Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
  • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
  • G01N21/47—Scattering, i.e. diffuse reflection
  • G01N21/4795—Scattering, i.e. diffuse reflection spatially resolved investigating of object in scattering medium

Definitions

• the present invention relates to a method for calculating an optical path distribution inside a scattering medium. More specifically, the time-resolved optical path distribution inside the scattering medium that can be applied to a device that moves the light incident position and the light detection position along the surface of the measurement target to obtain information inside the measurement target is described. It concerns the calculation method.
• the internal information measurement methods such as optical CT disclosed in the above-mentioned references (1) to (12) and the weighting functions applied to them include the following problems, and therefore, the measurement accuracy is low. And a big problem has arisen in usability. In fact, practical examples of optical CT having sufficient performance in the above fields have not been reported yet. That is, the first problem in the conventional optical CT and the like is that the analysis of the photon movement in the medium or the model of the photon movement is based on the light diffusion equation that applies diffusion approximation to the transport equation.
• the diffusion approximation is valid only for a medium large enough for the average free optical path length of photons in the medium, so that a relatively small medium, a complex internal structure, and a medium with a complicated shape are used There is a problem that it cannot be handled. Also, since the diffusion approximation is based on isotropic scattering, when applied to the measurement of a measurement target such as a biological tissue having anisotropic scattering characteristics, the anisotropic scattering is approximated by isotropic scattering. There is also a problem that a non-negligible error occurs due to the above.
• differential equations such as diffusion equations can be solved by setting boundary conditions (such as the shape of the medium or reflection characteristics at the interface) in advance, using any numerical calculation method such as the analytical or finite element method.
• boundary conditions such as the shape of the medium or reflection characteristics at the interface
• any numerical calculation method such as the analytical or finite element method.
• the second problem is that when calculating the internal information of the object to be measured, a weight function in a narrow sense (also called a contribution function), that is, a set of photons that constitute the impulse response of the medium It is that the average optical path length (weighted average) or the equivalent phase delay (measurement in the frequency domain) is applied.
• the weight function in a narrow sense (average optical path length or its equivalent phase delay) changes depending on the absorption coefficient and the absorption distribution, so that the handling becomes extremely complicated.
• the dependence on the absorption coefficient and the absorption distribution is usually neglected, but such an approximation causes a serious problem that the error increases.
• the measurement object is obtained by using the relationship between the signal light and the optical characteristics of the scattering medium.
• the handling of nonlinear effects (second and higher order terms) becomes extremely complicated.
• the calculation including the second-order and higher-order terms can be theoretically performed by a computer, but the calculation time is enormous even with the current fastest computer, and Is impossible. For this reason, terms of second and higher order are usually ignored. Therefore, this method has a problem that a large error occurs due to the interaction between the absorption regions when reconstructing an optical CT image of a medium having a plurality of relatively strong absorption regions. I was
• the present inventor has promoted a series of studies in order to overcome the above situation, considering that the following is important.
• it is important to realize a measurement method that obtains internal information of the measurement object, especially optical CT, which clarifies the details of the behavior of light moving through living tissue, which is a strong scattering medium, and detects it.
• the relationship between the signal light and the optical characteristics of the scattering medium containing the absorption component (scattering absorber) is described more strictly, and the signal light is used, and the light is used by utilizing the relationship between the signal light and the optical characteristics of the scattering medium. It means developing a new algorithm for reconstructing CT images.
• MBL Microscopic Beer-Lambert Law
• the present inventor proposes a photon propagation model (finite lattice model) corresponding to the scattering medium based on the MBL, and derives an analytical expression representing the relationship between the optical characteristics of the scattering medium and the signal light.
• a photon propagation model finite lattice model
• the present inventors describe these results in, for example, the following documents.
• Tsuchiya "Average value method: A new approach to practical optical computed tomography for a turbid medium such as human tissue", Jpn. J. Appl. Phvs.37, Parti.5A, pp.2717-2723 (1998); (19) Hiroshi Tsuchiya; "Reconstruction of optical CT image based on micro 'Veil'Lambert's rule and average method", 0 plus E, Vol. 21, No. 7, 814-821; (20) H. Zhang, M. Miwa, Y. Yamashita, and Y.
• Tsuchiya “Quantitation of absorbers in turbid media using time-integrated spectroscopy based on microscopic Beer -La mbert law ", Jpn. J. Ap. Phys. 37, Parti, pp. 2724-2727 (1998); (21) H. Zhang, Y. Tsuchiya, T. Urakami, M. Miwa, and Y. Yamashita: "Time integrated spectroscopy of turbid media based on the microscopic Beer-Lambert law: Consideration of the wavelength dependence of scattering properties", Optics Commun. 153, pp.314-322 (1998); (22) Y. Tsuchiya, H. Zhang , T. Urakami, M.
• This MBL states that, when viewed microscopically in a medium with an arbitrary scattering absorption distribution, photons propagating in the part where the absorption coefficient is a are exponentially formed by absorption along the propagating zigzag optical path of length 1. And the photon's survival rate becomes a value exp ( -a l) irrespective of the scattering characteristics and boundary conditions of the medium, and the attenuation due to absorption is / a l ''. For example, it is expressed by the following equation.
