Source: http://www.google.de/patents/US7616985
Timestamp: 2013-05-19 05:56:39
Document Index: 55734620

Matched Legal Cases: ['Application No. 60', 'Application No. 60', 'Application No. 60', 'art 1', 'art 1', 'art 2', 'art 1']

Patent US7616985 - Method and apparatus for 3-D imaging of internal light sources - Google PatenteSuche Bilder Maps Play YouTube News Gmail Drive Mehr » Erweiterte Patentsuche | Webprotokoll | Anmelden Erweiterte Patentsuche PatenteThe present invention provides systems and methods for obtaining a three-dimensional (3D) representation of one or more light sources inside a sample, such as a mammal. Mammalian tissue is a turbid medium, meaning that photons are both absorbed and scattered as they propagate through tissue. In the case...http://www.google.de/patents/US7616985?utm_source=gb-gplus-sharePatent US7616985 - Method and apparatus for 3-D imaging of internal light sources Ver�ffentlichungsnummerUS7616985 B2PublikationstypErteilung Anmeldenummer10/606,976 Ver�ffentlichungsdatum10. Nov. 2009Eingetragen25. Juni 2003 Priorit�tsdatum16. Juli 2002Auch ver�ffentlicht unterCN1678900AEP1521959A1EP1521959B1US7603167US7797034US7860549US20040021771US20050201614US20080018899US20100022872US20110090316WO2004008123A1 ErfinderMichael D. CableBradley W. RiceDaniel G. StearnsUrspr�nglich Bevollm�chtigterXenogen Corporation US-Klassifikation600/473600/407600/425600/476600/431250/363.1600/438Internationale KlassifikationA61K49/00A61B6/03A61B6/12 UnternehmensklassifikationG01N21/6456A61K49/0013G01N21/763 Europ�ische KlassifikationA61K49/00P4G01N21/76BG01N21/64P4ReferenzenPatentzitate (105)Nichtpatentzitate (63) Referenziert von (2)Externe LinksUSPTO USPTO-Zuordnung EspacenetMethod and apparatus for 3-D imaging of internal light sourcesUS 7616985 B2 Zusammenfassung The present invention provides systems and methods for obtaining a three-dimensional (3D) representation of one or more light sources inside a sample, such as a mammal. Mammalian tissue is a turbid medium, meaning that photons are both absorbed and scattered as they propagate through tissue. In the case where scattering is large compared with absorption, such as red to near-infrared light passing through tissue, the transport of light within the sample is described by diffusion theory. Using imaging data and computer-implemented photon diffusion models, embodiments of the present invention produce a 3D representation of the light sources inside a sample, such as a 3D location, size, and brightness of such light sources.
1. A method for obtaining a tree-dimensional representation of a light source distribution located inside a mammal, the method comprising:
obtaining a topographical surface representation of the mammal;
providing surface light image data from light emitted from a surface of the mammal originating from the light source distribution located inside the mammal; and
using a processing system, reconstructing a three-dimensional representation of the light source distribution internal to the mammal using the topographical surface representation and the surface light emission data.
2. The method of claim 1 further comprising dividing the topographical surface representation into a set of surface elements.
3. The method of claim 1 wherein the light source is comprised of bioluminescent or fluorescent emission.
4. The method of claim 1 further comprising applying a noise threshold to the surface light image data.
5. The method of claim 1 wherein the light source emits light that passes through mammal tissue.
6. The method of claim 1 wherein the mammal has a complex boundary.
7. The method of claim 1 further comprising producing multiple possible three-dimensional representations of the light source and the three-dimensional representation of the light source obtained is the representation that best fits the measured surface light image data.
8. The method of claim 1 further comprising placing the mammal on a stage included in an imaging chamber coupled to a camera configured to capture an image of the mammal on the stage.
9. The method of claim 2 wherein each surface element is approximated as planar.
10. The method of claim 2 further comprising creating a set of volume elements within the mammal.
11. The method of claim 10 wherein each volume element is modeled to contain a point light source at its center.
12. The method of claim 10 further comprising converting the surface light image data into photon density just inside the surface of the mammal.
