Melanin Absorption Coefficient

[Patrice Mieczkowski]

The melanins are considered to be polymers of the basic building blocks shown below. However, the details of the polymerization and the role of protein linkages in the natural melanin complex are not known. Although the widespread belief is that the insoluble eumelanins are highly polymeric cross-linked structures consisting of several hundred monomeric units, Prota et al. (1988) point out that this belief is based on still ambiguous evidence.

The building blocks of eumelanin and pheomelanin. Curly red lines indicate sites of attachment to the extended polymer and possibly to proteins. The details of these attachments in the total complex structure are not known. Click here to see synthesis of melanin from tyrosine or DOPA.

Melanin is synthesized enzymatically at roughly 10-nm granular sites studding the internal walls of the melanosome, a roughly 1-μm diameter organelle. Melanosomes may contain a variable amount of melanin. The melanosomes of the retinal pigmented epithelium (RPE) have a very dense concentration of melanin. Cutaneous melanosomes are variable and may have 1/4th to 1/10th the melanin concentration of the RPE melanosomes. And there are some melanosomes devoid of melanin.

The volume fraction of melanosomes in a particular epithelial layer, such as the cutaneous epidermis or the RPE, can vary. The average epidermal absorption coefficient depends on both the melanosomal μa and the volume fraction (fv) of melansomes in the epidermis. In skin, the volume fraction of melanosomes is estimated to vary as [Jacques 1996]:

The molecular structure of the extended melanin polymer is neither wellcharacterized nor unique, so citing the concentration as [moles/liter]is difficult. There is possibly some degree of protein incorporation inthe polymer, so citing the concentration as [mg/ml] may be misleading.

If one is in interested in the stoichiometric efficiency of photonabsorption by the chromophore monomers in melanin and any subsequentphotochemical reactions, then one would like to know the extinctioncoefficient [cm-1 (moles/liter)-1] for the chromophore monomers incorporated in the extendedmelanin polymer. The concentration (moles/liter)-1 refers to the number density of chromophore monomers that comprise the polymer.

If one is in interested in the effects caused by irradiatingmelanosomes in vivo, then one would like to know the average absorptioncoefficient μa [cm-1]for the interior of a melanosome. For example, the amount of thermalheating of a melanosome by a pulsed laser is of current clinicalinterest due to the various laser treatments of skin and retina. Theamount of photons absorbed by a melanosome is pertinent to oxidativereactions catalyzed by melanosomes exposed to blue or ultravioletlight.

Ifone is interested in the amount of light transport into the skin andout of the skin which is important for dosimetry of laser treatmentsand interpretation of optical spectroscopy and imaging, then one wouldlike to know the optical depth (μad,where d is epidermal thickness) of the epidermis. The epidermis is sothin that its optical effect can be treated as a simple absorptionfilter (epidermal transmission T = exp(-μad) for collimatedbeam normal to skin surface). If one wishes to model the distributionof photons in the epidermis and reflectance from the epidermis usingMonte Carlo simulations, then one desires the average absorptioncoefficient of the epidermis: μa = (Optical depth)/d.

At this time, only an estimate of the ext.coeff of monomers within eumelanin and pheomelanin can be offered. If one assumes that the melanin polymer is composed only of subunits of known molecular weight linked by the most minimal linkages between subunits and ignores any inert mass due to attached protein or optically inert moieties, then one can convert melanin concentration expressed as [mg/ml] into concentration expressed as [moles/liter]. Sarno and Swartz cite the extinction coefficient of eumelanin and pheomelanin expressed as [cm-1 (mg/ml)-1]. Multiplication by the molecular weight (MW [g/mole]) of the monomers changes the units to [cm-1 (moles/liter)-1]:ext.coeff [moles/liter] = (ext.coeff [mg/ml])(MW [g/mole])

Realistic hair should have a minimum of variance between each strand.The shader allows for this by specifying two values, Random Colorand Random Roughness, which remap the specified Melanin/Roughness values tothe range \(Color/Roughness \pm Randomization\%\).

Specify how much the glints are smoothed in the direction of the hair shaft.Too low values will smoothen the hair to the point of looking almost metallic,making glints look like Fireflies; while setting it too high will result in a Lambertian look.

Simulate a shiny coat of fur, by reducing the Roughness to the given factoronly for the first light bounce (diffuse).Range \([0, 1]\) equivalent to a reduction of \([0\%, 100\%]\) of the original Roughness.