• f (l) is the probability density function of the photon actually measured, and f ° (l) is when there is no absorption Is a detection probability density function.
• Equation (1) states that in a medium having an arbitrary scattering and absorption distribution, absorption and scattering are independent phenomena, and that the principle of superposition with respect to absorption is valid. This shows that in the case of a multi-component system, the total absorbance is given by the sum of the absorbances of the respective components.
• the present inventors derive an equation representing the relationship between various optical responses and optical characteristics of the scattering medium from the MB expressed by the above equation (1), and show that the various responses of the scattering medium depend on absorption. It was clarified that terms can be described separately from terms that do not depend on absorption. Therefore, if this attenuation term is spectroscopically measured using multi-wavelength light, the absolute value of the concentration of the absorption component in the scattering medium can be calculated from the relationship between the absorption coefficient and the absorption coefficient specific to the absorption component. Quantification is now possible.
• the above-mentioned measurement method based on MBL has a great feature in principle that it is not affected by the medium shape, boundary conditions, and scattering, and can be applied to anisotropic scattering media and small media.
• the absorption coefficient and the concentration of the absorption component measured here can be measured correctly for a scattering medium with uniform absorption
• the measurement for a non-uniform medium with non-uniform absorption distribution indicates It is the average absorption coefficient and average concentration (weighted average for the optical path distribution). Therefore, in order to realize high-precision optical CT, it became necessary to know the optical path distribution.
• the present inventors have further developed a method of analyzing the behavior of light in a scattering medium based on MBL, and applied the method to a non-uniform scattering medium (heterogeneous system) in which scattering and absorption are unevenly distributed.
• various measurement methods have been developed to quantitatively measure the concentration distribution of the absorption component in the scattering medium without being affected by the shape and scattering characteristics of the medium.
• Specific measurement methods derived by the present inventors based on MBL so far include, for example, time-resolved measurement (TRS) using impulse response, and time integration measurement (TIS) using time integration of impulse response.
• Time-resolved gate integration measurement using time gate integration of impulse response
• phase modulation measurement in the frequency domain PMS
• optical CT image reconstruction based on the average method AFM
• the conventional CT weighting method still uses the conventional weight function, that is, the average optical path length or its equivalent phase delay.
• the absorption coefficient of voxel i of a virtual medium having a uniform absorption coefficient v described by a finite lattice model is slightly changed, and its light output is calculated by Monte Carlo calculation, path integration (Path Integral), and transport equation.
• the above-mentioned conventional measurement method of obtaining a weight function (or contribution function) corresponding to various measurement methods uses the voxel Since it is necessary to perform the forward problem calculation such as the light diffusion equation for the number of times equal to the total number, the calculation time becomes extremely long, and the measurement time becomes extremely long after all.
• the conventional measurement method using the narrowly defined weight function average optical path length or a corresponding phase delay
• the measurement accuracy is not sufficient.
• the accuracy of the measurement is to be improved, there is a problem that the calculation time is further increased, and as a result, the measurement time is further increased.
• the present invention has been made in view of the above-mentioned conventional problems, and has as its object to provide a method capable of accurately and quickly calculating an optical path distribution inside a heterogeneous scattering absorber such as a living body. And From the optical path distribution calculated in this way, it is possible to quickly calculate a weighting function Wi corresponding to various specific measurement methods for quantitatively measuring the concentration distribution of the absorption component inside the scatterer. it can.
• the inventor of the present invention has eagerly studied the MBL-based analysis method and the like to achieve the above object.As a result, the time resolution in the voxel i of the medium to be measured divided into N (1 ⁇ N) voxels is
• the time-resolved optical path length li in voxel i of this virtual medium can be described by Monte Carlo calculation, or the numerical value of path integral, transport equation, or light diffusion equation It is possible to calculate directly and quickly using the result of calculating the photon movement in the virtual medium by calculation. Headings, we have reached the present invention.
• the basic principle of the conventional Monte Carlo calculation is to count the number of occurrences of the scattering event in voxel i in the finite lattice model, and this concept is applied to the conventional weight function. .
• the optical path length can be estimated from the relationship between the number of scatterings and the mean free optical path length.
• the time-resolved optical path length which is the object of the present invention, cannot be determined accurately. Therefore, in order to avoid such a conventional problem, the present invention uses a new method of calculating the time-resolved optical path length li in voxel i from the photon existence probability in voxel i of the medium.
• a light incident position where the impulse light is incident on the surface of the virtual medium, and an impulse response s (t) at time t of the impulse light incident from the light incident position and propagated in the virtual medium are detected.
• a third step of setting the light detection position
• the photon set constituting the impulse response s (t) detected at the time t at the light detection position is the light detection position.
• the absorption coefficient of voxel i of the virtual medium described in the finite lattice model is slightly changed, and various weighting functions are calculated from the calculated values of the ratio of the output light intensity before and after the absorption coefficient change or the difference in attenuation.
