CN107411716B - Method for measuring optical parameters of turbid medium based on incomplete P3 approximate forward model - Google Patents
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Abstract
The invention discloses a method for measuring optical parameters of turbid media based on a incomplete P3 approximate forward model, which mainly comprises the following steps: establishing an approximate forward model of the incomplete P3 of the radiance, and developing an analytical algorithm based on the inverse of the optical parameters of the approximate forward model of the incomplete P3 so as to obtain the absorption coefficient and the reduced scattering coefficient of the turbid medium to be detected. The developed defect P3 is more compact in expression compared to the conventional P3 and describes the propagation of light in large absorbing or small scattering tissues more accurately than the diffusion approximation. The developed incomplete P3-based analytical reconstruction algorithm can more accurately reconstruct the optical parameters of the turbid medium with large absorption or small scattering compared with the traditional fitting algorithm based on P3approximation and the analytical reconstruction algorithm based on diffusion approximation. The resolving speed of the analytic deconstruction algorithm is high, and the method is expected to be applied to optical parameter online monitoring. The measurement method provided by the invention does not need to measure the intensity of a light source used by an experimental system, and is beneficial to practical application.
Description
Technical Field
The invention belongs to the field of optical parameter measurement in tissue optical research, and particularly relates to a defect P3 approximate forward model and an analytic inversion algorithm developed based on the forward model to obtain optical parameters, absorption coefficients and reduced scattering coefficients of turbid media (tissue bodies).
Background
Optical parameter measurements are of great interest in the field of biomedical photonics. In particular in laser therapy, in vivo optical parameter measurements can be used to calculate the light flux for the purpose of on-line optimization of the light dose [1, 2 ]. Steady state measurement techniques are commonly used for optical parameter measurements of turbid media (tissue volumes) due to simple equipment and low cost [3-5 ]. Although surface diffuse reflectance measurements allow non-invasive optical parameter measurements of tissues such as skin, the technique cannot be used for the detection of internal organs such as the prostate due to low optical penetration depth [3 ]. The detection of the internal organs needs to be achieved by means of minimally invasive measurements. The methods currently used are the spatially resolved photon density measurement method and the diffuse reflectance spectral measurement method [4, 5 ]. The photon density measurement method needs to absolutely correct the light intensity of a light source and a detector of the system through an integrating sphere, and is not favorable for clinical application [6 ]. In addition, diffuse reflectance measurement is generally performed by using a probe formed by coupling a plurality of optical fibers to measure diffuse reflectance at a plurality of Source Detector Separation (SDS), and measurement data at a limited source detection distance limits accuracy of optical parameter reconstruction [7 ].
The steady state radiance technology measures the light intensity in different directions under the fixed SDS, and provides a new degree of freedom for measuring optical parameters. The technology only needs the measurement data of the angular radiance under one to two SDS, reduces the damage to the tissue caused by the translation of the detector in the interstitial measurement process, and gradually develops into a new minimally invasive measurement technology [6, 8, 9 ]]. At present, there are two main algorithms for reconstructing optical parameters by using radiance measurement data: fitting algorithm based on P3approximation and analytic expression solving method [6, 9, 10 ] based on Diffusion Approximation (DA)]. Wherein, the fitting algorithm can only back out the transmission albedo a ═ mu's/(μa+μ′s) Optical parameter greater than 0.9, where μaAnd mu'sAbsorption coefficient and reduced scattering coefficient, respectively. This is due to the lack of solution uniqueness of the radiance shape based fitting algorithm in solving the optical parameters, i.e., a series of optical parameter pairs (μ)a,μ′s) Lower radiance of the same shape [9 ]]. In addition, although the DA approximation based analytical expression method avoids the non-uniqueness of the solution in the fitting algorithm, the method is only applicable if the DA approximation condition is satisfied, i.e., high a' [6]]. While in interstitial laser treatment, cases with a' as low as 0.5 are encountered [9]. There is a need to develop a forward model that is more accurate than DA, and to be able to develop a reverse model based on this forward modelAnd (4) a structural analysis algorithm, namely solving the optical parameters of the turbid medium (tissue body) through an analytical expression.