Optional factor for modulating the component which is transmitted into the hair,reflected off the backside of the hair and then transmitted out of the hair. Thiscomponent is oriented approximately around the incoming direction, and picks up thecolor of the pigment inside the hair. Keep this 1.0 for physical correctness

This mode defines the color as the quantity andratio of the pigments which are commonly found in hair and fur,eumelanin (prevalent in brown-black hair) and pheomelanin (red hair).The quantity is specified in the Melanin input, and the ratio between them in Melanin Redness.Increasing concentrations darken the hair (the following are with Melanin Redness \(1\)):

Specifies the attenuation coefficient \(\sigma_a\), as applied by the Beer-Lambert law.This mode is intended mainly for technical users who want to use coefficients from the literaturewithout any sort of conversion.

A part of my studies that fascinated me quite a lot was the biological background used in skin shading. Not sure if this aspect receives much love in games (let me know if you actively do use these concepts!), but I can see lots of potential, especially from an authoring point of view.

From [Donner and Jensen 2006]. I will talk about the scattering structures later in the post.Melanin is the pigment that most influences the skin colour and it is mostly found in the upper layer of the skin, the epidermis.
We can identify two types of them; the eumelanin is a dark or brown pigment and the pheomelanin that has a lighter, reddish-yellow colour.
Intuitively, a high concentration of melanin is found in dark skin where it is mostly eumelanin; on the contrary, in lighter skins such as the Asian or Caucasian ones, there is much less melanin and there is an higher percentage of pheomelanin.

Haemoglobin, found at dermis level, is a protein responsible for the transport of oxygen and produces a pink-purple nuance on the skin. Small amounts of heamoglobin correspond to a pale effect on skin colour, while an high concentration makes the skin appear more pink/red.

Wait, do we care about that much biology? As CG community we know that to correctly represent the world we have to study it thoroughly, so it should come at no surprise that to develop skin appearance models, looking at biological parameters can be useful.

[Donner and Jensen 2006] proposed a spectral shading model which permits the manipulation of chromophores via three parameters: Haemoglobin fraction, Melanin Fraction, Melanin type blend (that describe eumelanin/pheomelanin ratio) + they add a parameter for skin oiliness for the specular contribution.

This work is taken forward by [Donner et al. 2008], where they introduce more physiological parameters and make them spatially-varying (whereas in [Donner and Jensen 2006] spatial variation is limited to the use of an albedo modulation texture). This paper is truly great, I am not going deeper into it for the sake of brevity of the post, but check it, it is well worth a read.

But that is not all. Skin colour varies constantly, also very rapidly. Think about it, we blush, we look pale, we get red after some exercise etc. A great model for this variation is proposed by [Jimenez et al. 2010] . Even to a non-biologist like me, it is clear that all of the variations I mentioned are depending on the blood flow and what is in blood that influences most the skin colour? Oh well, our dear Haemoglobin of course! So the great contribution of [Jimenez et al. 2010] is the proposal of a colour appearance model with spatially-varying haemoglobin distribution that allows appearance transfer between characters.

The key observation made to propose this model was that for a wide range of appearances the haemoglobin distribution is close to a Gaussian one. Starting from an acquired or painted neutral haemoglobin map, various emotions or states can be simply modelled with a bias + scale. This way they transform a neutral distribution to any desired combinations:

With the same idea of usual blend shapes. Each blend shape has its own set of scale/bias textures and the weights used for these are the same used for classic animation rigs.
Note that because of the low frequency nature of these info, we can efficiently store scales and biases in low resolution textures, how convenient!

Once we have all our infos about chromophores, [Jimenez et al. 2010] provides us with a great precomputed table that we can use to extract albedo colour from melanin and haemoglobin maps/distributions:

From [Igarashi et al. 2005]Wait! I told you in the dipole post that we can ignore the single scattering! Yes. I did, and I still stand my ground. As I said previously in this post, the epidermis is the main responsible for absorption, but most of the scattering in fact occurs at the dermis (the layer under the epidermis). Here the main scatterers are collagen fibres that scatter in forward direction. These scatterers are so densely packed that the multiple scattering events can be seen as isotropic even if single fibre scattering events are not. And this should explain my claim on the dipole post that it is fine to approximate subsurface scattering as a diffusion phenomenon.

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