13. The method of claim 10 further comprising defining a cost function and a set of constraints for obtaining a solution for the three-dimensional representation of the light source distribution.
14. The method of claim 10 further comprising varying one of a) the number of volume elements, and b) the configuration of volume elements, to produce a set of solutions for the three-dimensional representation of the source distribution.
15. The method of claim 10 further comprising optimizing the three-dimensional representation of the light source distribution by calculating the surface light emission for each solution and selecting a solution which minimizes a difference between a calculated and measured surface emission.
16. The method of claim 10 wherein the transport of light within the mammal from a given volume element to a given surface element is described by a Green's function.
17. The method of claim 11 wherein the three-dimensional representation of the light source distribution is approximated by a set of point light sources.
18. The method of claim 12 wherein there is a linear relation between the light source emission strength in a given volume element and the photon density just inside a surface element.
19. The method of claim 13 wherein the cost function is related to a sum of source strengths for each point source in the mammal, and the constraints include the following conditions: (i) that the source strengths be positive definite and (ii) that the resulting photon density at the object surface produced by the distribution of point sources be everywhere less than the measured surface photon density.
20. The method of claim 13 wherein the cost function and constraints are described mathematically by a system of linear equations, and a solution for the three-dimensional representation of the source distribution is obtained using a SIMPLEX method.
21. The method of claim 13 further comprising including a weighting factor in the cost function that can be varied to produce a set of solutions for the three-dimensional representation of the source distribution.
22. The method of claim 13 further comprising varying the number of surface elements to produce a set of solutions for the three-dimensional representation of the source distribution.
23. The method of claim 19 wherein obtaining the three-dimensional representation maximizes the cost function subject to the constraints.
24. The method of claim 14 wherein the varying the number of volume elements and varying the configuration of volume elements both comprise adaptive meshing.
25. The method of claim 24 wherein the adaptive meshing increases the number of volume elements used to describe the three-dimensional representation of the light source.
26. The method of claim 25 wherein the adaptive meshing removes volume elements having zero light source strength.
27. The method of claim 16 wherein the Green's function is defined as a solution for light diffusion in a homogenous half space having a planar boundary perpendicular to the line connecting the volume element and the surface element.
28. The method of claim 16 wherein the mammal interior is approximated to be inhomogeneous.
29. The method of claim 16 wherein the Green's function is defined in a look-up table.
30. The method of claim 16 wherein the Green's function is calculated using Monte Carlo simulations or Finite Element Modeling.
31. The method of claim 4 wherein the noise threshold is related to one of the peak intensity in the surface light image data and the dynamic range in the surface light image data.
32. The method of claim 4 wherein the surface representation is divided into a set of surface elements and all surface elements having surface emission below the noise threshold are removed.
33. The method of claim 31 wherein the noise threshold is related to the peak intensity in the surface light image data divided by dynamic range in the surface light image data.
34. The method of claim 5 wherein the animal tissue is approximated to be homogenous.
35. The method of claim 7 further comprising:
moving the stage to a first position in the imaging chamber; and
capturing a first image set of the mammal from the first position using the camera.
36. The method of claim 7 further comprising:
moving the stage to one or more other positions in the imaging chamber, wherein the other positions have different angles relative to a fixed datum associated with the camera than the first position; and
capturing additional image sets of the mammal from the other positions using the camera.
37. The method of claim 7 wherein the surface light image data is obtained at a plurality of different wavelengths.
38. The method of claim 8 wherein the first image set is comprised of a luminescent image, a structured light image, and a photographic image.
39. The method of claim 36 wherein obtaining the surface representation comprises building a topographic representation of the mammal based on structured light data included in one or more structured light images.
CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority under 35 U.S.C. �119(e) from co-pending (1) U.S. Provisional Application No. 60/395,357, entitled �Method and Apparatus for 3-D Imaging of Internal Light Sources�, by Daniel G. Stearns, et al., (2) U.S. Provisional Application No. 60/396,458, entitled �In Vivo 3D Imaging of Light Emitting Reporters�, by Bradley W. Rice, et al. and (3) U.S. Provisional Application No. 60/396,313, entitled �3D in Vivo Imaging of Light Emitting Reporters�, by Bradley W. Rice, et al. These applications were all filed on Jul. 16, 2002 and are incorporated by reference for all purposes.
