oxygen saturation (SO2) were 0.97 for the oxygenated blood specimen and 0.10 for the deoxygenated blood specimen. (a) and (c) are the PA spectra before compensation and (b) and (d) are the PA spectra after compensation by introducing the optical contrast agent. Solid curves represent the references.

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To further validate this technique, we have also conducted the PA measurements of the blood specimens in vessels buried 3-mm deep in fresh chicken breast tissues. The PA spectra of an oxygenated (SO2 = 0.98) and a deoxygenated (SO2 = 0.27) blood specimens in a slab of chicken breast in comparison with the references are shown in Fig. 6. For each blood specimen, we can see a clearly improved matching between the SPAT outcome and the reference after the compensation by introducing the optical contrast agent. By using the method described above, the goodness of fit R2 was improved from 0.983 to 0.997 for the oxygenated blood specimen, and from 0.980 to 0.995 for the deoxygenated blood specimen. For oxygenated blood specimen, the computed blood oxygen saturation levels from the PA measurements before and after the compensation are 0.86 and 0.95 respectively; while for deoxygenated blood specimen, the computed blood oxygen saturation levels from the PA measurements before and after the compensation are 0.39 and 0.26 respectively. After the compensation by introducing the optical contrast agent, PA measurements of blood oxygen saturation have a better match with the references provided by the blood gas analyzer.

 

Fig. 6. Photoacoustic spectra of an oxygenated (circle) and a deoxygenated (square) canine blood specimens embedded 3-mm deep in a chicken breast tissue. The blood oxygen saturation (SO2) were 0.98 for the oxygenated blood specimen and 0.27 for the deoxygenated blood specimen. (a) and (c) are the PA spectra before compensation and (b) and (d) are the PA spectra after compensation by introducing the optical contrast agent. Solid curves represent the references.

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Results of our photoacoustic experiments on oxygenated and deoxygenated blood specimens in the scattering media including the diluted milk and the chicken breast tissues reveal that 1) the optical properties such as the scattering and absorption of a scattering medium affect the spectrum of the light fluence reaching the target tissue in the medium, which may result in a mismatch between the SPAT measurement and the true absorption spectrum of the target tissue; 2) the spectrum of the local light fluence at the target tissue such as a blood vessel within a scattering medium could be measured by introducing an optical contrast agent and then performing differential SPAT measurement; and 3) the measured spectrum of the local light fluence could be used to compensate the SPAT result for better revealing of the optical absorption spectrum of the target tissue.

5. Conclusion

This work presents a novel method to measure the spectroscopic tissue optical absorption in a highly scattering medium by using the emerging SPAT technology aided by extrinsic optical contrast agents. Preliminary studies on phantoms and ex vivo chicken breast tissues have proven the feasibility of this method. After the compensation by considering the local light fluence, a quantitative photoacoustic measurement of the subsurface tissue optical absorption spectrum can be achieved with improved accuracy. This technique makes SPAT a potentially powerful tool in mapping and quantifying chromophore distribution in biological tissues, which may contribute significantly to imaging and diagnosis at the molecular and genetic levels. Moreover, by using this method, highly accurate quantification of blood oxygen saturation in subsurface tissues can be achieved in a noninvasive manner without being affected by background tissue and sample surface. This may prove very useful in cancer diagnosis and characterization by grading objectively the hypoxia in a target tumor.

In future work, the feasibility of this technique will be examined further through the experiments on living animals. For in vivo application, different tissues may have different accumulation of an exogenous contrast agent, especially when the applied contrast medium is not a blood pool agent. However, as indicated in this work, the concentration of a contrast agent in a target tissue or vessel does not need to be known before quantifying the blood oxygen saturation in the tissue or vessel. Therefore, this technique can potentially evaluate the oxygenation states of a group of vessels in a target tissue each with different contrast agent concentration. In a living tissue with potentially large number of blood vessels, introducing of a contrast agent may change the distribution of light fluence in the tissue which may affect the accuracy of this SPAT technique, especially when the contrast agent concentration in the blood is too high and, as a result, the induced optical absorption is too strong. On the other hand, generating extra optical absorption strong enough for differential measurement by introducing sufficient contrast agent is also essential in this SPAT technique. Therefore, determining the appropriate dose of contrast agent administration for in vivo application is one of the main challenges and will be investigated in future work.

Acknowledgments

This work was supported by National Institute of Health (NIH) under grant no. R01 AR055179 & R01 CA91713 and Department of Defense under grant no. W81XWH-07-1-0231.

