Diffusion tensor optical coherence tomography

Abstract

In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.

Figure 1

DT-OCT concept diagram. Left: Electron microscopy of artificial ECM after remodeling by stromal fibroblasts in vitro shows heterogeneity of fiber alignment (boxed regions and scalebar 6µm). Middle: Diffusion of nanoparticles in an anisotropic medium is larger in the direction parallel to the long axis of the pores. Right: OCT beams that probe a volume at different angles are used to measure the component of diffusion along each wave vector k, noting that the wavefront of each beam is at near the focus.

Figure 2

Diagram of a sample being probed from the optimal six different directions for a given NA, with the wave vectors of these directions corresponding to k₁ to k₆.

Figure 3

A 4-F system with two galvanometer mirrors, one conjugate to the entrance pupil of the objective (position galvo), and the other conjugate to the focus (incident angle galvo), permitting one to independently manipulate the position and incident direction of a focused beam. The red beam travels along the central axis of the system with neither galvo tilted. The green beam is tilted by the position galvo, so that the ray ends up at an off-axis image point. The blue beam is tilted by the incident angle galvo, so it is incident at the image point at an off-axis angle.

Figure 4

Diagram of a simple example of DT-OCT by probing a point in a medium with two different incident angles θ₁ and θ₂. The diffusion constant in the plane is D_‖ and perpendicular to the plane is D_┴.

Figure 5

A: SEM images of artificial ECM 48 hours after seeding with RMF cells of varying densities, with average translational diffusion rates (D_T) of nanorods in each culture from (Blackmon et al. 2016). B and C: Error in diffusion tensor anisotropy (D_Δ) and drift velocity magnitude, respectively, of simulated measurements using D_ISO equal to D_T from each of the culture conditions. (Scalebar = 3 µm).

Figure 6

Simulated measured diffusion rates by DT-OCT versus the underlying actual diffusion rate used in the simulation along the principle axes x, y, and z. Anisotropy was swept from 0 to 1 for a fixed average diffusion rate D_ISO matched to that from nanorods diffusing in artificial ECM seeded with reduction mammoplasty fibroblasts. The dotted line indicates measured = actual.