[ reference documents ]
1.G.Shafirstein,D.Bellnier,E.Oakley,S.Hamilton,M.Potasek,K.Beeson,andE.Parilov,“Interstitial Photodynamic Therapy-A Focused Review,”Cancers 9(2),12(2017)。
2.V.K.Nagarajan and B.Yu,“Monitoring of tissue optical propertiesduring thermal coagulation of ex vivo tissues,”Lasers Sur.Med.48(7),686–694(2016)。
3.S.-Y.Tzeng,J.-Y.Guo,C.-C.Yang,C.-K.Hsu,H.-J.Huang,S.-J.Chou,C.-H.Hwang,and S.-H.Tseng,“Portable handheld diffuse reflectance spectroscopysystem for clinical evaluation of skin:a pilot study in psoriasis patients,”Biomed.Opt.Express 7(2),616–628(2016)。
4.T.C.Zhu,J.C.Finlay,and S.M.Hahn,“Determination of the distributionof light,optical properties,drug concentration,and tissue oxygenation in-vivoin human prostate during motexafin lutetium-mediated photodynamic therapy,”J.Photoch.Photobio.B 79(3),231–241(2005)。
5.T.M.Baran,M.C.Fenn,T.H.Foster,“Determination of optical propertiesby interstitial white light spectroscopy using a custom fiber optic probe,”J.Biomed.Opt.18(10),107007(2013)。
6.S.Grabtchak and W.M.Whelan,“Separation of absorption and scatteringproperties of turbid media using relative spectrally resolved cw radiancemeasurements,”Biomed.Opt.Express 3(10),2371–2380(2012)。
7.T.M.Baran,J.D.Wilson,S.Mitra,J.L.Yao,E.M.Messing,D.L.Waldman,andT.H.Foster,“Optical property measurements establish the feasibility ofphotodynamic therapy as a minimally invasive intervention for tumors of thekidney,”J.Biomed.Opt.17(9),0980021(2012)。
8.D.J.Dickey,R.B.Moore,D.C.Rayner,and J.Tulip,“Light dosimetry usingthe P3 approximation,”Phys.Med.Biol.46(9),2359(2001)。
9.L.C.L.Chin,A.E.Worthington,W.M.Whelan,and I.A.Vitkin,“Determinationof the optical properties of turbid media using relative interstitialradiance measurements:Monte Carlo study,experimental validation,andsensitivity analysis,”J.Biomed.Opt.12(6),064027(2007)。
10.E.L.Hull and T.H.Foster,“Steady-state reflectance spectroscopy inthe P3 approximation,”J.Opt.Soc.Am.A 18(3),584–599(2001)。
Disclosure of Invention
Aiming at the requirement of interstitial measurement on the optical parameters of turbid media (tissue bodies), the invention provides an optical parameter analysis solving method based on a incomplete P3 approximate forward model.
In order to solve the technical problem, the invention provides a method for measuring the optical parameters of a turbid medium based on a defect P3 approximate forward model, which comprises the following steps:
step one, establishing an approximation forward model of the incomplete P3 of the radiance, wherein the expression is as follows:
in the formula (1), r is a source detection distance, theta is an angle of a detection direction relative to a radial direction vector, and S0Is the intensity of the light source, Pl(cos θ) is Legendre polynomial, Ql(-vr) is a modified second-type spherical Bessel function, the expression of which is given in recursive form as follows:
v in the formula (1) is a progressive attenuation coefficient, and the expression is as follows:
in formula (3), ξ ═ 27 μaμ′s+28μaσ3+35σ2σ3，ζ＝3780μaμ′sσ2σ3(ii) a Wherein, muaTo absorption coefficient,. mu.sAs scattering coefficient, σlFor absorption coefficient of order l, define σl＝μa+μs(1-gl) L is 2,3, wherein g is an anisotropy factor, μ's＝μa+μs(1-g) is reduced scattering coefficient;
h in formula (1)l(v), l ═ 0.., 3, is:
c' in formula (1) is:
in the formula (5), v+For instantaneous attenuation coefficient, define
Step two, developing an optical parameter analysis and reconstruction algorithm based on the incomplete P3 approximate forward model, thereby obtaining the absorption coefficient mu of the detected turbid mediumaAnd reduced scattering coefficient mu'sThe method comprises the following steps:
step 2-1, firstly, determining two source detection distances r and r 'and four angles theta corresponding to the two source detection distances r and r' respectivelyiI-0, 3, and then four angles θ at two source probe distances r and r' are measured, respectivelyi0, emissivity at 3: l ism(r,θi)，Lm(r′,θi)；
Step 2-2, solving S in the formula (1) by using the formula (6)0C′hl(ν)Ql(-νr),l＝0,1,2，
The right side of formula (6) is abbreviated as fl(r,θ0,θ1,θ2,θ3) Where l is 0,1,2, formula (6), αi(r,θ0,θ1,θ2)、αi(r,θ0,θ1,θ3)、βij(θ0,θ1,θ2) And βij(θ0,θ1,θ3) Comprises the following steps:
step 2-3, solving a gradual attenuation coefficient v:
construction of f0(r,θ0,θ1,θ2,θ3) And f0(r′,θ0,θ1,θ2,θ3) The ratio of:
q in formula (8)0(-νr′)＝(-νr′)-1exp (-vr'), solving formula (8) to obtain a gradual attenuation coefficient v as:
step 2-4, solving h1(v) and h2(ν)：
Construction of fl(r,θ0,θ1,θ2,θ3) L is 1,2 and f0(r,θ0,θ1,θ2,θ3) The ratio of:
h is obtained by the formula (10)1(v) and h2(v) is:
step 2-5, obtaining the absorption coefficient mu of the turbid medium to be detected according to the formula (4)aAnd reduced scattering coefficient mu's：
Compared with the prior art, the invention has the beneficial effects that:
(1) the incomplete P3approximation forward model established in the present invention can describe the propagation of light in large absorbing or small scattering tissues more accurately than the conventional diffusion approximation forward model. Compared with the traditional P3 approximate forward model, the expression is more concise, and the analytical expression for constructing the reverse optical parameters is used.