• I was calculating Wi.
• it is necessary to perform the forward problem calculation such as the light diffusion equation the number of times equal to the total number N of voxels, so the calculation time is long, and the measurement time is extremely long. Solves this problem.
• the parameters of all voxels are calculated in parallel for a pair of a light incident position and a detection position, so that the calculation time can be further reduced.
• the method for calculating the optical path distribution inside the scattering medium of the present invention has been found for the first time to directly and accurately calculate the time-resolved optical path length l i.
• a set of photons with an optical path length of 1 that constitutes the impulse response s (t) is a photon that exists in voxel i at time t '(0 ⁇ t' ⁇ t) before being detected at the light detection position.
• Ui (t ', t) can be calculated by calculating two forward problems as shown in equation (2.2).
• Upi (t ') can be calculated by inputting impulse light from the light incident position P of the finite lattice model.
• Uqi (t-1 ') can also be calculated by inputting impulse light from the light detection position q of the finite lattice model.
• Eq. (2.2) The specific calculation method for the two forward problems represented by Eq. (2.2) will be described later in detail.
• the weighted average Li of the time-resolved optical path length li with respect to time can be quickly calculated using this. Can be.
• the specific calculation method of the time-resolved optical path length li was not known, so the time-resolved optical path length li was first determined, and then the weighted average Li and the weight of the time-resolved optical path length li were calculated. There was no idea to calculate the function Wi. In fact, no example of a measurement method that directly calculates and uses the time-resolved optical path length li has been reported so far. Further, in the present invention, since the time-resolved optical path length li of voxel i can be calculated quickly and directly, it can be used for various predetermined measurements for quantitatively measuring the concentration distribution of the absorption component inside the medium to be measured.
• the weight function Wi corresponding to the specific measurement method can be calculated quickly.
• the specific measurement methods such as TRS, TIS, TGS, PMS, and AVM based on MBL are used.
• TRS, TIS, TGS, PMS, and AVM based on MBL are used.
• the relationship between the time-resolved optical path length li in voxel i in the medium to be measured and the measurement values measured by various measurement methods and the corresponding weight functions has already been clarified by the present inventors. I have.
• the weighting function for attenuation is equal to the time-resolved optical path length li in TRS, the time-resolved optical path length li in TIS is weighted average Li (also called average optical path length Li) or time-resolved It is described using the dispersion of the optical path length li.
• the time-resolved optical path length li in voxeli in the medium to be measured the average optical path length Li that is a weighted average thereof, and the time-resolved
• Wi a weight function Wi described using the relationship between the variance of the optical path length li and the like, and it is known that these are expressed by Eqs. I have.
• the “time-resolved optical path distribution” in the method for calculating the optical path distribution inside the scattering medium according to the present invention means, as shown in FIG. 1, that a three-dimensional measurement medium is divided into N (1 ⁇ N) voxel
• the optical path distribution of a set of photons where the optical path length of B is 1 is shown.
• this time-resolved optical path distribution is a function of optical path length 1, that is, a function of time t.
• the amount of attenuation of the output optical signal in various specific measurement methods is expressed as a function of the product of the time-resolved optical path length li and the absorption coefficient of voxel i.
• the weighted average Li of this time-resolved optical path length li with respect to time is called the average optical path length of voxel i, and the N-dimensional vector [Li] whose elements are called the average optical path length distribution.
• each “voxel20” in FIGS. 1 and 2 is used.
• “voxel i” is used instead of “voxel20”.
• the weight function is defined as the contribution of the absorption information to the physical quantity of interest.
• TRS time integration
• the determinant for image reconstruction in optical CT is described as the product of matrices, that is, [weighting function] ⁇ [absorption coefficient difference]. Difference], that is, the absorption distribution can be calculated.
• the scattering characteristics between the medium to be measured and the virtual medium described above may be non-uniform.
• Concrete calculations of the forward problem include Monte Carlo calculation, Path Integral ⁇ ⁇ numerical calculation of the transport equation, Numerical calculations of the light diffusion equation can be used.
• the “predetermined measurement method” to which the time-resolved optical path length li obtained by the method for calculating the optical path distribution inside the scattering medium of the present invention is not particularly limited. Is based on MBL derived time-resolved measurement (TRS), time-integrated measurement (TIS;), time-resolved gate integral measurement (TGS), and phase modulation measurement (PMS) in the frequency domain.
• An internal measurement method of the scattering medium such as an optical CT image reconstruction method (AVM), or a measurement method that is not based on MBL as described in the literatures (1) to (12) may be used.
• a second step that assumes
• a light incident position where the impulse light is incident on the surface of the virtual medium, and an impulse response s (t) at a time t of the impulse light incident from the light incident position and propagated in the virtual medium are detected.
• a third step of setting the light detection position
• the photon set constituting the impulse response s (t) detected at the time t at the light detection position is the light detection position.
• the photon set constituting the impulse response s (t) detected at the time t at the light detection position is the light detection position.
