B., and Revsbech, N. P. (1995). {\displaystyle {\mu _{a}}} Therefore, we treated the tissue as a homogenous turbid (i.e., light scattering) medium. The ‘Monte Carlo’ is an aquatic plant that originates from Asia, South America, and most prominently in Argentina. is the total interaction coefficient (i.e., the sum of the absorption and scattering coefficients). The Favia speciosa coral had brown/gray tissue which was about 2 mm thick as measured with microsensors (Wangpraseurt et al., 2014a). During the laser measurements no other light was applied. We also decided to use only tissue culture plants in this layout to avoid introducing nasty algaes or unwanted critters. The Monte Carlo results obtained are in good agreement with the experiment result. Monte Carlo simulations are a well-established and versatile approach toward modeling light propagation in tissues. The calibration constant K only affects the magnitude of the fit, not the shape (Tuchin, 2007). Photochem. Measurement of the optical properties of the skull in the wavelength range 650–950 nm. {\displaystyle 2\pi } The analysis was followed for a the center member bar. The model is easily extended for multi-layered media, however. However, because the model was not affected by skeletal absorption, the lowest simulated μa value (μa = 0.01) was assumed representative for the skeleton, which matched known μa values for a range of coral skeletons, i.e., μa = ∼0.01 cm-1 at 600–650 nm (Marcelino et al., 2013). Ser. Sci. A key approach involves the use of optical reflection spectroscopy in combination with radiative transfer modeling of the experimental data with Monte Carlo simulations calculating the photon probability distribution within biological tissues (Wang et al., 1995). Description Usage Arguments Details Value Author(s) References Examples. The general tendency is that such voids reduce the μs’ (Marcelino et al., 2013), which would further support the efficient light propagation of skeletons proposed here. At the same time, intense tissue light scattering leads to a rapid loss in irradiance facilitating the presence of moderate light environments for symbionts close to the skeleton. 86, 247–254. To solve the inverse radiative transfer problem for our two layer model, i.e., the extraction of inherent optical properties based on measured light distributions, we first estimated the bulk optical properties of the coral skeleton. Photosynthetic efficiencies of planktonic free-living Symbiodinium are much lower than in hospite (Enriquez et al., 2005; Stambler and Dubinsky, 2005; Rodriguez-Roman et al., 2006; Brodersen et al., 2014). doi: 10.1007/s11434-007-0514-4, Lichtenberg, M., Larkum, A. W. D., and Kühl, M. (2016). Specifically, we develop a 3D Monte Carlo simulation that is based on the widely used Monte Carlo code of photon propagation for multilayered tissues (Wang et al., 1995). doi: 10.1002/bies.950170411, Teran, E., Mendez, E. R., Enriquez, S., and Iglesias-Prieto, R. (2010). A diffusion theory model of spatially resolved, steady state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo. These findings support earlier suggestions regarding the strong tissue light scattering properties of faviid corals and their role in modulating coral light fields (Kühl et al., 1995; Wangpraseurt et al., 2012, 2014a,b; Brodersen et al., 2014). To keep total energy constant, a Russian roulette technique is often employed for photons below a certain weight threshold. For example, see the movie, where a Monte Carlo simulation of a pencil beam incident on a semi-infinite medium models both the initial ballistic photon flow and the later diffuse propagation. The optical properties of biological tissue offer an exciting approach to biomedical imaging. The major unknown parameters in our model are the refractive index and the anisotropy of scattering, g, describing the relative forward propagation of light via scattering. Monte Carlo Modeling of Photon Propagation Reveals Highly Scattering Coral Tissue Front Plant Sci. The optical properties of the coral tissue were varied over 5 μa values (0.01, 0.056, 0.0316, 1.78, and 10 cm-1) and 5 μs’ values (0.1, 0.562, 3.15, 17.8, and 100 cm-1). These optical properties of the skeleton were then used for the extraction of the optics of coral tissue (see below). 