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References

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  1. R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging 2, 113–123 (2003).
    [Crossref] [PubMed]
  2. X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol. 21, 803–806 (2003).
    [Crossref] [PubMed]
  3. S. Yang, Da. Xing, Q. Zhou, L. Xiang, and Y. Lao, “Functional imaging of cerebrovascular in small animals using high resolution photoacoustic tomography,” Med. Phys. 34, 3294–3301 (2007).
    [Crossref] [PubMed]
  4. C. G. A. Hoelen, F. F. M. de Muil, R. Pongers, and A. Dekker, “Three-dimensional photoacoustic imaging of blood vessels in tissue,” Opt. Lett. 23, 648–650 (1998).
    [Crossref]
  5. R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, and F. F. M. de Mul, “In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor,” IEEE J. Sel. Top. Quantum Electron. 9, 343–346 (2003).
    [Crossref]
  6. X. Wang, X. Xie, G. Ku, and L. V. Wang, “Noninvasive imaging of hemoglobin concentration and oxygenation in the rat brain using high-resolution photoacoustic tomography,” J. Biomed. Opt. 11, 024015 (2006).
    [Crossref] [PubMed]
  7. H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging,” Nat. Biotechnol. 24, 848–851 (2006).
    [Crossref] [PubMed]
  8. Y. Y. Petrov, I. Y. Petrova, I. A. Patrikeev, R. O. Esenaliev, and D. S. Prough, “Multiwavelength optoacoustic system for noninvasive monitoring of cerebral venous oxygenation: a pilot clinical test in the internal jugular vein,” Opt. Lett. 31, 1827–1829 (2006).
    [Crossref] [PubMed]
  9. G. F. Lungfu, M. Li, X. Xie, L. V. Wang, and G. Stoica, “In vivo imaging and characterization of hypoxia-induced neovascularization and tumor invasion,” Int. J. Oncology 30, 45–54 (2007).
  10. B. Liu, D. Reinecke, R. A. Kruger, and K. M. Stantz, “Phantom and in vivo measurements of hemoglobin concentration and oxygen saturation using PCT-S small animal scanner,” Proc. SPIE 6437, 64371X1–64371X9 (2007).
  11. K. M. Stantz, B. Liu, M. Cao, D. Reinecke, K. Miller, and R. Kruger, “Photoacoustic spectroscopic imaging of intra-tumor heterogeneity and molecular identification,” Proc. SPIE 6086, 608605 (2006).
    [Crossref]
  12. D. Yang, Da. Xing, S. Yang, and L. Xiang, “Fast full view photoacoustic imaging by combined scanning with a linear transducer array,” Opt. Express 15, 15566–15575 (2007).
    [Crossref] [PubMed]
  13. Y. Lao, Da Xing, S. Yang, and L. Xiang, “Noninvasive photoacoustic imaging of the developing vasculature during early tumor growth,” Phys. Med. Biol. 53, 4203–4212 (2008).
    [Crossref] [PubMed]
  14. L. Xiang, Da. Xing, H. Gu, D. Yang, S. Yang, L. Zeng, and W. R. Chen, “Real-time optoacoustic monitoring of vascular damage during photodynamic therapy treatment of tumor,” J. Biomed. Opt. 12, 014001 (2007)
    [Crossref] [PubMed]
  15. P-C. Lie, C-R. C. Wang, D-B. Shieh, C-W. Wei, C-K. Liao, C. Poe, S. Jhan, A-A. Ding, and Y-N. Wu, “In vivo photoacoustic molecular imaging with simulataneous multiple selective targeting using antibody-conjugated gold nanorods,” Opt. Express 16, 18605–18615 (2008).
    [Crossref]
  16. X. Wang, D. L. Chamberland, and D. A. Jamadar, “Noninvasive photoacoustic tomography of human peripheral joints toward diagnosis of inflammatory arthritis,” Opt. Lett. 32, 3002–3004 (2007).
    [Crossref] [PubMed]
  17. A. A. Oraevsky, S. L. Jacques, R. O. Esenaliev, and F. K. Tittel, “Laser based optoacoustic imaging in biological tissues,” Proc. SPIE 2134A, 122–128 (1994).
  18. R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS) - Reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
    [Crossref] [PubMed]
  19. M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77, 041101 (2006).
    [Crossref]
  20. X. Wang, G. Ku, M. A. Wegiel, D. J. Bornhop, G. Stoica, and L. V. Wang, “Noninvasive photoacoustic angiography of animal brains in vivo with near-infrared light and an optical contrast agent,” Opt. Lett. 29,730–732 (2004).
    [Crossref] [PubMed]
  21. Y. Wang, X. Xie, X. Wang, G. Ku, K. L. Gill, D. P. O’Neal, G. Stoica, and L. V. Wang, “Photoacoustic tomography of a nanoshell contrast agent in the in vivo rat brain,” Nano Lett. 4, 1689–1692 (2004).
    [Crossref]
  22. M. Sivaramakrishnan, K. Maslov, H. F. Zhang, G. Stoica, and L. V. Wang, “Limitations of quantitative photoacoustic measurements of blood oxygenation in small vessels,” Phys. Med. Biol. 52, 1349–1361 (2007).
    [Crossref] [PubMed]
  23. J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52, 141–168 (2007).
    [Crossref]
  24. K. Maslov, H. F. Zhang, and L. V. Wang, “Effects of wavelength-dependent fluence attenuation on the noninvasive photoacoustic imaging of hemoglobin oxygen saturation in subcutaneous vasculature in vivo,” Inverse Probl. 23, S113–S122 (2007).
    [Crossref]
  25. H. F. Zhang, K. Maslov, M. Sivaramakrishnan, G. Stoica, and L. V. Wang, “Imaging of hemoglobin oxygen saturation variations in single vessels in vivo using photoacoustic microscopy,” Appl. Phys. Lett. 90, 053901 (2007).
    [Crossref]
  26. S. A. Prahl, “Optical absorption of hemoglobin,” http://omlc.ogi.edu/spectra/hemoglobin/.
  27. S. Marengo, C. Pépin, T. Goulet, and D. Houde, “Time-gated transillumination of objects in highly scattering media using a subpicosecond optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 5, 895–901 (1999).
    [Crossref]
  28. Z. Zhao and R. Myllylä, “The effects of optical scattering on pulsed photoacoustic measurement in weakly absorbing liquids,” Meas. Sci. Technol. 12, 2172–2177 (2001).
    [Crossref]
  29. Z. Zhao and R. Myllylä, “Scattering photoacoustic study of weakly-absorbing substances in aqueous suspensions,” J. Phys. IV France 137, 385–390 (2006).
    [Crossref]

2008 (2)

2007 (10)

X. Wang, D. L. Chamberland, and D. A. Jamadar, “Noninvasive photoacoustic tomography of human peripheral joints toward diagnosis of inflammatory arthritis,” Opt. Lett. 32, 3002–3004 (2007).
[Crossref] [PubMed]

L. Xiang, Da. Xing, H. Gu, D. Yang, S. Yang, L. Zeng, and W. R. Chen, “Real-time optoacoustic monitoring of vascular damage during photodynamic therapy treatment of tumor,” J. Biomed. Opt. 12, 014001 (2007)
[Crossref] [PubMed]

D. Yang, Da. Xing, S. Yang, and L. Xiang, “Fast full view photoacoustic imaging by combined scanning with a linear transducer array,” Opt. Express 15, 15566–15575 (2007).
[Crossref] [PubMed]

S. Yang, Da. Xing, Q. Zhou, L. Xiang, and Y. Lao, “Functional imaging of cerebrovascular in small animals using high resolution photoacoustic tomography,” Med. Phys. 34, 3294–3301 (2007).
[Crossref] [PubMed]

G. F. Lungfu, M. Li, X. Xie, L. V. Wang, and G. Stoica, “In vivo imaging and characterization of hypoxia-induced neovascularization and tumor invasion,” Int. J. Oncology 30, 45–54 (2007).