• the time-resolved optical path length li of voxel i can be calculated quickly and directly, so that the weighted average Li of the time-resolved optical path length li with respect to time can be quickly calculated using this.
• various specific measurement methods for quantitatively measuring the concentration distribution of the absorbing component inside the medium to be measured using this can be used.
• the weight function Wi corresponding to the method can be calculated quickly.
• FIG. 1 is a schematic diagram showing a finite lattice model for analyzing internal photon movement of a medium to be measured.
• FIG. 2 shows a set of photons that form the impulse response B detected at the time t at the light detection position q when the impulse light A is incident from the light incidence position p in the finite lattice model shown in Fig. 1.
• FIG. 3 is a schematic diagram showing a path of a set of photons passing through voxel i and its probability.
• Figure 3 shows the photon existence probability density U i (t ', t) in voxel i at time t' in the finite grid model shown in Fig. 2, and the photon existence probability density Upi (t 'in voxel i at time t'. 12) is a graph showing an example of a time waveform of the photon existence probability density Uqi (tt ') in voxel i at time and.
• FIG. 4 shows the cumulative photon existence probability U i (t) in voxel i at time 0 ⁇ t' ⁇ t, the photon existence probability density U i (t ', t) in voxel i at time t', and time It is a graph which shows typically the relationship of the photon existence probability density Upq (t ', t) in all voxe 1 in t'.
• FIG. 5 is a flowchart showing an embodiment of a method for calculating an optical path distribution inside a scattering medium according to the present invention.
• FIG. 6 is a flowchart showing a second embodiment of the optical path distribution calculation method inside the scattering medium according to the present invention.
• the analysis method developed by the present inventors based on MBL to analyze the behavior of light in a scattering medium is based on a non-uniform scattering medium in which scattering and absorption are unevenly distributed (non-uniform scattering medium).
• System The analysis method based on MBL allows the various optical responses (light output) of the inhomogeneous scattering medium to be described separately as attenuation terms that depend on absorption and terms that do not depend on absorption. It is deduced that the term can be described by the optical path distribution and the absorption distribution in the measured medium.
• optical CT for quantifying the concentration distribution of the absorption component in the medium to be measured becomes possible.
• the following points (i) to (V) are satisfied in the finite lattice model of the medium to be measured and the virtual medium corresponding thereto.
• the assumption that the refractive index distribution in the medium to be measured is uniform is that when a nonuniform scattering absorber such as a living body is selected as the medium to be measured, the main component of the living body is water. For this reason, the refractive index distribution may be regarded as uniform. Therefore, in the following description, a medium to be measured having a uniform refractive index distribution is considered unless otherwise specified.
• the above optical path distribution is a function of time and is independent of the number of incident photons (that is, photon density), absorption or absorption distribution of the medium to be measured, and the optical path assuming that the medium to be measured has no absorption. Equal to the distribution.
• This time-resolved optical path distribution [li] has the same scattering characteristics (may be non-uniform) and boundary conditions as the medium to be measured, but has a uniform absorption and no absorption. Can be virtually calculated.
• Figure 1 shows a finite lattice model for analyzing the internal photon movement of the non-uniform scattering absorber that is the medium to be measured.
• the finite lattice model 10 shown in FIG. 1 shows the medium to be measured and has the same shape, scattering distribution, and boundary conditions with respect to the medium to be measured, and has a uniform refractive index distribution and absorption.
• impulse response B when the absorption coefficient of the medium represented by the finite lattice model 10 in FIGS. 1 and 2 is zero, “impulse response B” is replaced by “impulse response s (t;)”. In other words, the response may be described as a response when there is no absorption.
• the impulse response B is described as the impulse response h (t), that is, the response when there is absorption. There is.
• the size and shape of the voxel i of the finite grid model 10 of the virtual medium shown in Fig. 1 are such that the absorption distribution in the voxel i of the corresponding measured medium can be regarded as uniform or uniform.
• the size and shape of voxel i also determines the total number of all voxels. That is, the size, shape, and total number of all voxel i of the virtual medium are arbitrary as long as the absorption in voxel i can be considered to be uniform as described above.
• the size and shape of the actual voxel i are determined according to the measurement methods used or the CT image resolution required for those measurement methods.
• the light of the finite lattice model 10 is Consider a set of photons whose optical path length is 1 in the impulse response B measured at the detection position q, that is, h (t).
• the photon incident position p and the photon detection position q are arbitrary.
• the optical path distribution of voxel i in the finite lattice model 10 is represented by an N-dimensional vector [li] with the time-resolved optical path length li in voxel i as an element.
• the time-resolved optical path length li in voxel i is the average of the optical path lengths of these individual photons in voxel i (the collective average ).
• the time-resolved optical path distribution [li] of the set of photons composing the impulse response h (t) of the medium to be measured is irrelevant to the absorption of the medium to be measured. It is equal to the time-resolved optical path distribution [li] of the set of photons that make up the impulse response s (t) of the virtual medium.
• the time-resolved set of photons that make up the impulse response h (t) of the medium to be measured is obtained.
• Type optical path distribution [li] can be obtained.