21, 1219–1230. In contrast, the scattering coefficient of the coral skeleton was μs’ = 3.4 cm-1, which facilitated the efficient propagation of light to otherwise shaded coral tissue layers, thus supporting photosynthesis in lower tissues. It is a perfect foreground plant that if given sufficient lighting and nutrients can grow into a thick carpet of green foliage. (2011). Interspecies and spatial diversity in the symbiotic zooxanthellae density in corals from northern south China sea and its relationship to coral reef bleaching. The Monte Carlo simulations were matched to the measurements on the intact coral with a non-linear least squares fitting routine (as above). If g approaches a value of 1 this indicates that the scattering is primarily in the forward direction. Through random interaction with a large set of photons, a characteristic light distribution is obtained that is governed by the optical parameters and the tissue geometry outlined in the model. To understand the recent observation of lateral light transfer in faviid coral tissues and extract its inherent optical properties, the optical data generated in Wangpraseurt et al. doi: 10.1007/s00338-005-0071-8, Iglesias-Prieto, R., Matta, J. L., Robins, W. A., and Trench, R. K. (1992). The calibration constant CALIB was specified as CALIB = K/Mskeleton(2 mm), and the experimental data were calibrated as ϕ(r)skeleton = CALIB Mskeleton(r) (Figure 2). Rep. 6:26599. doi: 10.1038/srep26599, Marcelino, L. A., Westneat, M. W., Stoyneva, V., Henss, J., Rogers, J. D., Radosevich, A., et al. New York, NY: Plenum Press. Med. 44, 231–251. Although symbiont-bearing corals partly rely on heterotrophic energy via particle and prey capture, most (>95%) of their energy demand is covered by endosymbiotic microscopic dinoflagellate algae of the genus Symbiodinum (Falkowski et al., 1984) that carry out photosynthesis within the gastrodermis of the coral tissue. Responses to arbitrary source geometries can be constructed using the method of Green's functions (or convolution, if enough spatial symmetry exists). This technique uses a roulette constant m to determine whether or not the photon will survive. doi: 10.1242/jeb.091116, Wangpraseurt, D., Polerecky, L., Larkum, A. W. D., Ralph, P. J., Nielsen, D. A., Pernice, M., et al. *Correspondence: Daniel Wangpraseurt, daniel.wangpraseurt@bio.ku.dk, Front. Prog. In Photodynamic therapy (PDT) light is used to activate chemotherapy agents. It was further shown that under excess levels of incident irradiance Symbiodinium in aboral tissue layers were able to photosynthesise efficiently compared to Symbiodinium in oral tissue layers, which were strongly photoinhibited under the same levels of incident irradiance (Lichtenberg et al., 2016). SJ, TP, and MK contributed new reagents/analytic tools; DW, SJ, TP, and MK analyzed data; and DW, SJ, and MK wrote the paper. (2010) used slices of skeleton and an integrating sphere while Marcelino et al. All other times, the photon weight is set to 0 and the photon is terminated. Mar. Estimating the daily contribution of carbon from zooxanthellae to coral animal respiration. The disadvantage is that they are computationally and time expensive given that a large number of photons need to be simulated (typically >1 × 106 photons). doi: 10.1007/s003380050249. Falkowski, P. G., Jokiel, P. L., and Kinzie, R. (1990). The fiber-optic microprobes were accurately positioned at and in direct contact with the tissue surface by the aid of a dissecting microscope and the use of the automatic profiling function of the micromanipulator (see Wangpraseurt et al., 2012). Coral Reefs 16, S129–S138. Opt. There are many interesting endogenous contrasts, including absorption from blood and melanin and scattering from nerve cells and cancer cell nuclei. 