Non-flat layered tissues for MCCL

[janakarana]

Is your feature request related to a problem? Please describe.
For some studies or analyses, certain tissues cannot be assumed as flat layers. For example, skin cannot be assumed to be flat if large source-detector separations are considered. Instead of using a mesh-based Monte Carlo model, I want to see if MCCL can have concave or convex surfaces.

Describe the solution you'd like
I would like to see the possibility of using the existing "MultiConcentricInfiniteCylinder" tissue to get convex and concave tissues (See Figure). To do this, the virtual boundaries should be defined at the inner and outer cylindrical surfaces of a hollow cylinder. Such implementation will allow detectors to capture the photons exiting from the cylinder. We can consider that all detectors are normal to the surface.

Describe alternatives you've considered
Defining all layer boundaries by analytical equations.

[hayakawa16]

I've tried to code this up in fits and starts. At first I tried to write code that has a pseudo-"air" Layer (like air in OPs but very small but non-zero mua) region the surrounds the multi-concentric infinite cylinders. This had problems at the initial interface between air and outer cylinder. Then I tried to create a MultiLayerInfiniteCylinderTissue much like a MultiLayerTissue but with our current InfiniteCylinderTissueRegions. Now I'm realizing that I need to create an associated LayerInfiniteCylinderTissueRegion so that it is a "tube" rather than a solid cylinder to make all of the TissueRegion methods work out like RayIntersectBoundary.

I'm floundering a bit. Any comments are welcome.

[dcuccia]

I'm not sure I appreciate what the main technical problem is, but two morsels come to mind:

1. in the past, when we had "internal" air gaps, we'd used zero absorption and very low scattering with g=1. Is that doable here?

2. not sure why we need to do anything special for the outside. Can we just define a normally-incident cylindrical source that's matched to the tissue?

[hayakawa16]

Hi @dcuccia, thanks for your comments! Per your 1: yes! I agree. We had air gaps before. I was initially sure I could get a layer of "air" with the cylinders inside to work. Since the current fiber reflectance detectors could be only be on the reflectance plane, we put the outermost cylinder close to that plane. @janakarana defined very large cylinders and tried to verify code with a MultiLayerTissue of same geometry. This could not be accomplished. Per your 2: the sources are currently defined so that they can be anywhere. I would need to define a new internal fiber detector that could rest on the surface of the outermost cylinder in the air layer.

@janakarana would like refractive index mismatch air above and below the layered cylinders. He has two problems he is analyzing that has a concave downward reflectance geometry, and another that has a concave upward reflectance geometry with a fiber source and several fiber detectors (https://www.mathsisfun.com/calculus/concave-up-down-convex.html).

Are you possibly available at 1pm tomorrow (@lmalenfant cancelled our meeting because she is out this week but you and I could meet)? If not, do you feel that having an "air" LayerTissueRegion that encompasses a series of InfiniteCylinderRegions (with axis along y-axis), with n>1 and mismatch between cylinders, and innermost cylinder being air should work? This would assume I define a new internal fiber detector.

[hayakawa16]

Now that Issue #136 is closed and methods in MultiConcentricInclusionTissue have been fixed, I can work on this issue now.

When I initially approached this problem, I thought of two ways to solve it:
a) define an "air" LayerRegion (with air layer above and below as usual) and concentric cylinder layers with an innermost cylinder of "air", or
b) define a MultiLayerInfiniteCylinder tissue (much like MultiLayerTissue) with air above and below (inside) the layers of mismatched, concentric infinite cylinders layers.

The ease/complication of the two options arises when thinking about how to define the detectors and the virtual boundaries (VBs) to which they are attached (note we have a one-to-one mapping between VBs and detectors).

In a) the new VB could be based on a tissue region surface. There would need to be a reflectance VB on the surface of the outermost cylinder and a transmittance VB on innermost "air" cylinder, but could be general in case other tissue region surfaces would require VBs in the future. This would work for the figure on the left. For the figure on the right, the reflectance VB would be on the innermost cylinder and transmittance would be on the outermost cylinder. So this might be confusing.
In b) there would two new VBs, DiffuseReflectanceInfiniteCylinder on outermost cylinder and DiffuseTransmittanceInfiniteCylinder. In this case the handing of VBs and detectors would be similar to MultiLayerTissue. However, I would have to modify code in MonteCarloSimulation because it currently assumes for all simulations, there is a reflectance and transmittance plane VB.