• the relationship between the amount of attenuation and the optical path length in the medium to be measured, which is a non-uniform scattering medium, will be described. Since absorption and scattering are independent, it is sufficient to assume here that the virtual medium 10 shown in FIG. 1 has the same absorption distribution as the medium to be measured. However, other conditions are the same as those of the finite lattice model 10 of the medium to be measured.
• the relationship between the optical path length 1 and the optical path length distribution li is expressed by the following equation based on the findings (i) to (V) described above and the MBL.
• ⁇ ai is the absorption coefficient of voxel i
• s (t) is the impulse response of the virtual medium detected at the detection position q of the virtual medium assuming that the measured medium has no absorption
• h (t) is the The impulse response of the medium to be measured detected at the output position q is shown.
• the last side (right side) of Eq. (5) is derived from the fact that the time-resolved optical path length li does not depend on absorption or absorption distribution.
• Equations (4) and (5) show the impulse response h (t) expressed by equation (3) in differential and integral forms, respectively. From equation (5), the impulse response h (t) of the inhomogeneous scattering medium is described separately as a term Ins (t) that does not depend on absorption and an attenuation term that depends on absorption expressed by the following equation (16). We can see that we can do it.
• the attenuation ln [h (t) / s (t)] of this optical response is expressed by the time-resolved optical path distribution [li] and the absorption distribution [ ⁇ ai ] in the medium to be measured. It turns out that it can be described.
• the time-resolved optical path distribution in the medium to be measured is expressed in the virtual medium, It should be noted that this is equivalent to the time-resolved optical path distribution when there is none. Therefore, in time-resolved measurement (TRS), the weighting function for the amount of attenuation is equal to the time-resolved optical path length distribution [li], and optical CT image reconstruction using this relationship becomes possible.
• the image reconstruction algorithm is the simplest.
• TIS using the time integral of the impulse response h (t), TGS using the integral of the impulse response h (t) within a predetermined time range, and sine wave modulated light are used.
• AVM which gives a virtual medium a uniform absorption as a reference and measures a deviation from the reference value.
• the attenuation or attenuation deviation can be described separately as an attenuation term that depends on absorption and a term that does not depend on absorption.
• the deviation can be described by the time-resolved optical path distribution and the absorption distribution in the medium to be measured, and the attenuation function or the weight function for the attenuation deviation can be obtained from this relationship.
• the weighting function for the attenuation or attenuation deviation at 13 ⁇ 1 ⁇ 3 can be described by the average optical path length, the phase delay, and their higher-order partial derivatives.
• the optical response in the case of T IS corresponds to the time integration of the impulse response h (t) described above, and can be expressed as the following equation.
• Li is the average optical path length Li of voxeli of the photon set constituting the time integral I detected at the detection position, that is, the weighted average ⁇ 10 of the time-resolved optical path length li. Show. ]
• This average optical path length (weighted average of the time-resolved optical path length li) Li depends on the scattering characteristics of the scatterer, the boundary conditions, and the absorption and absorption distribution. At this time, it should be noted that the integral of the second term on the right side of Eq. (8) cannot be expressed as a product as in Eq. (5). Therefore, the weighting function for the amount of attenuation depends not only on the average path length Li, but also on the absorption, which complicates the optical CT reconstruction algorithm.
• AVM measurement that gives a uniform absorption as a reference to a virtual medium and measures the medium to be measured as a deviation from the reference value.
• the attenuation difference between the measured medium and the virtual medium in voxel i (attenuation deviation) ⁇ is expressed as follows using the absorption coefficient difference (absorption coefficient deviation) and the weight function Wi.
• Wi Li ( ⁇ ⁇ ) + - ⁇ ⁇ ! '+
• Bi ( ai ) indicates the attenuation for each voxel i with respect to the time integral I of the impulse response h (t) of the measured medium
• ⁇ Bi ( ⁇ ai ) represents the attenuation deviation of Bi ( ⁇ ai ) with respect to Bi (/ J,
• Li (z v ) is the average optical path length of voxel i of the virtual medium when the absorption coefficient is ⁇ (the average optical path length with respect to time integral I. , / Ai
• Wi is a weighting function for the attenuation deviation ABi ( ai ), and is expressed as a function of the absorption coefficient deviation Aai and the first and higher-order partial derivatives (L, L ', LV ").]
• the first and higher order partial derivatives can be directly calculated from the time-resolved waveform obtained for the virtual medium.
• TIS time-resolved integration method
• TGS phase modulation method
• the absorption coefficient of voxel i of the measured medium is // ai
• the impulse response h (t) of the finite lattice model 10 of the virtual medium shown in FIG. 1 is expressed by the following equation by substituting // ai2 0 into equation (3).
• the impulse response s (t) of the virtual medium detected at the light detection position q is the value of the measured medium detected at the light detection position q assuming that the measured medium has no absorption. It is equal to the impulse response h (t).
• FIG. 2 shows that, in a virtual medium described by the finite lattice model 10 shown in FIG.