B. Liu, D. Reinecke, R. A. Kruger, and K. M. Stantz, “Phantom and in vivo measurements of hemoglobin concentration and oxygen saturation using PCT-S small animal scanner,” Proc. SPIE 6437, 64371X1–64371X9 (2007).

M. Sivaramakrishnan, K. Maslov, H. F. Zhang, G. Stoica, and L. V. Wang, “Limitations of quantitative photoacoustic measurements of blood oxygenation in small vessels,” Phys. Med. Biol. 52, 1349–1361 (2007).
[Crossref] [PubMed]

J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52, 141–168 (2007).
[Crossref]

K. Maslov, H. F. Zhang, and L. V. Wang, “Effects of wavelength-dependent fluence attenuation on the noninvasive photoacoustic imaging of hemoglobin oxygen saturation in subcutaneous vasculature in vivo,” Inverse Probl. 23, S113–S122 (2007).
[Crossref]

H. F. Zhang, K. Maslov, M. Sivaramakrishnan, G. Stoica, and L. V. Wang, “Imaging of hemoglobin oxygen saturation variations in single vessels in vivo using photoacoustic microscopy,” Appl. Phys. Lett. 90, 053901 (2007).
[Crossref]

2006 (6)

Z. Zhao and R. Myllylä, “Scattering photoacoustic study of weakly-absorbing substances in aqueous suspensions,” J. Phys. IV France 137, 385–390 (2006).
[Crossref]

K. M. Stantz, B. Liu, M. Cao, D. Reinecke, K. Miller, and R. Kruger, “Photoacoustic spectroscopic imaging of intra-tumor heterogeneity and molecular identification,” Proc. SPIE 6086, 608605 (2006).
[Crossref]

X. Wang, X. Xie, G. Ku, and L. V. Wang, “Noninvasive imaging of hemoglobin concentration and oxygenation in the rat brain using high-resolution photoacoustic tomography,” J. Biomed. Opt. 11, 024015 (2006).
[Crossref] [PubMed]

H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging,” Nat. Biotechnol. 24, 848–851 (2006).
[Crossref] [PubMed]

Y. Y. Petrov, I. Y. Petrova, I. A. Patrikeev, R. O. Esenaliev, and D. S. Prough, “Multiwavelength optoacoustic system for noninvasive monitoring of cerebral venous oxygenation: a pilot clinical test in the internal jugular vein,” Opt. Lett. 31, 1827–1829 (2006).
[Crossref] [PubMed]

M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77, 041101 (2006).
[Crossref]

2004 (2)

X. Wang, G. Ku, M. A. Wegiel, D. J. Bornhop, G. Stoica, and L. V. Wang, “Noninvasive photoacoustic angiography of animal brains in vivo with near-infrared light and an optical contrast agent,” Opt. Lett. 29,730–732 (2004).
[Crossref] [PubMed]

Y. Wang, X. Xie, X. Wang, G. Ku, K. L. Gill, D. P. O’Neal, G. Stoica, and L. V. Wang, “Photoacoustic tomography of a nanoshell contrast agent in the in vivo rat brain,” Nano Lett. 4, 1689–1692 (2004).
[Crossref]

2003 (3)

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, and F. F. M. de Mul, “In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor,” IEEE J. Sel. Top. Quantum Electron. 9, 343–346 (2003).
[Crossref]

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging 2, 113–123 (2003).
[Crossref] [PubMed]

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol. 21, 803–806 (2003).
[Crossref] [PubMed]

2001 (1)

Z. Zhao and R. Myllylä, “The effects of optical scattering on pulsed photoacoustic measurement in weakly absorbing liquids,” Meas. Sci. Technol. 12, 2172–2177 (2001).
[Crossref]

1999 (1)

S. Marengo, C. Pépin, T. Goulet, and D. Houde, “Time-gated transillumination of objects in highly scattering media using a subpicosecond optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 5, 895–901 (1999).
[Crossref]

1998 (1)

1995 (1)

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS) - Reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[Crossref] [PubMed]

1994 (1)

A. A. Oraevsky, S. L. Jacques, R. O. Esenaliev, and F. K. Tittel, “Laser based optoacoustic imaging in biological tissues,” Proc. SPIE 2134A, 122–128 (1994).

Appledorn, C. R.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS) - Reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[Crossref] [PubMed]

Beard, P.

J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52, 141–168 (2007).
[Crossref]

Bornhop, D. J.

Cao, M.

K. M. Stantz, B. Liu, M. Cao, D. Reinecke, K. Miller, and R. Kruger, “Photoacoustic spectroscopic imaging of intra-tumor heterogeneity and molecular identification,” Proc. SPIE 6086, 608605 (2006).
[Crossref]

Chamberland, D. L.

Chen, W. R.

L. Xiang, Da. Xing, H. Gu, D. Yang, S. Yang, L. Zeng, and W. R. Chen, “Real-time optoacoustic monitoring of vascular damage during photodynamic therapy treatment of tumor,” J. Biomed. Opt. 12, 014001 (2007)
[Crossref] [PubMed]

de Muil, F. F. M.

de Mul, F. F. M.

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, and F. F. M. de Mul, “In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor,” IEEE J. Sel. Top. Quantum Electron. 9, 343–346 (2003).
[Crossref]

Dekker, A.

Delpy, D.

J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52, 141–168 (2007).
[Crossref]

Ding, A-A.

Elwell, C.

J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52, 141–168 (2007).
[Crossref]

Esenaliev, R. O.

Fang, Y. R.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS) - Reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[Crossref] [PubMed]

Gill, K. L.

Y. Wang, X. Xie, X. Wang, G. Ku, K. L. Gill, D. P. O’Neal, G. Stoica, and L. V. Wang, “Photoacoustic tomography of a nanoshell contrast agent in the in vivo rat brain,” Nano Lett. 4, 1689–1692 (2004).
[Crossref]

Goulet, T.

S. Marengo, C. Pépin, T. Goulet, and D. Houde, “Time-gated transillumination of objects in highly scattering media using a subpicosecond optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 5, 895–901 (1999).
[Crossref]

Gu, H.

L. Xiang, Da. Xing, H. Gu, D. Yang, S. Yang, L. Zeng, and W. R. Chen, “Real-time optoacoustic monitoring of vascular damage during photodynamic therapy treatment of tumor,” J. Biomed. Opt. 12, 014001 (2007)
[Crossref] [PubMed]

Hoelen, C. G. A.