FIELD OF THE INVENTION The present invention relates generally to imaging with light. In particular, the present invention relates to systems and methods for obtaining a three-dimensional representation of a light source or light source distribution inside a turbid sample, which is particularly useful in biomedical imaging and research applications.
BACKGROUND OF THE INVENTION Bioluminescent imaging is a non-invasive technique for performing in vivo diagnostic studies on animal subjects in the areas of medical research, pathology and drug discovery and development. Bioluminescence is typically produced by cells that have been transfected with a luminescent reporter such as luciferase and can be used as a marker to differentiate a specific tissue type (e.g. a tumor), monitor physiological function, track the distribution of a therapeutic compound administered to the subject, or the progression of a disease. A wide range of applications have been demonstrated including areas of oncology, infectious disease, and transgenic animals. In vivo imaging of cells tagged with fluorescent reporters is a related technology that has also been general, absorption in mammalian tissues is high in the blue-green part of the spectrum (<600 nm) and low in the red and NIR part of the spectrum (600-900 nm). Firefly luciferase has a rather broad emission spectrum ranging from 500-700 nm, so at least part of the emission is in the low absorption region. Since the mean-free-path for scattering in tissue is short, on the order of �0.5 mm, photons from deep sources are scattered many times before reaching the surface. Bioluminescent imaging systems effectively record the spatial distribution of these photons emitted from the surface of the subject.
SUMMARY OF THE INVENTION The present invention provides systems and methods for obtaining a three-dimensional (3D) representation of one or more light sources inside a sample, such as a mammal. Mammalian tissue is a turbid medium, meaning that photons are both absorbed and scattered as they propagate through tissue. In the case where scattering is large compared with absorption, such as red to near-infrared light passing through tissue, the transport of light within the sample is described by diffusion theory. Using imaging data and computer-implemented photon diffusion models, embodiments of the present invention produce a 3D representation of the light sources inside a sample, such as a 3D location, size, and brightness of such light sources.
In one implementation, light transport device 120 includes an angled mirror 121 that reflects light from the sample 106 on stage 204 through aperture 122. Outer wall 123 is substantially cylindrical and includes aperture 122 that enables light to pass from the sample 106 on stage 204 via mirror 121 to imaging lens 262 (FIG. 2B). Outer wall 123 of light transport device 120 also prevents residual light in interior cavity of chamber 12 not directly associated with the current viewing angle of stage 204 from reaching lens 262. This is partially performed by configuring mirror 121 to be sufficiently long to span the length of stage 204. As the stage is positioned at various positions about the stationary axis of the light transport device 120; outer wall 123 and mirror 121 cooperate to collect light primarily from the angular direction of stage 204 which is then reflected towards lens 262.
Emission of light from a sample surface is generally specified in units of radiance, defined as photons/sec/cm2/steradian. The imaging system described herein is calibrated to report surface intensity in units of radiance. The surface radiance can be related to the photon density just inside the sample surface, using a model for photon propagation at the tissue-air interface. The photon density just inside the surface can then be related to the distribution of light emitting reporters inside the sample using a diffusion model. Thus, the present invention relates the surface radiance of a turbid sample measured with an imaging system to the distribution of light emission inside the sample. More specifically, the present invention produces a 3D representation of an internal light source using reconstruction techniques that utilize the light data emitted from the sample surface. The reconstruction techniques employ an input data set that consists of a) a topographical surface representation of the sample, and b) a set of measurements (e.g. surface images) of the light radiance-over at least a portion of the surface. To facilitate processing, the surface representation may be divided into surface elements and the interior of the sample may be divided into volume elements or voxels that constitute a volume element mesh. The light source distribution within the sample is described by elements of the volume element mesh.