• the photon existence probability density Ui (t ', t) in voxel i at time t' described by introducing the new time variable t 'described above is obtained by applying the reciprocity principle (reciprocity theorem) as follows. It can be expressed like an expression.
• the principle of reciprocity is approximately established for the incidence of collimated light and the incidence of pencil beam, but when the reciprocity principle is applied more strictly, light called isotropic light incidence is used.
• an incident method is used.
• This is an isotropic light incidence method In this case, the principle of reciprocity is more accurately established.
• this isotropic light incidence method is a light incidence method that has been reported by the inventor. For example, Japanese Patent Application No. 5-301979, Y. Tsuchiya, K. Ohta, and T. Urakami: Jpn.J Appl. Phys. 34, Part 1, ⁇ ⁇ 2495-2501 (1995).
• Upi (t,) and Uqi (tt,) expressed by the above equation (2.2) are simply referred to as “photon existence probability density Upi (t ′) in voxel i at time t ′. ) j, "Photon existence probability density Uqi (t-t ';) in voxel i at time t-t'".
• Figure 3 shows the photon existence probability density Ui (t ', t) in voxeli at time t' in the finite lattice model 10 expressed by Eq. (2.2) above, and voxel i in time t '.
• 7 is a graph showing an example of the photon existence probability density Upi (t ';) of the photon existence probability density Uqi (t-1';) in voxeli at time t-t '.
• Ui (t ', t) can be calculated by calculating the two forward problems shown in Eq. (2.2).
• Upi (t,) can be calculated by inputting impulse light A from the light incident position p of the finite lattice model 10.
• Uqi (t ⁇ t ′) can also be calculated by inputting impulse light A from the light detection position q of the finite lattice model 10.
• Monte Carlo calculation, path integral (Path Integral), numerical calculation of transport equation, numerical calculation of light diffusion equation, etc. can be used.
• the calculation algorithm is simpler and the calculation time is shorter than the conventional problem calculation in the case of the conventional absorption.
• Ui (t) expressed by the above equation (2.3) represents the impulse response s (t), and represents the cumulative probability of photon existence in voxel i of a set of photons having an optical path length of 1. In the description of, it is simply described as "the cumulative photon existence probability Ui (t) in voxel i at time O ⁇ t ' ⁇ t".
• the photon existence cumulative probability U (t) is expressed as the impulse response s (detected at time t at the light detection position q when the impulse light A is incident from the light incident position p into the finite lattice model 10: t), the photon set whose optical path length is 1 propagates through the finite lattice model 10 from the light incident position p to the light detection position q in the finite lattice model 1 during the time O ⁇ t ' ⁇ t. Indicates the cumulative probability that exists in 0 (in all voxel).
• the photon existence probability density Ui (t ', t) in voxel i at time t' is 1
• FIG. 4 shows the cumulative photon existence probability U: (t) in voxel i at time 0 ⁇ t' ⁇ t, the photon existence probability density Ui (t ', t) in voxeli at time t', and Time t '
• Fig. 4 schematically shows the relationship between the photon existence probability densities Upq (t ', t) in all voxels at.
• reference numeral 30 in FIG. 4 indicates a photon.
• the photon set forming the impulse response s (t) detected at the time t at the light detection position q is Li (t ', t) is the time-resolved optical path length in voxeli at any time t', and the photon existence probability in voxel i at time t ' It is proportional to the density Ui (t ', t).
• the time-resolved optical path length li (t), which is the time integral of li (t ', t) is also proportional to the photon existence cumulative probability Ui (t), which is the time integral of Ui (t', t).
• the set of photons constituting the impulse response s (t) detected at the time t at the light detection position q is If we consider a set of photons whose optical path length is 1, the optical path length 1 is proportional to the photon existence cumulative probability U (t).
• Such a time-resolved optical path length li is directly used for image reconstruction of the time-resolved optical CT using the time-resolved response. That is, the weight function in the time-resolved optical CT is equal to the time-resolved optical path length ⁇ .
• the time-resolved optical path length li is a basic quantity for describing a weight function in various measurement methods.
• FIG. 5 is a flowchart showing an embodiment of a method for calculating an optical path distribution inside a scattering medium according to the present invention. It is one chart. Hereinafter, the flowchart shown in FIG. 5 will be described.
• the medium to be measured which is a scattering medium, is divided into N (1 ⁇ N) voxels having a predetermined size and a uniform absorption distribution (S1). .
• the shape, boundary conditions, and scattering distribution are the same as the medium to be measured, the refractive index distribution is uniform, and it can be considered that there is no absorption. Assume a virtual medium (S2).
• the light detection position q to be detected is set (S3).
• the impulse light A is made to enter the virtual medium from the light incident position p, and the impulse response s (t) detected at the light detection position is calculated (S4).
• the set of photons with an optical path length of 1 that constitutes the impulse response s (t) detected at the point of time voxel i at time t '(0 ⁇ f ⁇ t) before being detected at the light detection position Calculate the photon existence probability density U i (t ', t) existing in (S 5).