Hondebrink, E.

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, and F. F. M. de Mul, “In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor,” IEEE J. Sel. Top. Quantum Electron. 9, 343–346 (2003).
[Crossref]

Houde, D.

S. Marengo, C. Pépin, T. Goulet, and D. Houde, “Time-gated transillumination of objects in highly scattering media using a subpicosecond optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 5, 895–901 (1999).
[Crossref]

Jacques, S. L.

A. A. Oraevsky, S. L. Jacques, R. O. Esenaliev, and F. K. Tittel, “Laser based optoacoustic imaging in biological tissues,” Proc. SPIE 2134A, 122–128 (1994).

Jamadar, D. A.

Jhan, S.

Kiser, W. L.

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging 2, 113–123 (2003).
[Crossref] [PubMed]

Kolkman, R. G. M.

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, and F. F. M. de Mul, “In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor,” IEEE J. Sel. Top. Quantum Electron. 9, 343–346 (2003).
[Crossref]

Kruger, G. A.

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging 2, 113–123 (2003).
[Crossref] [PubMed]

Kruger, R.

K. M. Stantz, B. Liu, M. Cao, D. Reinecke, K. Miller, and R. Kruger, “Photoacoustic spectroscopic imaging of intra-tumor heterogeneity and molecular identification,” Proc. SPIE 6086, 608605 (2006).
[Crossref]

Kruger, R. A.

B. Liu, D. Reinecke, R. A. Kruger, and K. M. Stantz, “Phantom and in vivo measurements of hemoglobin concentration and oxygen saturation using PCT-S small animal scanner,” Proc. SPIE 6437, 64371X1–64371X9 (2007).

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging 2, 113–123 (2003).
[Crossref] [PubMed]

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS) - Reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[Crossref] [PubMed]

Ku, G.

X. Wang, X. Xie, G. Ku, and L. V. Wang, “Noninvasive imaging of hemoglobin concentration and oxygenation in the rat brain using high-resolution photoacoustic tomography,” J. Biomed. Opt. 11, 024015 (2006).
[Crossref] [PubMed]

X. Wang, G. Ku, M. A. Wegiel, D. J. Bornhop, G. Stoica, and L. V. Wang, “Noninvasive photoacoustic angiography of animal brains in vivo with near-infrared light and an optical contrast agent,” Opt. Lett. 29,730–732 (2004).
[Crossref] [PubMed]

Y. Wang, X. Xie, X. Wang, G. Ku, K. L. Gill, D. P. O’Neal, G. Stoica, and L. V. Wang, “Photoacoustic tomography of a nanoshell contrast agent in the in vivo rat brain,” Nano Lett. 4, 1689–1692 (2004).
[Crossref]

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol. 21, 803–806 (2003).
[Crossref] [PubMed]

Lao, Y.

Y. Lao, Da Xing, S. Yang, and L. Xiang, “Noninvasive photoacoustic imaging of the developing vasculature during early tumor growth,” Phys. Med. Biol. 53, 4203–4212 (2008).
[Crossref] [PubMed]

S. Yang, Da. Xing, Q. Zhou, L. Xiang, and Y. Lao, “Functional imaging of cerebrovascular in small animals using high resolution photoacoustic tomography,” Med. Phys. 34, 3294–3301 (2007).
[Crossref] [PubMed]

Laufer, J.

J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52, 141–168 (2007).
[Crossref]

Li, M.

G. F. Lungfu, M. Li, X. Xie, L. V. Wang, and G. Stoica, “In vivo imaging and characterization of hypoxia-induced neovascularization and tumor invasion,” Int. J. Oncology 30, 45–54 (2007).

Liao, C-K.

Lie, P-C.

Liu, B.

B. Liu, D. Reinecke, R. A. Kruger, and K. M. Stantz, “Phantom and in vivo measurements of hemoglobin concentration and oxygen saturation using PCT-S small animal scanner,” Proc. SPIE 6437, 64371X1–64371X9 (2007).

K. M. Stantz, B. Liu, M. Cao, D. Reinecke, K. Miller, and R. Kruger, “Photoacoustic spectroscopic imaging of intra-tumor heterogeneity and molecular identification,” Proc. SPIE 6086, 608605 (2006).
[Crossref]

Liu, P.

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS) - Reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[Crossref] [PubMed]

Lungfu, G. F.

G. F. Lungfu, M. Li, X. Xie, L. V. Wang, and G. Stoica, “In vivo imaging and characterization of hypoxia-induced neovascularization and tumor invasion,” Int. J. Oncology 30, 45–54 (2007).

Marengo, S.

S. Marengo, C. Pépin, T. Goulet, and D. Houde, “Time-gated transillumination of objects in highly scattering media using a subpicosecond optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 5, 895–901 (1999).
[Crossref]

Maslov, K.

H. F. Zhang, K. Maslov, M. Sivaramakrishnan, G. Stoica, and L. V. Wang, “Imaging of hemoglobin oxygen saturation variations in single vessels in vivo using photoacoustic microscopy,” Appl. Phys. Lett. 90, 053901 (2007).
[Crossref]

K. Maslov, H. F. Zhang, and L. V. Wang, “Effects of wavelength-dependent fluence attenuation on the noninvasive photoacoustic imaging of hemoglobin oxygen saturation in subcutaneous vasculature in vivo,” Inverse Probl. 23, S113–S122 (2007).
[Crossref]

M. Sivaramakrishnan, K. Maslov, H. F. Zhang, G. Stoica, and L. V. Wang, “Limitations of quantitative photoacoustic measurements of blood oxygenation in small vessels,” Phys. Med. Biol. 52, 1349–1361 (2007).
[Crossref] [PubMed]

H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging,” Nat. Biotechnol. 24, 848–851 (2006).
[Crossref] [PubMed]

Miller, K.

K. M. Stantz, B. Liu, M. Cao, D. Reinecke, K. Miller, and R. Kruger, “Photoacoustic spectroscopic imaging of intra-tumor heterogeneity and molecular identification,” Proc. SPIE 6086, 608605 (2006).
[Crossref]

Miller, K. D.

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging 2, 113–123 (2003).
[Crossref] [PubMed]

Myllylä, R.