I ⁡ ( θ 2 ) = c 4 ⁢ π ⁢ ⁢ n 2 ⁢ T ⁡ ( θ ) ⁢ cos ⁢ ⁢ θ 2 ⁢ d ⁢ ⁢ Ω ⁢ ⌊ 1 + 3 2 ⁢ 1 - R eff 1 + R eff ⁢ cos ⁢ ⁢ θ ⌋ ⁢ ρ ( 1 ) Here, c is the speed of light, n is the index of refraction of the sample medium, T is the transmission coefficient for light exiting the sample through the surface element, and θ is the internal emission angle, which is related to the external emission angle θ2,through Snell's law:
R eff = R ϕ + R j 2 - R ϕ + R j R ϕ = ∫ 0 π 2 ⁢ 2 ⁢ sin ⁢ ⁢ θ ⁢ ⁢ cos ⁢ ⁢ θ ⁢ ⁢ R ⁡ ( θ ) ⁢ ⅆ θ R j = ∫ 0 π 2 ⁢ 3 ⁢ sin ⁢ ⁢ θ ⁢ ⁢ cos 2 ⁢ ⁢ θ ⁢ ⁢ R ⁡ ( θ ) ⁢ ⅆ θ R ⁡ ( θ ) = { 1 2 ⁢ ( n ⁢ ⁢ cos ⁢ ⁢ θ 2 - cos ⁢ ⁢ θ n ⁢ ⁢ cos ⁢ ⁢ θ 2 + cos ⁢ ⁢ θ ) 2 + 1 2 ⁢ ( n ⁢ ⁢ cos ⁢ ⁢ θ - cos ⁢ ⁢ θ 2 n ⁢ ⁢ cos ⁢ ⁢ θ + cos ⁢ ⁢ θ 2 ) 2 ⁢ ⁢ for ⁢ ⁢ θ < arcsin ⁡ ( 1 / n ) 1 ⁢ for ⁢ ⁢ θ > arcsin ⁢ ⁢ ( 1 / n ) ( 3 ) Thus, the internal reflectivity Reff depends on the index of refraction of the medium underneath a surface element. In tissue for example, Reff is typically in the range of 0.3-0.5.
FIG. 5B illustrates a process flow 520 for using imaging system 10 of FIG. 1 to obtain imaging data in accordance with one embodiment of the present invention (504 from process flow 500). Process flow 520 begins by placing a sample such as a specimen or assay to be imaged for light emission on stage 204 within imaging chamber 12 (521). Using computer 28, a user inputs a desired position for stage 204. Alternatively, the desired position for stage 204 is already known based on an automated data collection method. Transport mechanism 202 moves stage 204 to the desired position according to a control signal provided by computer 28 (522). Light transport device 120 may also re-position according to a control signal provided by computer 28. Imaging chamber 12 and associated image components are then prepared for photographic image capture of the sample (523). Preparation may include launching imaging and acquisition software (e.g., �LivingImage� as provided by Xenogen Corporation of Alameda, Calif.) on computer 28 and initializing camera 20. Further preparations may include closing door 18, activating the photographic capture option in the software, focusing camera 20 to a specific depth of the sample or animal, and turning on the lights in chamber 12. Preparations may also include focusing the lens of camera 20, selectively positioning an appropriate the lens filter of camera 20, setting the f-stop of camera 20, etc.
A photographic image is then captured (524). In an alternative embodiment, a �live mode� is used during photographic imaging of the sample to observe the sample in real time. The live mode includes a sequence of photographic images taken frequently enough to simulate live video. Upon completion of photographic capture, the photographic image data is transferred to an image processing unit 26 and/or a processor in computer system 28. These may be used to manipulate and store the photographic image data as well as process the data for display on computer monitor 38.
At this point, a user may manipulate and store the luminescence image data as well as process it for display on the computer display 38. The manipulation may also include overlaying the luminescent image with the photographic image and displaying the two images together as a 2-D �overlay� image, with the luminescence data typically shown in pseudocolor to show intensity. As mentioned, the photon emission data may represent the specific pixels on the camera 20 that detect photons over the duration of the image capture period. This overlay image may then be the basis for user analysis; and may be analyzed and manipulated as desired. In particular, an analysis may include a summation of the illumination magnitudes over the pixels within a portion of the luminescence representation. Note that although the discussion will focus on a single luminescence representation for the overlay image, the process flow 520 may include taking multiple luminescence representations from the same position of stage 204, e.g., at the same time or a later time (530).