• the photon existence probability densities of all voxels constituting the finite lattice model 10 can be calculated in parallel or simultaneously for one light incident position. This eliminates the time-consuming conventional calculation of changing the absorption coefficient of each voxel and repeating the forward problem a number of times equal to the total number N of voxels, which is time-consuming. Is shortened.
• the photon set constituting the impulse response s (t) detected at the time t at the photodetection position q from the photon existence probability density Ui (t ', t) is voxel i Calculate the cumulative photon existence probability Ui (t) existing in (S6).
• the time-resolved optical path length li of voxel i is calculated using the photon existence cumulative probability Ui (t) and the impulse response s (t) according to the equation (2.13) (S8).
• the method for calculating the optical path distribution inside the scattering medium of the present invention has the same scattering characteristics and boundary conditions as the medium to be measured, but assumes that there is no absorption. Since the forward problem shown in Eq. (2.2) is solved for the virtual medium obtained, the calculation time is shorter than the conventional problem calculation with absorption. Furthermore, the time-consuming conventional title calculation of repeatedly solving the forward problem by the number of times equal to the total number of voxels by changing the absorption coefficient of each voxel becomes unnecessary, and the time-resolved optical path length li in voxel i is directly and Can be calculated quickly.
• a method of directly calculating a weight function Wi corresponding to a predetermined measurement method from the time-resolved optical path length li calculated for each arbitrary voxel i of the virtual medium There is a method of calculating a weighted average Li for the time of the time-resolved optical path length li calculated for each time, and calculating a weighting function Wi corresponding to a predetermined measurement method using the weighted average Li.
• the time-resolved optical path length li was first determined, and then the time-resolved optical path length li was calculated. While there was no idea to calculate the weighted average Li and weighting function Wi of li, this method of calculating the weighting function quickly calculated the time-resolved optical path length li of voxel i. It can be directly calculated, so that it can be used for various specific measurement methods for quantitatively measuring the weighted average Li of the time-resolved optical path length li or the concentration distribution of the absorption component inside the medium to be measured. The corresponding weight function Wi can be calculated quickly. A specific calculation method of the weight function corresponding to the optical CT using various optical responses using the time-resolved optical path length li calculated for each arbitrary voxel i of the virtual medium will be described later.
• FIG. 6 is a flowchart showing a second embodiment of the method for calculating the optical path distribution inside the scattering medium according to the present invention.
• the flowchart shown in FIG. 6 will be described.
• the medium to be measured which is a scattering medium
• the shape, boundary conditions, and scattering distribution are the same as the medium to be measured, the refractive index distribution is uniform, and it can be considered that there is no absorption. Assume a virtual medium (S2).
• the light detection position q to be detected is set (S3).
• the photon existence probability densities of all the voxels constituting the finite lattice model 10 can be calculated in parallel or simultaneously for one light incident position. For this reason, the conventional time-consuming calculation of changing the absorption coefficient of each voxel and repeatedly solving the forward problem as many times as the total number N of voxels is unnecessary, and the calculation time is significantly reduced.
• the photon set constituting the impulse response s (t) detected at the time t at the photodetection position q from the photon existence probability density Ui (t ', t) is voxel i Calculate the cumulative photon existence probability Ui (t) existing in (S6).
• the time-resolved optical path length li of voxel i is calculated by using the photon existence cumulative probability Ui (t) and the sum U (t) of all the voxels according to (2.13) (S11) ).
• the method of calculating the optical path distribution inside the scattering medium of the present invention is the same as that of the medium to be measured. Since the forward problem shown in Eq. (2.2) is solved for a virtual medium that has the scattering characteristics and boundary conditions but has no absorption, the total problem is calculated as compared to the conventional problem calculation with absorption. It can be seen that the calculation time is shortened.
• the flowchart shown in FIG. In the later stage it corresponds to a predetermined measurement method for quantitatively measuring the concentration distribution of the absorption component inside the measured medium using the time-resolved optical path length li calculated for each arbitrary voxel i of the virtual medium Is calculated.
• a method of calculating a weighted average Li of the time-resolved optical path length li calculated with respect to time and calculating a weighting function Wi corresponding to a predetermined measurement method using the weighted average Li is a method of directly calculating the weighting function Wi corresponding to a predetermined measurement method from the time-resolved optical path length li calculated for each voxel i of the virtual medium, and first, for each voxel i of the virtual medium.
• This method of calculating the weight function can quickly and directly calculate the time-resolved optical path length li of voxel i, and use this to calculate the weighted average Li of the time-resolved optical path length li or the inside of the medium to be measured. It is possible to quickly calculate the weighting function Wi corresponding to the predetermined various specific measurement methods for quantitatively measuring the concentration distribution of the absorption component in.
• the method of calculating the optical path distribution inside the scattering medium according to the present invention can be applied to optical CT using various optical responses.
• the time-resolved optical path length ⁇ ⁇ calculated for each voxel i of the virtual medium is used to calculate the concentration of the absorption component inside the measured medium.
• a weight function Wi corresponding to a predetermined measurement method for quantitatively measuring the cloth is calculated.