Z. Zhao and R. Myllylä, “Scattering photoacoustic study of weakly-absorbing substances in aqueous suspensions,” J. Phys. IV France 137, 385–390 (2006).
[Crossref]

Z. Zhao and R. Myllylä, “The effects of optical scattering on pulsed photoacoustic measurement in weakly absorbing liquids,” Meas. Sci. Technol. 12, 2172–2177 (2001).
[Crossref]

O’Neal, D. P.

Y. Wang, X. Xie, X. Wang, G. Ku, K. L. Gill, D. P. O’Neal, G. Stoica, and L. V. Wang, “Photoacoustic tomography of a nanoshell contrast agent in the in vivo rat brain,” Nano Lett. 4, 1689–1692 (2004).
[Crossref]

Oraevsky, A. A.

A. A. Oraevsky, S. L. Jacques, R. O. Esenaliev, and F. K. Tittel, “Laser based optoacoustic imaging in biological tissues,” Proc. SPIE 2134A, 122–128 (1994).

Pang, Y.

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol. 21, 803–806 (2003).
[Crossref] [PubMed]

Patrikeev, I. A.

Pépin, C.

S. Marengo, C. Pépin, T. Goulet, and D. Houde, “Time-gated transillumination of objects in highly scattering media using a subpicosecond optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 5, 895–901 (1999).
[Crossref]

Petrov, Y. Y.

Petrova, I. Y.

Poe, C.

Pongers, R.

Prahl, S. A.

S. A. Prahl, “Optical absorption of hemoglobin,” http://omlc.ogi.edu/spectra/hemoglobin/.

Prough, D. S.

Reinecke, D.

B. Liu, D. Reinecke, R. A. Kruger, and K. M. Stantz, “Phantom and in vivo measurements of hemoglobin concentration and oxygen saturation using PCT-S small animal scanner,” Proc. SPIE 6437, 64371X1–64371X9 (2007).

K. M. Stantz, B. Liu, M. Cao, D. Reinecke, K. Miller, and R. Kruger, “Photoacoustic spectroscopic imaging of intra-tumor heterogeneity and molecular identification,” Proc. SPIE 6086, 608605 (2006).
[Crossref]

Reinecke, D. R.

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging 2, 113–123 (2003).
[Crossref] [PubMed]

Shieh, D-B.

Sivaramakrishnan, M.

H. F. Zhang, K. Maslov, M. Sivaramakrishnan, G. Stoica, and L. V. Wang, “Imaging of hemoglobin oxygen saturation variations in single vessels in vivo using photoacoustic microscopy,” Appl. Phys. Lett. 90, 053901 (2007).
[Crossref]

M. Sivaramakrishnan, K. Maslov, H. F. Zhang, G. Stoica, and L. V. Wang, “Limitations of quantitative photoacoustic measurements of blood oxygenation in small vessels,” Phys. Med. Biol. 52, 1349–1361 (2007).
[Crossref] [PubMed]

Stantz, K. M.

B. Liu, D. Reinecke, R. A. Kruger, and K. M. Stantz, “Phantom and in vivo measurements of hemoglobin concentration and oxygen saturation using PCT-S small animal scanner,” Proc. SPIE 6437, 64371X1–64371X9 (2007).

K. M. Stantz, B. Liu, M. Cao, D. Reinecke, K. Miller, and R. Kruger, “Photoacoustic spectroscopic imaging of intra-tumor heterogeneity and molecular identification,” Proc. SPIE 6086, 608605 (2006).
[Crossref]

Steenbergen, W.

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, and F. F. M. de Mul, “In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor,” IEEE J. Sel. Top. Quantum Electron. 9, 343–346 (2003).
[Crossref]

Stoica, G.

G. F. Lungfu, M. Li, X. Xie, L. V. Wang, and G. Stoica, “In vivo imaging and characterization of hypoxia-induced neovascularization and tumor invasion,” Int. J. Oncology 30, 45–54 (2007).

H. F. Zhang, K. Maslov, M. Sivaramakrishnan, G. Stoica, and L. V. Wang, “Imaging of hemoglobin oxygen saturation variations in single vessels in vivo using photoacoustic microscopy,” Appl. Phys. Lett. 90, 053901 (2007).
[Crossref]

M. Sivaramakrishnan, K. Maslov, H. F. Zhang, G. Stoica, and L. V. Wang, “Limitations of quantitative photoacoustic measurements of blood oxygenation in small vessels,” Phys. Med. Biol. 52, 1349–1361 (2007).
[Crossref] [PubMed]

H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging,” Nat. Biotechnol. 24, 848–851 (2006).
[Crossref] [PubMed]

Y. Wang, X. Xie, X. Wang, G. Ku, K. L. Gill, D. P. O’Neal, G. Stoica, and L. V. Wang, “Photoacoustic tomography of a nanoshell contrast agent in the in vivo rat brain,” Nano Lett. 4, 1689–1692 (2004).
[Crossref]

X. Wang, G. Ku, M. A. Wegiel, D. J. Bornhop, G. Stoica, and L. V. Wang, “Noninvasive photoacoustic angiography of animal brains in vivo with near-infrared light and an optical contrast agent,” Opt. Lett. 29,730–732 (2004).
[Crossref] [PubMed]

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol. 21, 803–806 (2003).
[Crossref] [PubMed]

Tittel, F. K.

A. A. Oraevsky, S. L. Jacques, R. O. Esenaliev, and F. K. Tittel, “Laser based optoacoustic imaging in biological tissues,” Proc. SPIE 2134A, 122–128 (1994).

Wang, C-R. C.

Wang, L. V.

G. F. Lungfu, M. Li, X. Xie, L. V. Wang, and G. Stoica, “In vivo imaging and characterization of hypoxia-induced neovascularization and tumor invasion,” Int. J. Oncology 30, 45–54 (2007).