In another embodiment, process flow 520 and imaging apparatus 10 reconstruct the 3D surface topography of the sample using a sequence of images. By taking images from several viewing angles, e.g., about every 45 degrees, the entire 3D surface of the sample can be reconstructed by �stitching� together the partial surface reconstructions obtained from each view. A sequence of images may then be taken at different viewing angles and used in reconstructing the sample's 3D surface topography. The 3D surface topography and image data may also be used in reconstructing the 3D location, brightness, and size of the light source within the sample. Once the images are received by processor 28, a suitable reconstruction algorithm is applied to the data to obtain the 3D surface topography. As one of skill in the art will appreciate, there are numerous algorithms for reconstructing a surface from structured light images. For example, the phase shift of each line at all points on the image can be determined from a 2D Fourier transform. Such a process is described in detail in the article entitled �Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,� by M. Takeda, H. Ina and S. Kobayshi, JOSA 72, 156-160 (1982), which article is incorporated herein by reference in its entirety. The actual surface height is then computed by �unwrapping� the phase map. Such a process is described in detail in the textbook entitled �Two-Dimensional Phase Unwrapping, Theory, Algorithms, and Software� by D. C. Ghiglia and M. D. Pritt, (John Whiley and Sons, New York, N.Y., 1998), which textbook is incorporated herein by reference in its entirety. Together, a structured light photographic representation of the sample and a luminescence representation of the sample may be combined to form a structured light superposition or 3D overlay image, with the luminescence data typically shown in pseudocolor to visually characterize intensity.
Subsequently when the sample is in the imaging chamber, the sample is imaged with structured light (512 and FIG. 4C). Structured light uses a series of lines of light that are projected down on a sample at an angle (at about 30 degrees, for example) to the surface normal. The lines bend as they pass over the sample, and the bend in the lines can be used to determine the height of the surface at all locations that are illuminated by a structured light projector (such as structured light projector 170 described above). As shown in FIG. 2D, structured light projector 170 is attached to and rotates with light transport device 120. In this case, structured light projector 170 consists of a Kohler illumination system where a slide is illuminated by a light source and then an image of the slide is projected onto the sample or background. The projection angle is large enough to get sufficient �bend� in the lines to achieve spatial resolution, but small enough that large shadows are not present.
Surface topography for the sample is then calculated (516 and FIG. 4G). In this case, this is performed by �unwrapping� the phase map. Several unwrapping algorithms are available to those of skill in the art for this task. For example, the phase shift of each line at all points on the image can be determined from using Fourier profilometry techniques. With these methods, a 2D Fast-Fourier transform (FFT) of the fringe data (FIG. 4D) is taken to determine the phase shift of the lines everywhere in the image (FIG. 4F). Since the phase will shift by many multiples of 2π for a typical object, the phase exhibits 2π jumps as seen in FIG. 4F. These phase jumps are �unwrapped� in order to determine the actual surface.
In addition, process flow 540 divides the sample interior volume into volume elements (542). In one embodiment, each volume element is considered to contain a point light source at its center. A solid mesh of volume elements then defines a collection of point sources used to approximate the actual light source distribution. In some cases, the density of the solid mesh increases near the light source to provide increased information in this space, while density of the solid mesh decreases in areas where no activity of interest is taking place (no light generation or transport). In addition, as will be described below with respect to loop 556, the volume element size may vary during solution attainment according to various adaptive meshing techniques. For example, the initial volume element size may range from about 0.1 cm3 to about 1 cm3, and the final volume element size for volume elements close to the source may reduce from about 1*10−3 cm3 to about 1*10−2 cm3. In a specific example, the initial volume element size may be about 1 cm3, and the final volume element size for volume elements close to the source may reduce to about 8*10−3 cm3.