• TIS time integration measurement
• TGS time-resolved gate integration measurement
• PMS phase modulation measurement in the frequency domain
• TIS average method
• the optical path distribution inside the scattering medium of the present invention is applied to an optical CT using an optical response such as time integration measurement (TIS), time-resolved gate integration measurement (TGS), and phase modulation measurement (PMS) in the frequency domain.
• TIS time integration measurement
• TGS time-resolved gate integration measurement
• PMS phase modulation measurement
• a weight function described using the average optical path length Li and optical path length dispersion of voxel i for the impulse response h (t) is used.
• the weight function Wi is defined as a weight function for a reference medium having a uniform absorption distribution.
• the model considered at this time is one in which the absorption coefficient of voxel i of the virtual medium described by the finite lattice model 10 shown in FIG. 1 is // ai .
• the time integral I of the impulse response h (t) is given by the following equation.
• s (t) indicates the impulse response h (t) detected at the detection position assuming that the medium to be measured does not absorb
• Li indicates the average optical path length at voxel i (the weighted average of the time-resolved optical path length li at voxel i) of the set of photons constituting the time integral I detected at the detection position.
• 1 n I is described separately as a term that is not related to absorption and a term (attenuation) that depends on the absorption coefficient ⁇ ai of each voxel.
• the average optical path length Li of voxel i is an amount that depends on the scattering characteristics of the scatterer, the boundary conditions, and the absorption-absorption distribution, and is given by the following equation.
• the weight function Wi used for the corresponding optical CT is defined for a virtual medium having a uniform absorption coefficient // and is given by the following equation. Model in this case is obtained by the absorption coefficient of voxel i of the model shown in FIG. 1 and ⁇ v.
• ⁇ v is shows the constant absorption coefficient given to the virtual media
• a ⁇ ai denotes the absorption coefficient deviation / i ai for ⁇ les
• Li (/ V ) indicates the average optical path length in voxel i of a virtual medium having a constant absorption coefficient ⁇ v (weighted average of time-resolved optical path length li in voxel i),
• L (/ v ) indicates the average optical path length of the impulse response h (t) of the virtual medium given a fixed absorption coefficient /// (weighted average of the optical path length 1 in the virtual medium given the absorption coefficient v ) ), Wi is previously described (9)
• Ri weight function der for attenuation amount deviation ABi ( ⁇ ai) in the formula, the absorption coefficient deviation a ai and the primary and higher-order partial differential coefficients (L, L ' , LV ”) function expressed.
• the first and higher order partial derivatives can be calculated directly from the time-resolved waveform obtained for the virtual medium.
• the time-resolved gate integral signal Ig of the impulse response h (t) of a scattering medium in which absorption is unevenly distributed is given by the following equation.
• L gi is the average optical path length at voxel i of the set of photons that make up the time gate integral I g of the impulse response h (t) (weighted average of the time-resolved optical path length li within the gate time of voxel i) Is shown. ]
• the time range of the gate integration is [tl, t2]. If this is set to [0, ⁇ ], the time integration signal I of the impulse response h (t) obtained in the previous section is obtained.
• the weighting function Wgi used for the corresponding light CT is defined for a virtual medium having a uniform absorption coefficient // and is given by the following equation.
• ⁇ ai indicates the deviation of the absorption coefficient of // ai , as shown in the above equation (4.4).
• Lgi ( ⁇ ) is the average path length at voxel i of the set of photons constituting the time gate integral Ig of the impulse response h (t) of the virtual medium (weighting of the time-resolved path length li within the gate time of voxel i). Average
• Lg ( v ) is the average optical path length (weighted average) of a set of photons constituting the time gate integral Ig of the impulse response h (t) of the virtual medium given a certain absorption coefficient ⁇ .
• Wi is a weight function for the attenuation amount deviation ABgi (/ ai) when previously described (9) damping amount deviation ABi the ( ⁇ ai) was applied to the TGS, the absorption coefficient deviation A / ai and primary and partial derivatives of higher order (Lg, Lg ', L g ", ⁇ ) is expressed by a function of.]
• the response obtained by PMS for a scattering medium with non-uniform absorption distribution is a Fourier transform of the impulse response h (t) for the scattering medium with non-uniform absorption distribution, and is given by the following equation.
• R and X denote the real part and the imaginary part, respectively, and A and ⁇ denote the amplitude and the phase delay, respectively.
• R, X, A and 0 can be easily measured with a lock-in amplifier or the like. Also, where ( ⁇ ⁇ '9) " « i
• the forward problem is solved for a virtual medium that has the same scattering characteristics and boundary conditions as the medium to be measured, but assumes no absorption, and v xel i Since the time-resolved optical path length li can be calculated directly and quickly, the calculation time is shorter than in the conventional problem calculation with absorption. Furthermore, the time-consuming conventional forward problem calculation of changing the absorption coefficient of each voxel and solving the forward problem by the number of times equal to the total number of voxels is unnecessary. Therefore, it is possible to provide a method capable of quickly calculating the optical path distribution inside a heterogeneous scattering absorber such as a living body.

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