M. Sivaramakrishnan, K. Maslov, H. F. Zhang, G. Stoica, and L. V. Wang, “Limitations of quantitative photoacoustic measurements of blood oxygenation in small vessels,” Phys. Med. Biol. 52, 1349–1361 (2007).
[Crossref] [PubMed]

H. F. Zhang, K. Maslov, M. Sivaramakrishnan, G. Stoica, and L. V. Wang, “Imaging of hemoglobin oxygen saturation variations in single vessels in vivo using photoacoustic microscopy,” Appl. Phys. Lett. 90, 053901 (2007).
[Crossref]

K. Maslov, H. F. Zhang, and L. V. Wang, “Effects of wavelength-dependent fluence attenuation on the noninvasive photoacoustic imaging of hemoglobin oxygen saturation in subcutaneous vasculature in vivo,” Inverse Probl. 23, S113–S122 (2007).
[Crossref]

M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77, 041101 (2006).
[Crossref]

H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging,” Nat. Biotechnol. 24, 848–851 (2006).
[Crossref] [PubMed]

X. Wang, X. Xie, G. Ku, and L. V. Wang, “Noninvasive imaging of hemoglobin concentration and oxygenation in the rat brain using high-resolution photoacoustic tomography,” J. Biomed. Opt. 11, 024015 (2006).
[Crossref] [PubMed]

Y. Wang, X. Xie, X. Wang, G. Ku, K. L. Gill, D. P. O’Neal, G. Stoica, and L. V. Wang, “Photoacoustic tomography of a nanoshell contrast agent in the in vivo rat brain,” Nano Lett. 4, 1689–1692 (2004).
[Crossref]

X. Wang, G. Ku, M. A. Wegiel, D. J. Bornhop, G. Stoica, and L. V. Wang, “Noninvasive photoacoustic angiography of animal brains in vivo with near-infrared light and an optical contrast agent,” Opt. Lett. 29,730–732 (2004).
[Crossref] [PubMed]

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol. 21, 803–806 (2003).
[Crossref] [PubMed]

Wang, X.

X. Wang, D. L. Chamberland, and D. A. Jamadar, “Noninvasive photoacoustic tomography of human peripheral joints toward diagnosis of inflammatory arthritis,” Opt. Lett. 32, 3002–3004 (2007).
[Crossref] [PubMed]

X. Wang, X. Xie, G. Ku, and L. V. Wang, “Noninvasive imaging of hemoglobin concentration and oxygenation in the rat brain using high-resolution photoacoustic tomography,” J. Biomed. Opt. 11, 024015 (2006).
[Crossref] [PubMed]

X. Wang, G. Ku, M. A. Wegiel, D. J. Bornhop, G. Stoica, and L. V. Wang, “Noninvasive photoacoustic angiography of animal brains in vivo with near-infrared light and an optical contrast agent,” Opt. Lett. 29,730–732 (2004).
[Crossref] [PubMed]

Y. Wang, X. Xie, X. Wang, G. Ku, K. L. Gill, D. P. O’Neal, G. Stoica, and L. V. Wang, “Photoacoustic tomography of a nanoshell contrast agent in the in vivo rat brain,” Nano Lett. 4, 1689–1692 (2004).
[Crossref]

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol. 21, 803–806 (2003).
[Crossref] [PubMed]

Wang, Y.

Y. Wang, X. Xie, X. Wang, G. Ku, K. L. Gill, D. P. O’Neal, G. Stoica, and L. V. Wang, “Photoacoustic tomography of a nanoshell contrast agent in the in vivo rat brain,” Nano Lett. 4, 1689–1692 (2004).
[Crossref]

Wegiel, M. A.

Wei, C-W.

Wu, Y-N.

Xiang, L.

Y. Lao, Da Xing, S. Yang, and L. Xiang, “Noninvasive photoacoustic imaging of the developing vasculature during early tumor growth,” Phys. Med. Biol. 53, 4203–4212 (2008).
[Crossref] [PubMed]

L. Xiang, Da. Xing, H. Gu, D. Yang, S. Yang, L. Zeng, and W. R. Chen, “Real-time optoacoustic monitoring of vascular damage during photodynamic therapy treatment of tumor,” J. Biomed. Opt. 12, 014001 (2007)
[Crossref] [PubMed]

D. Yang, Da. Xing, S. Yang, and L. Xiang, “Fast full view photoacoustic imaging by combined scanning with a linear transducer array,” Opt. Express 15, 15566–15575 (2007).
[Crossref] [PubMed]

S. Yang, Da. Xing, Q. Zhou, L. Xiang, and Y. Lao, “Functional imaging of cerebrovascular in small animals using high resolution photoacoustic tomography,” Med. Phys. 34, 3294–3301 (2007).
[Crossref] [PubMed]

Xie, X.

G. F. Lungfu, M. Li, X. Xie, L. V. Wang, and G. Stoica, “In vivo imaging and characterization of hypoxia-induced neovascularization and tumor invasion,” Int. J. Oncology 30, 45–54 (2007).

X. Wang, X. Xie, G. Ku, and L. V. Wang, “Noninvasive imaging of hemoglobin concentration and oxygenation in the rat brain using high-resolution photoacoustic tomography,” J. Biomed. Opt. 11, 024015 (2006).
[Crossref] [PubMed]

Y. Wang, X. Xie, X. Wang, G. Ku, K. L. Gill, D. P. O’Neal, G. Stoica, and L. V. Wang, “Photoacoustic tomography of a nanoshell contrast agent in the in vivo rat brain,” Nano Lett. 4, 1689–1692 (2004).
[Crossref]

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol. 21, 803–806 (2003).
[Crossref] [PubMed]

Xing, Da

Y. Lao, Da Xing, S. Yang, and L. Xiang, “Noninvasive photoacoustic imaging of the developing vasculature during early tumor growth,” Phys. Med. Biol. 53, 4203–4212 (2008).
[Crossref] [PubMed]

Xing, Da.

L. Xiang, Da. Xing, H. Gu, D. Yang, S. Yang, L. Zeng, and W. R. Chen, “Real-time optoacoustic monitoring of vascular damage during photodynamic therapy treatment of tumor,” J. Biomed. Opt. 12, 014001 (2007)
[Crossref] [PubMed]

D. Yang, Da. Xing, S. Yang, and L. Xiang, “Fast full view photoacoustic imaging by combined scanning with a linear transducer array,” Opt. Express 15, 15566–15575 (2007).
[Crossref] [PubMed]

S. Yang, Da. Xing, Q. Zhou, L. Xiang, and Y. Lao, “Functional imaging of cerebrovascular in small animals using high resolution photoacoustic tomography,” Med. Phys. 34, 3294–3301 (2007).
[Crossref] [PubMed]

Xu, M.

M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77, 041101 (2006).
[Crossref]

Yang, D.