When the mediuminside the sample is assumed or modeled as homogeneous, one useful form for the Green's function is a simplified approximation in which the surface of the sample is treated locally as a planar interface oriented perpendicular to a line connecting a volume element center and a surface element. The photon density at the surface is the analytical solution for a point source in a semi-infinite slab using the partial-current boundary condition. Since the solution is only a function of the distance between the volume element and the surface, the simplified Green's function can be calculated for all pairs of volume elements and surface vertices with minimal computational expense.
ρ j ≅ ∑ i ⁢ G ij ⁢ S i ( 4 ) where the index i enumerates the volume elements and Si is the value of the strength of the point source (photons/sec) inside the ith volume element.
D∇ 2ρ−μa cρ=−U i( x ) (5)
D = c 3 ⁢ ( μ A + μ S ′ ) ( 6 ) In this case, the Green's function is the solution to Eq. (5) subject to the boundary condition imposed by the surface of the sample. For a sample modeled as homogeneous, a useful approximate solution for the Green's function uses a planar approximation at the surface boundary.
G ij = 1 2 ⁢ π ⁢ ⁢ D ⁢ { exp ⁡ ( - μ eff ⁢ r ij ) r ij - 1 z b ⁢ exp ⁡ ( r ij / z b ) ⁢ E 1 ⁡ [ ( μ eff + 1 z b ) ⁢ r ij ] } ( 7 ) Here rij=|xj−xi|, E1 is the first order exponential integral and
μeff=√{square root over (3 μA(μA+μS′))}tm (8)
z b = 2 ⁢ D c ⁢ 1 + R eff 1 - R eff ( 9 ) In the simplified model just described, the simplified Green's function depends only on the distance between the volume element and the surface. It is not necessary to use an analytical form such as the simplified approximation to define the Green's function.
The present invention does not rely on an analytical form such as the approximation described above. In another embodiment, a look-up table may define the Green's function. The look-up table may be created by previous measurements of photon transport in a sample (or similar sample approximated to be substantially equal to the current sample), or by computational simulations using techniques such as Monte Carlo or finite element modeling. This particular method is useful for samples consisting of inhomogeneous media, such as animal subjects. In this case, the optical properties, μa and μs from Eq. 8, now have spatial dependence.
The planar boundary approximations discussed above work best for smooth surfaces with a large radius of curvature, and for cases where the absorption coefficient is not too small (μα>0.1 cm−1). An advantage of the planar approximation technique described above is that it is computationally convenient for solving the diffusion equation with an arbitrary complex boundary such as a mouse. Areas with more structure, such as the head or the limbs of a mouse, may benefit from a more accurate model of the boundary. Using a finite element modeling code to calculate the Green's functions is one option to obtain a more accurate boundary model. Finite element codes such as Flex PDE, from PDE Solutions, Inc. may be used for example. Another option will be to extend the planar surface approximation to first order in curvature, which may allow continued use of analytic expressions for Gij.
Once the Green's function is determined, the reconstruction is obtained by solving the system of linear equations that relate the photon density at the surface to the source distribution inside the object. Process flow 540 then proceeds by solving for all the internal volume elements (546). More specifically, given the modeling described above, the reconstruction techniques solve the system of linear equations that relate the photon density at the surface to the source distribution inside the sample. Thus, once the Green's function is determined, it may be evaluated for every volume element�surface element pair, in order to obtain the system of linear equations (Eq. 4). The final step of the reconstruction method is to solve the linear system, Eq. (4), for the source strengths Si. Referring back to Eq. (4), since ρ is known, and Gij can be determined as described above, the reconstruction techniques then solve for Si. Typically, there is no exact solution to the linear system because the collection of point sources is only an approximation of the actual source distribution. One suitable reconstruction is then the best approximate solution of the linear system.
Cost = ∑ j ⁢ S j ( 10 ) The cost function is subject to one or more linear constraints. A first suitable set of constraints is that the source strengths be positive definite:
∑ j ⁢ G ij ⁢ S j ≤ ρ i ( 12 ) In a specific embodiment, an optimum solution for source strengths Si is found by maximizing the cost function (10) subject to constraints (11) and (12).
