Monte Carlo simulation of the spatial resolution and depth sensitivity of two-dimensional optical imaging of the brain

Abstract

Absorption or fluorescence-based two-dimensional (2-D) optical imaging is widely employed in functional brain imaging. The image is a weighted sum of the real signal from the tissue at different depths. This weighting function is defined as "depth sensitivity." Characterizing depth sensitivity and spatial resolution is important to better interpret the functional imaging data. However, due to light scattering and absorption in biological tissues, our knowledge of these is incomplete. We use Monte Carlo simulations to carry out a systematic study of spatial resolution and depth sensitivity for 2-D optical imaging methods with configurations typically encountered in functional brain imaging. We found the following: (i) the spatial resolution is <200 μm for NA≤0.2 or focal plane depth≤300 μm. (ii) More than 97% of the signal comes from the top 500 μm of the tissue. (iii) For activated columns with lateral size larger than spatial resolution, changing numerical aperature (NA) and focal plane depth does not affect depth sensitivity. (iv) For either smaller columns or large columns covered by surface vessels, increasing NA and/or focal plane depth may improve depth sensitivity at deeper layers. Our results provide valuable guidance for the optimization of optical imaging systems and data interpretation.

Figure 1

Schematic diagram of a camera-based optical imaging system. A collimated light beam illuminates the brain tissue. For absorption imaging, the backscattered light (marked by arrows) is collected by lens L₁ and imaged onto a two dimensional detector plane by lens L₂. For fluorescence imaging, a BPF is inserted in front of the camera allowing the detection of the fluorescence. The system is arranged in a 4f configuration. f: focal length of L₁ and L₂. BS: beamsplitter. NA: numerical aperture.

Figure 2

Distributions of point disturbance in the absorption and fluorescence imaging. Absorption imaging: (a) A single array of point absorbers evenly distributed throughout the cortical depth (0–1 mm) and along the optical axis. (b) Multiple arrays of point absorbers evenly distributed throughout the cortical depth (0–1 mm) and with a lateral size of L. Fluorescence imaging: the distribution of a single array and multiple arrays of fluorescent targets are shown in (a, b), respectively. Their normalized staining profile can be either uniform (c) or nonuniform (d).

Figure 3

Definition of the spatial resolution. For absorption imaging: (a) The difference images due to individual point absorbers depicted in Fig. 2(a). (b) The summation of all these images. (c) The profile of the summed image along the radial direction. The spatial resolution is defined as the FWHM of this profile. For fluorescence imaging, the spatial resolution is defined similarly except that fluorescence targets replace point absorbers.

Figure 4

Definition of the depth sensitivity at the center of the detector. For absorption imaging, multiple arrays of point absorbers depicted in Fig. 2(b) are considered. The horizontal size of the array is L. (a) The contribution to the total intensity variation at the center of the detector from an individual layer of point absorbers at depth z is equivalent to the cropped image due to an individual point target at (0, 0, z) inside the tissue. (b) The total intensity variation at the center of the detector induced by all point absorbers within a certain depth is the summation over the area L² of the cropped image and depth. (c) The depth sensitivity is defined as the ratio of the contribution from an individual depth and the total contribution from all depths. The depth sensitivity of fluorescence imaging can be defined similarly except that fluorescence targets are used instead of point absorbers.

Figure 5

(a) A point absorber at (0, 0, z) in the absorption imaging acts as a negative light source that has an anistropic radiance –$I_0(z,\widehat{\Omega })$ in the direction of $\widehat{\Omega }$. (b) A fluorescent target at (0, 0, z) in the fluorescence imaging acts as an isotropic light source with an intensity of I₀(z).

Figure 6

Spatial profiles of the difference images due to the presence of a single array of point absorbers (or fluorescent targets) for both the absorption and fluorescence imaging. (a) The spatial profiles corresponding to NA = 0.2 and focal plane depths at 100 (blue), 300 (red), and 500 μm (black), respectively, for the absorption imaging. (b) The spatial profiles corresponding to three different NA at 0.1 (blue), 0.2 (red), and 0.4 (black), respectively, and focal plane depth = 300 μm for the absorption imaging. (c) The spatial profiles corresponding to NA = 0.2 and focal plane depths at 100 (blue), 300 (red), and 500 (black) μm, respectively, for the fluorescence imaging. (d) The spatial profiles corresponding to three different NA at 0.1 (blue), 0.2 (red), and 0.4 (black), respectively, and focal plane depth = 300 μm for the fluorescence imaging. In (c, d), straight and dashed lines represent the profiles corresponding to uniform and nonuniform distributions of the fluorescent targets, respectively.

Figure 7

Spatial resolution versus focal plane depth of the (a) absorption and (b) fluorescence imaging for NA of 0.1 (circle), 0.2 (star), and 0.4 (triange), respectively. In (b), straight and dashed lines represent the profiles corresponding to uniform and non-uniform distributions of the fluorescent targets, respectively.

Figure 8

Depth sensitivity for functionally activated columns of four different cross-sectional areas: (a) 10 × 10, (b) 50 × 50, (c) 100 × 100, and (d) 200 × 200 μm², respectively, for absorption imaging. In (a)–(d) NA is fixed at 0.2 and the focal plane depth is varied among 100 (blue), 300 (circle), and 500 (triangle) μm.

Figure 9

Depth sensitivity for functionally activated columns of four different cross-sectional areas: (a) 10 × 10, (b) 50 × 50, (c) 100 × 100, and (d) 200 × 200 μm², respectively, for absorption imaging. In (a)–(d), the focal plane depth NA is fixed at 300 μm and NA is varied among 0.1 (circle), 0.2 (star), and 0.4 (triangle).

Figure 10

Depth sensitivity for functionally activated columns of four different cross-sectional areas: (a) 10 × 10, (b) 50 × 50, (c) 100 × 100, and (d) 200 × 200 μm², respectively, for fluorescence imaging with the nonuniform distribution of the fluorescent targets. In (a)–(d), NA is fixed at 0.2 and the focal plane depth is varied among 100 (circle), 300 (star), and 500 (triangle) μm.

Figure 11

Depth sensitivity for functionally activated columns of four different cross-sectional areas: (a) 10 × 10, (b) 50 × 50, (c) 100 × 100, and (d) 200 × 200 μm², respectively, for fluorescence imaging with the nonuniform distribution of the fluorescent targets. In (a)–(d), the focal plane depth is fixed at 300 μm and NA is varied among 0.1 (circle), 0.2 (star), and 0.4 (triangle).

Figure 12

Percent contributions from different depths of the tissue and the surface vessel in the absorption imaging. (a) NA = 0.2 and focal plane depths of 100 (circle), 300 (star), and 500 (triangle) μm. (b) focal plane depth = 300 μm, NA = 0.1 (circle), 0.2 (star), and 0.4 (triangle). In (a, b), the horizontal size of the activated column is 400 μm. The vessel of 50 × 50 × 50 μm³ is embedded within the top tissue and a blood tissue volume of ~1% is used. SV: surface vessel.