(2) Compared with the traditional fitting algorithm based on the P3 approximate forward model and the analytic reconstruction algorithm based on the diffusion approximate forward model, the optical parameter analytic reconstruction algorithm based on the incomplete P3 approximate forward model can more accurately reconstruct the optical parameters of the turbid medium with large absorption or small scattering.
(3) The traditional fitting algorithm needs a large amount of experimental data to carry out fitting to solve the optical parameters, while the inverse configuration algorithm only needs 8 radiance measurement values, needs few experimental measurement values and is expected to be designed into a fiber probe for measuring the optical parameters of turbid media (tissue bodies).
(4) The invention can reverse the optical parameters of turbid medium (tissue) under single wavelength, so that the same laser can be used for optical parameter measurement and treatment in interstitial laser treatment, and the invention is more beneficial to clinical application.
(5) The analytical reconstruction algorithm provided by the invention directly solves the optical parameters of the turbid medium (tissue body) from the measurement data by using an analytical formula without iterative solution in the traditional fitting algorithm, so that the solving speed is high, and the analytical reconstruction algorithm is expected to be applied to the online monitoring of the optical parameters in interstitial laser treatment.
(6) Compared with absolute measurement, the analytic reconstruction algorithm provided by the invention does not need to measure the light source intensity used by an experimental system, and is more beneficial to clinical application.
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FIG. 1 shows a schematic diagram of two source-probe distances and four angles determined in the measurement method of the present invention.
Detailed Description
The technical solutions of the present invention are further described in detail with reference to the accompanying drawings and specific embodiments, which are only illustrative of the present invention and are not intended to limit the present invention.
Example (b): measured by emissivity Lm(r,θi),Lm(r′,θi) i-0.., 3. the measured medium is μ prepared using indian ink and 20% Intralipida＝0.5mm-1，μ′s＝0.5mm-1For example, where r and r' are selected to be 5mm and 10mm, θ0，θ1，θ2And theta3Selected from 40 °, 80 °, 120 ° and 160 °, the measurement systems used are steady state radiation interstitial measurement device systems, the main structures (see patent application No. 201610822322.3) are: the device comprises a light source module, a detection module, a displacement module and a control module; the light source module comprises a halogen tungsten lamp connected to one end of a light source optical fiber; the other end of the light source optical fiber is provided with an isotropic scattering head which is used for converting the light emitted by the halogen tungsten lamp into a point light source; the detection module comprises a side illumination optical fiber and a spectrometer, wherein one end of the side illumination optical fiber is coupled to the spectrometer, and the other end of the side illumination optical fiber is a detection inclined plane which forms an angle of 45 degrees with the axis of the optical fiber and is used for detecting an incident optical signal vertical to the axis of the optical fiber; the displacement module comprises a manual precision displacement table, an electric translation table and an electric rotating table, a metal upright post is fixed above the electric translation table, the manual precision displacement table is fixed above the metal upright post, and the light source optical fiber is fixed with the manual precision displacement table through a metal fixing tube; the electric rotating platform is fixed on a metal bracket, and the side illumination optical fiber is vertically fixed on the electric rotating platform through a metal fixing pipe; the manual precision displacement table is used for adjusting the height of the light source optical fiber to enable the isotropic scattering head and the probe to be in a same-directionThe inclinometer is kept at the same horizontal height; the electric translation stage is used for moving the light source optical fiber in the horizontal direction; the electric rotating platform is used for rotating the side illumination optical fiber and determining the orientation of the detection inclined plane so as to change the photon receiving direction; the control module comprises a stepping motor control box and an upper computer; on one hand, the upper computer sends an instruction to the stepping motor control box so as to control the motion of the electric translation table and the electric rotation table; in another aspect, for controlling a spectrometer to detect an optical signal.