D. Yang, Da. Xing, S. Yang, and L. Xiang, “Fast full view photoacoustic imaging by combined scanning with a linear transducer array,” Opt. Express 15, 15566–15575 (2007).
[Crossref] [PubMed]

L. Xiang, Da. Xing, H. Gu, D. Yang, S. Yang, L. Zeng, and W. R. Chen, “Real-time optoacoustic monitoring of vascular damage during photodynamic therapy treatment of tumor,” J. Biomed. Opt. 12, 014001 (2007)
[Crossref] [PubMed]

Yang, S.

Y. Lao, Da Xing, S. Yang, and L. Xiang, “Noninvasive photoacoustic imaging of the developing vasculature during early tumor growth,” Phys. Med. Biol. 53, 4203–4212 (2008).
[Crossref] [PubMed]

L. Xiang, Da. Xing, H. Gu, D. Yang, S. Yang, L. Zeng, and W. R. Chen, “Real-time optoacoustic monitoring of vascular damage during photodynamic therapy treatment of tumor,” J. Biomed. Opt. 12, 014001 (2007)
[Crossref] [PubMed]

D. Yang, Da. Xing, S. Yang, and L. Xiang, “Fast full view photoacoustic imaging by combined scanning with a linear transducer array,” Opt. Express 15, 15566–15575 (2007).
[Crossref] [PubMed]

S. Yang, Da. Xing, Q. Zhou, L. Xiang, and Y. Lao, “Functional imaging of cerebrovascular in small animals using high resolution photoacoustic tomography,” Med. Phys. 34, 3294–3301 (2007).
[Crossref] [PubMed]

Zeng, L.

L. Xiang, Da. Xing, H. Gu, D. Yang, S. Yang, L. Zeng, and W. R. Chen, “Real-time optoacoustic monitoring of vascular damage during photodynamic therapy treatment of tumor,” J. Biomed. Opt. 12, 014001 (2007)
[Crossref] [PubMed]

Zhang, H. F.

M. Sivaramakrishnan, K. Maslov, H. F. Zhang, G. Stoica, and L. V. Wang, “Limitations of quantitative photoacoustic measurements of blood oxygenation in small vessels,” Phys. Med. Biol. 52, 1349–1361 (2007).
[Crossref] [PubMed]

H. F. Zhang, K. Maslov, M. Sivaramakrishnan, G. Stoica, and L. V. Wang, “Imaging of hemoglobin oxygen saturation variations in single vessels in vivo using photoacoustic microscopy,” Appl. Phys. Lett. 90, 053901 (2007).
[Crossref]

K. Maslov, H. F. Zhang, and L. V. Wang, “Effects of wavelength-dependent fluence attenuation on the noninvasive photoacoustic imaging of hemoglobin oxygen saturation in subcutaneous vasculature in vivo,” Inverse Probl. 23, S113–S122 (2007).
[Crossref]

H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging,” Nat. Biotechnol. 24, 848–851 (2006).
[Crossref] [PubMed]

Zhao, Z.

Z. Zhao and R. Myllylä, “Scattering photoacoustic study of weakly-absorbing substances in aqueous suspensions,” J. Phys. IV France 137, 385–390 (2006).
[Crossref]

Z. Zhao and R. Myllylä, “The effects of optical scattering on pulsed photoacoustic measurement in weakly absorbing liquids,” Meas. Sci. Technol. 12, 2172–2177 (2001).
[Crossref]

Zhou, Q.

S. Yang, Da. Xing, Q. Zhou, L. Xiang, and Y. Lao, “Functional imaging of cerebrovascular in small animals using high resolution photoacoustic tomography,” Med. Phys. 34, 3294–3301 (2007).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

H. F. Zhang, K. Maslov, M. Sivaramakrishnan, G. Stoica, and L. V. Wang, “Imaging of hemoglobin oxygen saturation variations in single vessels in vivo using photoacoustic microscopy,” Appl. Phys. Lett. 90, 053901 (2007).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

S. Marengo, C. Pépin, T. Goulet, and D. Houde, “Time-gated transillumination of objects in highly scattering media using a subpicosecond optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 5, 895–901 (1999).
[Crossref]

R. G. M. Kolkman, E. Hondebrink, W. Steenbergen, and F. F. M. de Mul, “In vivo photoacoustic imaging of blood vessels using an extreme-narrow aperture sensor,” IEEE J. Sel. Top. Quantum Electron. 9, 343–346 (2003).
[Crossref]

Int. J. Oncology (1)

G. F. Lungfu, M. Li, X. Xie, L. V. Wang, and G. Stoica, “In vivo imaging and characterization of hypoxia-induced neovascularization and tumor invasion,” Int. J. Oncology 30, 45–54 (2007).

Inverse Probl. (1)

K. Maslov, H. F. Zhang, and L. V. Wang, “Effects of wavelength-dependent fluence attenuation on the noninvasive photoacoustic imaging of hemoglobin oxygen saturation in subcutaneous vasculature in vivo,” Inverse Probl. 23, S113–S122 (2007).
[Crossref]

J. Biomed. Opt. (2)

L. Xiang, Da. Xing, H. Gu, D. Yang, S. Yang, L. Zeng, and W. R. Chen, “Real-time optoacoustic monitoring of vascular damage during photodynamic therapy treatment of tumor,” J. Biomed. Opt. 12, 014001 (2007)
[Crossref] [PubMed]

X. Wang, X. Xie, G. Ku, and L. V. Wang, “Noninvasive imaging of hemoglobin concentration and oxygenation in the rat brain using high-resolution photoacoustic tomography,” J. Biomed. Opt. 11, 024015 (2006).
[Crossref] [PubMed]

J. Phys. IV France (1)

Z. Zhao and R. Myllylä, “Scattering photoacoustic study of weakly-absorbing substances in aqueous suspensions,” J. Phys. IV France 137, 385–390 (2006).
[Crossref]

Meas. Sci. Technol. (1)

Z. Zhao and R. Myllylä, “The effects of optical scattering on pulsed photoacoustic measurement in weakly absorbing liquids,” Meas. Sci. Technol. 12, 2172–2177 (2001).
[Crossref]

Med. Phys. (2)

R. A. Kruger, P. Liu, Y. R. Fang, and C. R. Appledorn, “Photoacoustic ultrasound (PAUS) - Reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[Crossref] [PubMed]