The new fiber detector associated with the above VBs:
In a) a "direction" of the detector would need to be defined so that the specification of whether it is capturing cylinder outward flow (positive dot product with surface normal) or inward flow (negative dot product with surface normal).
In b) this is a bit easier because the definition of the VB would handle whether flow is in line with detector or not.

The transport:
In both we would start photons inside the topmost cylinder (outer for left figure, inner for right figure) so no loss due to specular between air layer and cylinder (n=1.4).

Any comments about whether a) or b) would be better solution, or possibly a suggested c)?

[hayakawa16]

@dcuccia, do you have any thoughts on this? I'm thinking option a) would be better direction to go, however I'm not sure how best to define the directional VBs. Possibly based on tissue region boundary is not the best because it is limiting and we might need option to detect away from boundary (like RadianceOfRhoAtZ).

[dcuccia]

I think I'd need to dive in a little deeper here. I'm not sure I appreciate the complexities/differences. Without thinking too hard, it seems to me that both drawing scenarios are represented by the the same tissue definition, but with sources and detectors in different locations. The analogy that comes to mind is that we don't have a TransmissionMultiLayeredTissue and ReflectanceMultiLayeredTissue, we just have a MultiLayeredTissue and different locations for sources and detectors. And if you have a detector, you need a corresponding virtual boundary to detect it (and optionally kill it - if this was a "full tube/lumen", you'd want to keep propagating the photon to the other side of the inner wall). Don't VBs have the concept of directionality built-in? E.g. if we wanted to detect flux (i.e. current) in a specific direction, how do we do that today?

[dcuccia]

If it's a cylindrical VB, the VB could be triggered if the vector is pointing "in" or "out"...

[hayakawa16]

Thanks for your response! True we don't have TransmissionMultiLayeredTissue and ReflectanceMultiLayeredTissue, however we have DiffuseReflectanceVirtualBoundary and DiffuseTransmittanceVirtualBoundary which are defined based on z-axis plane and a direction. So yes, directionality is built into VBs.
For this curved, layered geometry, we have been assuming concentric infinite (along y-axis) cylinders with an air innermost cylinder. These are all within a LayerTissueRegion of air. This means that the full cylinder (tube) is part of the system.
Just had an idea: since the detector in both figures is within the air layer (and over all "tissue" system), do think I could use something like our existing VBType.InternalSurface which instantiates the RadianceVB? This RadianceVB was written solely with dosimetry (i.e. at a z-axis plane and passing it in one direction). Instead, I could have a VBType.InfiniteCylinderSurface with a direction based on if dot product with surface normal (assumed to be outward pointed, away from center of curvature).

[dcuccia]

Thinking back, perhaps we could have defined tissue regions using surfaces, so we could just "re-use" those surfaces for VBs. From that spirit, I like your suggestion of the VBType.InfiniteCylinderSurface. and if you have a convention for "outward" directionality, then if it's a negative number, we know it's pointing inward (would definitely track flux in both directions and accumulate a positive or negative number, for generality).

[hayakawa16]

I guess I should define directionality of VBType in name, e.g. VBType.InfiniteCylinderSurfaceInNormalDirection and InfiniteCylinderSurfaceOutNormalDirection (that's kind of confusing). How about exactly how it would be calculated, InfiniteCylinderSurfaceDotNormalPositive and InfiniteCylinderSurfaceDotNormalNegative?

[hayakawa16]

I'm going to give this a try. I can always refactor names when we review code.
Thank you very much @dcuccia! This discussion help me tremendously!

[dcuccia]

That would be detector dependent, so defer to what Janaka needs, but recommend re-using as much as we can from existing detectors...

[hayakawa16]

@janakarana, I am going to use your 131 branch (the 131a branch has method b) above trials).

[janakarana]

@hayakawa16] Please go ahead and do any changes necessary. Thanks