Changes between Version 1 and Version 2 of doc/tec/biomet/uv_basic_model
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- Nov 22, 2018 2:31:36 PM (6 years ago)
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doc/tec/biomet/uv_basic_model
v1 v2 2 2 3 3 Seckmeyer et al. (2013) defined the biologically weighted exposure Exweighted _ [J] as the radiant energy received by exposed body surfaces of a human who stands on a horizontal plane. 4 4 5 Exweighted can be calculated by integrating the spectral radiance weighted with a biological action spectrum and the geometry of a human over all azimuth and zenith angles of the upper hemisphere and the exposure time. The complete equation of Exweighted, considering all dependencies, is complex and the calculation can be quite demanding. Therefore, multiple simplifying assumptions have been made, which are described in detail in Seckmeyer et al. 2013. The simpliffed equation of Exweighted, used in this model, is given as: 5 6 6 7 7 [[Image( expo_equation.png)]]8 [[Image(Bild1.png, 600px)]] 8 9 9 10 where L is the radiance, S the biological action spectrum and A_proj the human geometry. The solid angle dOmega represents the different directions in the sky and is defined as = sin _ d_d' , with _theta as the zenith angle.\\\\ … … 16 17 17 18 18 [[Image(expo_equation.png)]] 19 20 Figure 1.1: Schematic diagram of the quantities radiance (a) and (b) and irradiance (c). In (a) the receiving area dA is oriented normal to the source, while in (b) the angle between the normal of the area and the incident beam is 45°. The diagram (c) visualizes the irradiance, where radiation of any origin is received by the area element dA.\\ 19 [[Image(expo_quantities.png, 800px)]]\\ 20 Figure 1.1: Schematic diagram of the quantities radiance (a) and (b) and irradiance (c). In (a) the receiving area dA is oriented normal to the source, while in (b) the angle between the normal of the area and the incident beam is 45°. The diagram (c) visualizes the irradiance, where radiation of any origin is received by the area element dA.\\\\ 21 21 22 22 == Radiation Input for Exposure Model == 23 24 {{{#!td style="vertical-align:center; text-align:left" 23 25 To calculate the biologically-weighted UV exposure the spectral radiance L is weighted with a biological action spectrum. In this model, the action spectra for erythema, defined by the CIE (1998),and the action spectra for the vitamin D3 synthesis is used. 24 26 25 In Figure 2.1, the simulated (diffuse) sky radiance weighted with the vitamin D3 action spectrum is shown for Hannover on 21 March at solar noon. The radiance in Figure 2.1 is visualized as a polar plot, where the zenith is located in the center and the azimuth angles are marked around the plot. It should be noted, that similar to an astronomical map, the directions of east and west are inverted. 26 27 28 [[Image(expo_equation.png)]] 27 In Figure 2.1, the simulated (diffuse) sky radiance weighted with the vitamin D3 action spectrum is shown for Hannover on 21 March at solar noon. The radiance in Figure 2.1 is visualized as a polar plot, where the zenith is located in the center and the azimuth angles are marked around the plot. It should be noted, that similar to an astronomical map, the directions of east and west are inverted.\\\\ 29 28 30 29 Distribution of vitamin D3-weighted sky radiance in Hannover on 21 March at 31 30 solar noon. The position of the sun is marked with a black asterisk. Please note that the 32 31 high values around the sun position are caused by the high diffuse (scattered) radiation. 32 }}} 33 {{{#!td style="text-align:left;style=width: 50px" 34 [[Image(expo_radiance.png, 500px)]] 35 }}} 33 36 34 37 == Human Geometry == 38 39 {{{#!td style="vertical-align:center; text-align:left" 35 40 For the calculation of the exposure, the human geometry is taken into account. This is done by using projection areas of all uncovered surface areas of the human. For the calculation of the projection areas a, 3D voxel (volumetric pixel) model, segmented from data of a whole-body computed tomography scan of a patient, is used. The person was 38 years old, 176 cm of height and had a weight of 68.9 kg, thus approximately representing an average male adult (Valentin, 2002). 36 In Figure 2.2, a two-dimensional projection of the voxel model is shown for three different viewpoints. Additionally, the projection areas of a human with no clothing, summer clothing and winter clothing are visualized as function of the azimuth and zenith angle in form of polar plots. 41 In Figure 2.2, a two-dimensional projection of the voxel model is shown for three different viewpoints. Additionally, the projection areas of a human with no clothing, summer clothing and winter clothing are visualized as function of the azimuth and zenith angle in form of polar plots.\\\\ 37 42 38 39 [[Image(expo_equation.png)]]40 41 43 Figure 2.2: (a) Projection of the 3D voxel model with winter clothing, visualized for incident angles 30_, 60_ and 85_, with the front turned by 30_ in azimuth direction. Only hands and face are exposed to UV radiation, which is shown in light gray color and clothing shown in dark gray. (b)-(d) projection areas of the 3D voxel model oriented towards 180_/south, as a function of incident and azimuth angles. The minimal projection area in each plot is located in the middle of each picture, representing a view from the zenith at an incident angle of 90_. (b) Projection area of a human with winter clothing. The three asterisks mark the projections shown in (a). (c) Projection area of a human without any clothing, which results in nearly identical projection areas between the front and back of the human. (d) Projection area of a human with summer clothing, where face, hands, neck and arms are exposed.\\ 42 44 }}} 45 {{{#!td style="text-align:left;style=width: 50px" 46 [[Image(Expo_Proj.png, 600px)]] 47 }}} 43 48 44 49 … … 62 67 * UV radiation reflected from the ground can be neglected due to low albedo in this wavelength region. 63 68 * The reflectivity of the surface materials of the detected obstructions is low in the UV wavelength region and can be neglected 69 70 ==== References: ==== 71 - Seckmeyer, G., Schrempf, M., Wieczorek, A., Riechelmann, S., Graw, K., Seckmeyer, S., and Zankl, M.: A Novel Method to Calculate Solar UV Exposure Relevant to Vitamin D Production in Humans, Photochem. Photobiol., 89(4), 974-983, DOI: 10.1111/php.12074., 2013. 72 - Schrempf, M., Thuns, N., Lange, K., and Seckmeyer, G.: Einuss der Verschattung auf die Vitamin-D-gewichtete UV-Exposition eines Menschen, Aktuelle Derm, DOI: 10.1055/s-0043-105258., 2017. 73 - Schrempf, M., Thuns, N., Lange, K., and Seckmeyer, G.: Impact of Orientation on the Vitamin D Weighted Exposure of a Human in an Urban Environment, Int. J. Environ. Res. Public Health, 14(8), 920, DOI: 10.3390/ijerph14080920., 2017.\\