S. Yang, Da. Xing, Q. Zhou, L. Xiang, and Y. Lao, “Functional imaging of cerebrovascular in small animals using high resolution photoacoustic tomography,” Med. Phys. 34, 3294–3301 (2007).
[Crossref] [PubMed]

Mol. Imaging (1)

R. A. Kruger, W. L. Kiser, D. R. Reinecke, G. A. Kruger, and K. D. Miller, “Thermoacoustic molecular imaging of small animals,” Mol. Imaging 2, 113–123 (2003).
[Crossref] [PubMed]

Nano Lett. (1)

Y. Wang, X. Xie, X. Wang, G. Ku, K. L. Gill, D. P. O’Neal, G. Stoica, and L. V. Wang, “Photoacoustic tomography of a nanoshell contrast agent in the in vivo rat brain,” Nano Lett. 4, 1689–1692 (2004).
[Crossref]

Nat. Biotechnol. (2)

X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Noninvasive laser-induced photoacoustic tomography for structural and functional in vivo imaging of the brain,” Nat. Biotechnol. 21, 803–806 (2003).
[Crossref] [PubMed]

H. F. Zhang, K. Maslov, G. Stoica, and L. V. Wang, “Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging,” Nat. Biotechnol. 24, 848–851 (2006).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (4)

Phys. Med. Biol. (3)

M. Sivaramakrishnan, K. Maslov, H. F. Zhang, G. Stoica, and L. V. Wang, “Limitations of quantitative photoacoustic measurements of blood oxygenation in small vessels,” Phys. Med. Biol. 52, 1349–1361 (2007).
[Crossref] [PubMed]

J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52, 141–168 (2007).
[Crossref]

Y. Lao, Da Xing, S. Yang, and L. Xiang, “Noninvasive photoacoustic imaging of the developing vasculature during early tumor growth,” Phys. Med. Biol. 53, 4203–4212 (2008).
[Crossref] [PubMed]

Proc. SPIE (3)

B. Liu, D. Reinecke, R. A. Kruger, and K. M. Stantz, “Phantom and in vivo measurements of hemoglobin concentration and oxygen saturation using PCT-S small animal scanner,” Proc. SPIE 6437, 64371X1–64371X9 (2007).

K. M. Stantz, B. Liu, M. Cao, D. Reinecke, K. Miller, and R. Kruger, “Photoacoustic spectroscopic imaging of intra-tumor heterogeneity and molecular identification,” Proc. SPIE 6086, 608605 (2006).
[Crossref]

A. A. Oraevsky, S. L. Jacques, R. O. Esenaliev, and F. K. Tittel, “Laser based optoacoustic imaging in biological tissues,” Proc. SPIE 2134A, 122–128 (1994).

Rev. Sci. Instrum. (1)

M. Xu and L. V. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum. 77, 041101 (2006).
[Crossref]

Other (1)

S. A. Prahl, “Optical absorption of hemoglobin,” http://omlc.ogi.edu/spectra/hemoglobin/.

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Figures (6)

Fig. 1.
Fig. 1. Schematic of the experimental setup for SPAT measurement of tissue optical absorption spectrum. NDF: neutral density filter.
Fig. 2.
Fig. 2. Optical absorption spectrum of the contrast agent (IR dye FHI90011S) measured by SPAT.
Fig. 3.
Fig. 3. Typical photoacoustic signal measured from the vessel. Inset shows the typical photodiode signal of the laser pulse.
Fig. 4.
Fig. 4. Optical absorption spectra of an oxygenated (circle) and a deoxygenated (square) canine blood specimens obtained with the SPAT system in comparison with the references (solid curves). The blood oxygen saturation (SO2) were 1.00 for the oxygenated blood specimen and 0.33 for the deoxygenated blood specimen.
Fig. 5.
Fig. 5. Photoacoustic spectra of an oxygenated (circle) and a deoxygenated (square) canine blood specimens embedded in a scattering medium made from diluted whole milk. The blood oxygen saturation (SO2) were 0.97 for the oxygenated blood specimen and 0.10 for the deoxygenated blood specimen. (a) and (c) are the PA spectra before compensation and (b) and (d) are the PA spectra after compensation by introducing the optical contrast agent. Solid curves represent the references.
Fig. 6.
Fig. 6. Photoacoustic spectra of an oxygenated (circle) and a deoxygenated (square) canine blood specimens embedded 3-mm deep in a chicken breast tissue. The blood oxygen saturation (SO2) were 0.98 for the oxygenated blood specimen and 0.27 for the deoxygenated blood specimen. (a) and (c) are the PA spectra before compensation and (b) and (d) are the PA spectra after compensation by introducing the optical contrast agent. Solid curves represent the references.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

P 1 ( λ ) = ( λ ) C T ϕ ( λ ) ,
ε ( λ ) = ε HbO 2 ( λ ) S O 2 + ε Hb ( λ ) ( 1 S O 2 ) .
P 2 ( λ ) = ( λ ) C T ϕ ( λ ) + K ε dye C dye ( λ ) ϕ ( λ ) ,
ϕ ( λ ) = P 2 ( λ ) P 1 ( λ ) K ε dye ( λ ) C dye .
ε ( λ ) = P 1 ε dye ( λ ) C dye C T [ P 2 ( λ ) P 1 ( λ ) ] .
ε ( λ ) = Q ( λ ) C dye C T ,
ε HbO 2 ( λ 1 ) S O 2 + ε Hb ( λ 1 ) ( 1 S O 2 ) = Q ( λ 1 ) C dye C T ,
nd ε HbO 2 ( λ 2 ) S O 2 + ε Hb ( λ 2 ) ( 1 S O 2 ) = Q ( λ 2 ) C dye C T .
S O 2 = Q ( λ 2 ) ε Hb ( λ 1 ) Q ( λ 1 ) ε HbO 2 ( λ 2 ) Q ( λ 1 ) [ ε HbO 2 ( λ 2 ) ε Hb ( λ 2 ) ] Q ( λ 2 ) [ ε HbO 2 ( λ 1 ) ε Hb ( λ 1 ) ] .
ε HbO 2 ( λ ) C HbO 2 + ε Hb ( λ ) C Hb = Q ( λ ) C dye .

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