The process of measuring the optical parameters of the measured medium in the embodiment by using the method of the invention is as follows:
step one, establishing a incomplete P3 approximate forward model of radiance:
p3 is used to describe approximately the radiance measurement [10 ] under point source excitation in an infinite medium]. Due to the complexity of the P3 approximate expression, an analytical expression of the reconstructed optical parameters cannot be constructed. The invention provides a incomplete P3(incomplete P3 adaptation) with a simpler expression, which is abbreviated as P3inThe forward model. P3inThe asymptotic decay solution portion for the P3approximation is expressed as follows:
in the formula (1), r is a source detection distance, theta is an angle of a detection direction relative to a radial direction vector, and S0Is the intensity of the light source, Pl(cos θ) is Legendre polynomial, Ql(-vr) is a modified second-type spherical Bessel function, the expression of which is given in recursive form as follows:
v in the formula (1) is a progressive attenuation coefficient, and the expression is as follows:
in formula (3), ξ ═ 27μaμ′s+28μaσ3+35σ2σ3，ζ＝3780μaμ′sσ2σ3(ii) a Wherein, muaTo absorption coefficient,. mu.sAs scattering coefficient, σlFor absorption coefficient of order l, define σl＝μa+μs(1-gl) L is 2,3, wherein g is an anisotropy factor, μ's＝μa+μs(1-g) is reduced scattering coefficient;
h in formula (1)l(v), l ═ 0.., 3, is:
c' in formula (1) is:
in the formula (5), v+For instantaneous attenuation coefficient, define
Step two, developing an optical parameter analysis and reconstruction algorithm based on the incomplete P3 approximate forward model, thereby obtaining the absorption coefficient mu of the detected turbid mediumaAnd reduced scattering coefficient mu'sThe method comprises the following steps:
step 2-1, firstly determining two source detection distances of r '5 mm and r' 10mm and corresponding theta0＝40°、θ1＝80°、θ2120 ° and θ3Four angles of 160 deg., as shown in fig. 1, and then four angles theta at two source probe distances r and r' are measured, respectivelyi0, emissivity at 3: l ism(r,θi)，Lm(r′,θi)；
Step 2-2, solving the problem that the formula (1) contains v, h by using the formula (6)1(v) and h2(v) S0C′hl(ν)Ql(-νr),l＝0,1,2，
The right side of formula (6) is abbreviated as fl(r,θ0,θ1,θ2,θ3) Where l is 0,1,2, formula (6), αi(r,θ0,θ1,θ2)、αi(r,θ0,θ1,θ3)、βij(θ0,θ1,θ2) And βij(θ0,θ1,θ3) Comprises the following steps:
step 2-3, solving a gradual attenuation coefficient v:
for solving v while avoiding absolute measurements, i.e. eliminating the light intensity S0Construction of f0(r,θ0,θ1,θ2,θ3) And f0(r′,θ0,θ1,θ2,θ3) The ratio of:
q in formula (8)0(-νr′)＝(-νr′)-1exp (-vr'), solving formula (8) to obtain a gradual attenuation coefficient v as:
step 2-4, solving h1(v) and h2(ν)：
To solve for h1(v) and h2(v), construction fl(r,θ0,θ1,θ2,θ3) L is 1,2 and f0(r,θ0,θ1,θ2,θ3) The ratio of:
formula (9) has found v, thus Ql(-vr) (l ═ 0,1,2) is known, and h is obtained by substituting the formula (10)1(v) and h2(v) is:
step 2-5, obtaining the absorption coefficient mu of the turbid medium to be detected according to the formula (4)aAnd reduced scattering coefficient mu's：
Finally, the inverse structure result of the absorption coefficient and the reduced scattering coefficient of the liquid phantom is obtained as follows: mu.sa＝0.4852mm-1，μ′s＝0.5096mm-1The relative error is: 2.96% and 1.92%.
