Excitation-resolved fluorescence tomography with simplified spherical harmonics equations

Abstract

Fluorescence tomography (FT) reconstructs the three-dimensional (3D) fluorescent reporter probe distribution inside biological tissue. These probes target molecules of biological function, e.g. cell surface receptors or enzymes, and emit fluorescence light upon illumination with an external light source. The fluorescence light is detected on the tissue surface and a source reconstruction algorithm based on the simplified spherical harmonics (SP(N)) equations calculates the unknown 3D probe distribution inside tissue. While current FT approaches require multiple external sources at a defined wavelength range, the proposed FT method uses only a white light source with tunable wavelength selection for fluorescence stimulation and further exploits the spectral dependence of tissue absorption for the purpose of 3D tomographic reconstruction. We will show the feasibility of the proposed hyperspectral excitation-resolved fluorescence tomography method with experimental data. In addition, we will demonstrate the performance and limitations of such a method under ideal and controlled conditions by means of a digital mouse model and synthetic measurement data. Moreover, we will address issues regarding the required amount of wavelength intervals for fluorescent source reconstruction. We will explore the impact of assumed spatially uniform and nonuniform optical parameter maps on the accuracy of the fluorescence source reconstruction. Last, we propose a spectral re-scaling method for overcoming the observed limitations in reconstructing accurate source distributions in optically non-uniform tissue when assuming only uniform optical property maps for the source reconstruction process.

Figure 1

(a) FT with source multiplexing: a fluorescence image is taken for each source position (r_s). (b) HEFT with hyperspectral excitation: a fluorescence image is taken for each spectral band (λ_l). (A) Light source; (B) switch for source multiplexing (e.g. optical mirror); (C) source location r_s on tissue surface (e.g. narrow laser beam or optical fiber tip); (D) wavelength-selective filter; (E) macro-illumination at specified wavelength λ_l; (F) tissue with fluorescent source at location r; (G) fluorescence emission filter, and (H) optical detector (e.g. CCD camera).

Figure 2

Extinction spectrum of (oxy-)hemoglobin (Prahl 1999).

Figure 3

Boundary points of the active region that represent the curved surface of a mouse model. The SP₃ equations are solved on the interior grid points (not shown) of the active region, whereas the boundary equations are solved on the surface points (shown).

Figure 4

(a) Trans-illumination geometry. (b) Epi-illumination geometry. Both geometries use a white light source for fluorescence stimulation (A), a wavelength discriminating bandpass filter (B), an emission filter (C), and a CCD camera (D).

Figure 5

(a) Single-view HEFT set-up: V = 1. (b) Dual-view HEFT arrangement with two illumination positions: V = 2. (c) Quad-view HEFT arrangement with four illumination positions: V = 4.

Figure 6

Surface rendering of the Digimouse atlas outlining the organs: mouse skin, whole brain, masseter muscles, spine and skull, heart, liver, lungs, stomach, spleen, pancreas, kidneys, bladder, and testes (left: posterior view; right: lateral left view).

Figure 7

(a)–(d) 3D mouse model in four different planes from anterior (slice 3) to posterior (slice 12) containing the following organs: brain, heart, bone, liver, stomach, bladder, testes, kidneys, and the bulk tissue (interstitial matter). (e) Corresponding frontal planes in the original Digimouse model.

Figure 8

Optical properties assigned to the simplified mouse model at nine different excitation wavelengths in the range of 580–660 nm, and a single emission wavelength at 700 nm (marked by dots). The absorption coefficient (a) and the reduced scattering coefficient (b) are given for the following organs: brain (pink), liver (brown), heart (red), stomach (blue), kidneys (green), bones (black), and bulk tissue (gray).

Figure 9

(a) Fluorescence images of Qdots inside tissue taken for different excitation wavelengths (580–660 nm) on the top side (z = 12) of the tissue phantom. A capsule of Qdots is located 0.5 cm (z = 7) beneath the top tissue surface.

Figure 10

Image reconstructions of fluorescent Qdots embedded into chicken breast tissue for epi-illumination geometry and L = 9 wavelengths. Top row: lateral slices at depth z = 7. Bottom row: axial slices at y = 20. Original location of the capsule is depicted by a green-colored rectangle. (a) Single-view (V = 1) HEFT reconstructions. Detection and illumination plane is located at z = 12. (b) Dual-view (V = 2) HEFT reconstructions. Detection and illumination planes are located at z = 0 and z = 12.

Figure 11

Dual-view ex vivo reconstructions of fluorescent Qdots embedded into chicken breast tissue for (a) L = 1, (b) L = 3, (c) L = 5, and (d) L = 9 excitation wavelengths. Top row: lateral slices of Qdot distribution inside tissue at the depth z = 7. Bottom row: axial slices of Qdot distribution inside tissue at y = 20.

Figure 12

Dual-view reconstructions of synthetic measurement data for (a) L = 1, (b) L = 3, (c) L = 5, and (d) L = 9 excitation wavelengths. Top row: lateral slices of the fluorescence source inside the numerical model at the depth z = 7. Bottom row: axial slices of the fluorescence source inside the numerical model at y = 20.

Figure 13

Single-view HEFT reconstruction of a fluorescence source obtained for (a) the ideal case, i.e. with the original nonuniform optical parameter maps, (b) the real case with an assumed uniform optical parameter distribution, and (c) the re-scaling case with re-scaled measurement data based on a uniform optical parameter distribution. The top row of images shows frontal slices at z = 10. The bottom row of images shows transversal slices at (a) y = 37, (b) y = 35, and (c) y = 34. The original location of the fluorescence source is illustrated by a green circle.

Figure 14

Dual-view HEFT reconstruction of a single fluorescence source obtained for (a) the ideal case, (b) the real case, and (c) the re-scaling case. The top row of images shows frontal slices at z = 10. The bottom row of images shows transversal slices at (a) y = 38, (b) y = 34, and (c) y = 38. The original location of the fluorescence source is illustrated by a green circle.

Figure 15

3D isosurface rendering of the source obtained for the real-case simulation using dual-view HEFT reconstruction.

Figure 16

Quad-view HEFT reconstruction of a single fluorescence source obtained for (a) the ideal case, (b) the real case, and (c) re-scaling case. The top row of images shows frontal slices at z = 10. The bottom row of images shows transversal slices at (a) y = 38, (b) y = 34, and (c) y = 38. The original location of the fluorescence source is illustrated by a green circle.