# 医学光声成像

## 成像系统

### 光声/热声计算机断层扫描（PAT/TAT）

#### 原理

$\nabla^2p(\vec{r},t)-\frac{1}{v_s^2}\frac{\partial^2}{\partial{t^2}}p(\vec{r},t)=-\frac{\beta}{C_p}\frac{\partial}{\partial t}H(\vec{r},t) \qquad \qquad \quad \quad (1)$

$\left.p(\vec{r},t)=\frac{\beta}{4 \pi C_p} \int \frac{d \vec{r'}}{|\vec{r}-\vec{r'}|} \frac{\partial H(\vec{r'},t')}{\partial t'} \right|_{t'=t-|\vec{r}-\vec{r'}|/v_s} \qquad \quad \,\,\,\,(2)$

$p(\vec{r},t)=\frac{1}{4 \pi v_s^2} \frac{\partial}{\partial t} \left [\frac{1}{v_s t} \int d \vec{r'} p_0(\vec{r'}) \delta \left (t-\frac{|\vec{r}-\vec{r'}|}{v_s} \right) \right] \qquad \,(3)$

#### 重构算法

$\left.p_0(\vec{r})=\int_{\Omega_0} \frac{d \Omega_0}{\Omega_0} \left [2 p(\vec{r_0},v_s t) - 2 v_s t \frac{\partial p(\vec{r_0},v_s t)}{\partial (v_s t)} \right]\right|_{t=|\vec{r} - \vec{r_0}|/v_s}\qquad \quad(4)$

$d \Omega_0 = \frac{d S_0}{|\vec{r} - \vec{r_0}|^2} \frac{\hat n_0^s . (\vec{r} - \vec{r_0})}{|\vec{r} - \vec{r_0}|}.$

#### 光声/热声断层扫描的生物医学应用

##### 血流动力学监测[7][9]

$\mu_a(\lambda_1) = \ln(10)\varepsilon_{HbO2}(\lambda_1)C_{HbO2}+\ln(10)\varepsilon_{Hb}(\lambda_1)C_{Hb} \,$
$\mu_a(\lambda_2) = \ln(10)\varepsilon_{HbO2}(\lambda_2)C_{HbO2}+\ln(10)\varepsilon_{Hb}(\lambda_2)C_{Hb} \,$

$SO_2=\frac {C_{HbO2}} {C_{HbO2}+C_{Hb}}$

## 与其他成像手段的比较

Hz mm µm µm Mvx/s

## 参考文献

1. ^ 1.0 1.1 1.2 Zhang, H. F. et al. Functional photoacoustic microscopy for high-resolution and noninvasive in vivo imaging. Nature Biotechnology. 2006, 24 (7): 848–851. doi:10.1038/nbt1220. PMID 16823374.
2. ^ A. Grinvald et al. Functional architecture of cortex revealed by optical imaging of intrinsic signals. Nature. 1986, 324 (6095): 361–364. doi:10.1038/324361a0. PMID 3785405.
3. ^ 3.0 3.1 M. Xu and L.H. Wang. Photoacoustic imaging in biomedicine. Review of Scientific Instruments. 2006, 77 (4): 041101. doi:10.1063/1.2195024.
4. ^ Optical Properties Spectra
5. ^ 5.0 5.1 L.H. Wang and H.I. Wu. Biomedical Optics. Wiley. 2007. ISBN 978-0-471-74304-0.
6. ^ M. Xu et al. Universal back-projection algorithm for photoacoustic-computed tomography. Physical Review E. 2005, 71 (1): 016706. doi:10.1103/PhysRevE.71.016706.
7. ^ 7.0 7.1 7.2 X. Wang, et al. Non-invasive imaging of hemoglobin concentration and oxygenation in the rat brain using high-resolution photoacoustic tomography. Journal of Biomedical Optics. 2006, 11 (2): 024015. doi:10.1117/1.2192804. PMID 16674205.
8. ^ X. Jin, et al. Thermoacoustic tomography with correction for acoustic speed variations. Physics in Medicine and Biology. 2006, 51 (24): 6437–6448. doi:10.1088/0031-9155/51/24/010. PMID 17148827.
9. ^ 9.0 9.1 9.2 9.3 X. Wang, et al. Non-invasive laser-induced photoacoustic tomography for structural and functional imaging of the brain in vivo. Nature Biotechnology. 2003, 21 (7): 803–806. doi:10.1038/nbt839. PMID 12808463.
10. ^ 10.0 10.1 G. Ku, et al. Thermoacoustic and photoacoustic tomography of thick biological tissues toward breast imaging. Technology in Cancer Research and Treatment. 2005, 4 (5): 559–566. PMID 16173826.
11. ^ Zhang, H. F. et al. Imaging of hemoglobin oxygen saturation variations in single vessels in vivo using photoacoustic microscopy. Applied Physics Letters. 2007, 90 (5): 053901. doi:10.1063/1.2435697.