While the present invention has been described with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments, which are illustrative only and not restrictive, and various modifications which do not depart from the spirit of the present invention and which are intended to be covered by the claims of the present invention may be made by those skilled in the art.
Claims (1)
1. A method for measuring optical parameters of a turbid medium based on an approximate forward model of the defect P3, comprising the following steps:
step one, establishing an approximation forward model of the incomplete P3 of the radiance, wherein the expression is as follows:
in the formula (1), r is a source detection distance, theta is an angle of a detection direction relative to a radial direction vector, and S0Is the intensity of the light source, Pl(cos θ) is Legendre polynomial，Ql(-vr) is a modified second-type spherical Bessel function, the expression of which is given in recursive form as follows:
v in the formula (1) is a progressive attenuation coefficient, and the expression is as follows:
in formula (3), ξ ═ 27 μaμ′s+28μaσ3+35σ2σ3，ζ＝3780μaμ′sσ2σ3(ii) a Wherein, muaTo absorption coefficient,. mu.sAs scattering coefficient, σlFor absorption coefficient of order l, define σl＝μa+μs(1-gl) L is 2,3, wherein g is an anisotropy factor, μ's＝μa+μs(1-g) is reduced scattering coefficient;
h in formula (1)l(v), l ═ 0.., 3, is:
c' in formula (1) is:
in the formula (5), v+For instantaneous attenuation coefficient, define
Step two, developing an optical parameter analysis and reconstruction algorithm based on the incomplete P3 approximate forward model, thereby obtaining the absorption coefficient mu of the detected turbid mediumaAnd reduced scattering coefficient mu'sStep (b)The method comprises the following steps:
step 2-1, firstly, determining two source detection distances r and r 'and four angles theta corresponding to the two source detection distances r and r' respectivelyiI-0, 3, and then four angles θ at two source probe distances r and r' are measured, respectivelyi0, emissivity at 3: l ism(r,θi)，Lm(r′,θi)；
Step 2-2, solving S in the formula (1) by using the formula (6)0C′hl(ν)Ql(-νr),l＝0,1,2，
The right side of formula (6) is abbreviated as fl(r,θ0,θ1,θ2,θ3) Where l is 0,1,2, formula (6), αi(r,θ0,θ1,θ2)、αi(r,θ0,θ1,θ3)、βij(θ0,θ1,θ2) And βij(θ0,θ1,θ3) Comprises the following steps:
step 2-3, solving a gradual attenuation coefficient v:
construction of f0(r,θ0,θ1,θ2,θ3) And f0(r′,θ0,θ1,θ2,θ3) The ratio of:
q in formula (8)0(-νr′)＝(-νr′)-1exp (-vr'), solving formula (8) to obtain a gradual attenuation coefficient v as:
step 2-4, solving h1(v) and h2(ν)：
Construction of fl(r,θ0,θ1,θ2,θ3) L is 1,2 and f0(r,θ0,θ1,θ2,θ3) The ratio of:
h is obtained by the formula (10)1(v) and h2(v) is:
step 2-5, obtaining the absorption coefficient mu of the turbid medium to be detected according to the formula (4)aAnd reduced scattering coefficient mu's：
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| CN102495027A (en) * | 2011-12-05 | 2012-06-13 | 天津大学 | Method and device for measuring optical parameter of chaotic medium by multi-wavelength space resolution phase lock |
| CN106290199A (en) * | 2016-09-13 | 2017-01-04 | 天津大学 | Multi-wavelength optical parameter trans-construction method based on steady state of radiation rate interstitial measurement apparatus |
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| CN102495027A (en) * | 2011-12-05 | 2012-06-13 | 天津大学 | Method and device for measuring optical parameter of chaotic medium by multi-wavelength space resolution phase lock |
| CN106290199A (en) * | 2016-09-13 | 2017-01-04 | 天津大学 | Multi-wavelength optical parameter trans-construction method based on steady state of radiation rate interstitial measurement apparatus |
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| Title |
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| 基于P3近似的混合漫射近似模型及其实验研究;田会娟;《中国优秀硕士学位论文全文数据库(电子期刊)基础科学辑》;20090115(第12期);全文 * |
| 生物组织漫反射的P3近似模型及其实验研究;高宗慧;《中国优秀硕士学位论文全文数据库(电子期刊)基础科学辑》;20070615(第06期);全文 * |
| 辐射传输方程的三阶球谐展开(P3)近似的有限元法求解;马文娟等;《光子学报》;20110715;第40卷(第7期);全文 * |
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