The solution quality may be assessed (552). In one embodiment, the assessment measures the difference between the observed photon density and the calculated photon density. For example, a �chi squared� criteria may be used:
χ 2 = ∑ j ⁢ [ ρ j - ∑ i ⁢ G ij ⁢ S i ρ j ] 2 ( 13 ) The value of χ2 measures the difference between the observed photon density ρi and the calculated photon density
∑ i ⁢ G ij ⁢ S i over the surface of the sample.
Cost = ∑ i ⁢ S i / W i γ , W i = ∑ j ⁢ G ij ( 14 ) The weighting factor Wi is the contribution of the ith volume element to the photon density over the entire surface. The exponent γ adjusts the relative contribution to the cost function of the interior volume elements and those volume elements close to the surface. When γ=0, then the interior volume elements have relatively greater weight. When γ=1 the volume elements near the surface have greater weight. Process flow 540 may be iterated while varying γ to search for solutions where the source is both near and far from the surface. For example, the step size may be varied by about 0.01 to about 0.2 for a range of γ from 0 to 1. In a specific embodiment, the step size was varied by about 0.05 for a range of γ from 0 to 1. Once again, quality assessment (552) may be used to identify the best solution.
G ij = G i E ⁢ G ij F ( 15 ) The first Green's function, Gi E, describes the transport of excitation light from the excitation source at the surface of the sample to the ith volume element. The second Green's function, Gij F, describes the transport of the fluorescent light from the ith volume element to the jth surface element. Both Green's functions can be determined from analytical expressions, such as the simplified approximation described above in the case of a homogeneous medium, or from look-up tables in the case of an inhomogeneous medium. The excitation and fluorescent light are typically at different wavelengths, and thus the fluorescence does not stimulate additional fluorescence. The system of linear equations (4) is still valid, and process flow 540 can be used as outlined above to determine the fluorescent light source distribution.
A limited dynamic range is particularly evident when imaging bioluminescence from sources imbedded in tissue, because the light emission intensity typically varies over many orders of magnitude across the sample surface. If the imaging camera imposes a limited dynamic range and a region of highest intensity is set to the camera's upper limit, then there will probably be regions in the image where the emission intensity falls below the bottom of the dynamic range. These regions of the image will be received as noise; and correspond to a �noise floor�.
∑ j ∈ Q ⁢ G ij < κ ⁢ ⁢ ∑ j ∈ P ⁢ G ij ( 16 ) The constant κ may have a value in the range of 1-10. The criteria (16) is applied to each volume element during the formation of the initial volume grid (542) and at each iteration, if used.
χ 2 = ∑ j ⁢ 1 ρ j ⁡ [ ρ j - ∑ i ⁢ G ij ⁢ S i ] 2 ( 17 ) The reconstruction techniques of the present invention will typically be implemented by a suitable processor or computer-based apparatus. Referring to FIG. 6, an exemplary computer system 350 includes a central processing unit (CPU) 352, read only memory (ROM) 354, random access memory (RAM) 356, expansion RAM 358, input/output (I/O) circuitry 360, display assembly 362, input device 364, and expansion bus 366. Computer system 350 may also optionally include a mass storage unit 368 such as a disk drive unit or nonvolatile memory such as flash memory and a real-time clock 360.
It should be borne in mind that although computer system 350 is discussed in some detail herein to facilitate discussion, the invention may be practiced using a variety of suitable computer-implemented techniques. In general, any suitable computer system may be employed for obtaining a three-dimensional representation of a light source located inside a sample. Further, the inventive reconstruction techniques disclosed herein may be implemented via a computer network, such as a local area network (LAN), wide area network (WAN) or a global computer network such as the Internet. In the latter cases, the reconstruction techniques may be implemented at least in part as downloadable computer software and data (e.g., applets such as JAVA� applets from Sun Microsystems Inc.). The downloadable computer software and data may be kept on one or more servers on the network, accessible by any client computer or terminal capable and authorized for such access. Network computing techniques and implementations are well known in the art and are not discussed in great detail here for brevity's sake.
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