# 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

${\displaystyle \nabla ^{2}p({\vec {r}},t)-{\frac {1}{v_{s}^{2}}}{\frac {\partial ^{2}}{\partial {t^{2}}}}p({\vec {r}},t)=-{\frac {\beta }{C_{p}}}{\frac {\partial }{\partial t}}H({\vec {r}},t)\qquad \qquad \quad \quad (1)}$

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

${\displaystyle p({\vec {r}},t)={\frac {1}{4\pi v_{s}^{2}}}{\frac {\partial }{\partial t}}\left[{\frac {1}{v_{s}t}}\int d{\vec {r'}}p_{0}({\vec {r'}})\delta \left(t-{\frac {|{\vec {r}}-{\vec {r'}}|}{v_{s}}}\right)\right]\qquad \,(3)}$

#### 重构算法

${\displaystyle \left.p_{0}({\vec {r}})=\int _{\Omega _{0}}{\frac {d\Omega _{0}}{\Omega _{0}}}\left[2p({\vec {r_{0}}},v_{s}t)-2v_{s}t{\frac {\partial p({\vec {r_{0}}},v_{s}t)}{\partial (v_{s}t)}}\right]\right|_{t=|{\vec {r}}-{\vec {r_{0}}}|/v_{s}}\qquad \quad (4)}$

${\displaystyle d\Omega _{0}={\frac {dS_{0}}{|{\vec {r}}-{\vec {r_{0}}}|^{2}}}{\frac {{\hat {n}}_{0}^{s}.({\vec {r}}-{\vec {r_{0}}})}{|{\vec {r}}-{\vec {r_{0}}}|}}.}$

#### 光声/热声断层扫描的生物医学应用

##### 血流动力学监测[7][6]

${\displaystyle \mu _{a}(\lambda _{1})=\ln(10)\varepsilon _{HbO2}(\lambda _{1})C_{HbO2}+\ln(10)\varepsilon _{Hb}(\lambda _{1})C_{Hb}\,}$
${\displaystyle \mu _{a}(\lambda _{2})=\ln(10)\varepsilon _{HbO2}(\lambda _{2})C_{HbO2}+\ln(10)\varepsilon _{Hb}(\lambda _{2})C_{Hb}\,}$

${\displaystyle SO_{2}={\frac {C_{HbO2}}{C_{HbO2}+C_{Hb}}}}$

## 与其他成像手段的比较

Hz mm µm µm Mvx/s

## 参考文献

1. ^ A. Grinvald; 等. Functional architecture of cortex revealed by optical imaging of intrinsic signals. Nature. 1986, 324 (6095): 361–364. PMID 3785405. doi:10.1038/324361a0.
2. M. Xu and L.H. Wang. Photoacoustic imaging in biomedicine. Review of Scientific Instruments. 2006, 77 (4): 041101. doi:10.1063/1.2195024.
3. ^ Optical Properties Spectra
4. L.H. Wang and H.I. Wu. Biomedical Optics. Wiley. 2007. ISBN 978-0-471-74304-0.
5. ^ M. Xu; 等. Universal back-projection algorithm for photoacoustic-computed tomography. Physical Review E. 2005, 71 (1): 016706. doi:10.1103/PhysRevE.71.016706.
6. X. Wang; 等. Non-invasive laser-induced photoacoustic tomography for structural and functional imaging of the brain in vivo. Nature Biotechnology. 2003, 21 (7): 803–806. PMID 12808463. doi:10.1038/nbt839.
7. 引用错误：没有为名为XDW_2006的参考文献提供内容
8. ^ G. Ku; 等. Thermoacoustic and photoacoustic tomography of thick biological tissues toward breast imaging. Technology in Cancer Research and Treatment. 2005, 4 (5): 559–566. PMID 16173826.
9. ^ Zhang, H. F.; 等. 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.
10. ^ 引用错误：没有为名为Hao_NatureBio_PAM的参考文献提供内容