51, 2702–2710. In the method, local rules of photon transport are expressed as probability distributions which describe the step size of photon movement between sites of photon-tissue interaction and the angles of deflection in a photon's trajectory when a scattering event occurs. Oceanogr. By using a combination of radiative transfer modeling and optical data, we calculated a high reduced scattering coefficient of μs’ = 10 cm-1 at 636 nm for the tissue of a thick-tissued massive coral. The aim of this paper is to provide estimates of the inherent optical properties of coral tissue. With this in mind, we simply need to set the initial position of the photon packet as well as the initial direction. The leaves are small and round with a beautiful bright green coloration that can nicely offset any neutral toned substrate. doi: 10.1364/OPEX.12.000249, Li, S., Yu, K., Shi, Q., Chen, T., Zhao, M., and Zhao, J. Next, the light distribution was simulated for the case where light was uniformly delivered at a 45° direct sun angle. Between z = 0 to 2 mm, the back-reflected light escaping from the tissue adds to the delivered irradiance to yield a fluence rate in water that exceeds 1 cm-2. 92, 331–342. Using Monte Carlo simulations developed for medical tissue optics it is shown that for the investigated faviid coral, the coral tissue was a strongly light scattering matrix with a reduced scattering coefficient of μs’ = 10 cm-1 (at 636 nm). Tuchin, V. (2007). Photosynthetic response to elevated temperature in the symbiotic dinoflagellate Symbiodinium microadriaticum in culture. doi: 10.1364/AO.28.002331, Perrin, C. (2003). (2013) showed that there is a great variability in the magnitude of skeleton scattering and that there are species dependent differences in skeleton scattering, that partly correlate with coral bleaching susceptibility. Fiber-optic probes for small scale measurements of scalar irradiance. U.S.A. 89, 10302–10305. Each photon packet will repeatedly undergo the following numbered steps until it is either terminated, reflected, or transmitted. However, the details of light propagation through corals and the interaction between tissue and skeleton are still unclear, because the inherent optical properties of coral tissues that modulate tissue-light interactions remain unknown. We have provided an estimate of the inherent optical properties of intact massive faviid corals based on radiative transfer modeling of experimental data. Now, we can try using a Monte-Carlo technique instead. The Monte Carlo simulations used the scattering coefficient μs and the assumed g value to calculate the reduced scattering coefficient μs’ = μs × (1-g). doi: 10.1364/JOSA.51.000123, Brodersen, K. E., Lichtenberg, M., Ralph, P. J., Kühl, M., and Wangpraseurt, D. (2014). Limnol. The optical properties of the coral tissue were extracted by assigning the optical properties of the coral skeleton (μa = 0.01 cm-1, μs’ = 3.4 cm-1) and adding the coral tissue layer on top of the skeleton in the Monte Carlo model (Figure 1). Efficient light harvesting in deep-water zooxanthellate corals. 10, 788–792. The best fit of the experimental data (black) was μs’ = 3.4 cm-1 (n = 15 repetitions). Photobiol. These findings from a simple radiative transfer model are in good agreement with actual in vivo measurements of tissue fluence rate gradients in other massive corals (Wangpraseurt et al., 2012, 2014b). Mathematically, μs’ is defined as μs’ = μs (1-g). 5, 149–155. Charlton, T.F. Plant Cell Environ. Intense scattering in the upper tissue layers is followed by rapid light attenuation through the tissue and thus the presence of pronounced vertical light gradients. This typically involves measuring the lateral attenuation of the fluence rate (also called scalar irradiance) for several light source and light detector distances. Sci. Monte Carlo simulation of light distribution in a faviid coral for vertically incident collimated illumination. Temperature-induced bleaching of corals begins with impairment of the CO2 fixation mechanism in zooxanthellae. Soc. Simulations of vertical light propagation (636 nm) through a coral polyp predicted fluence rate maxima reaching about two times the incident just below the tissue surface (Figure 4B). Based on the extracted optical properties of the coral tissue and skeleton, we simulated photon propagation through an intact coral for different angles of incident irradiance. Another useful parameter is the reduced scattering coefficient μs’ which is used to describe light scattering in the diffusional regime, i.e., where significant scattering events have occurred so that light moves by diffusion down photon concentration gradients (Jacques, 2013). [1][2][3][4], This basic approach can itself be parallelized by using multiple GPUs linked together. Here, we used a value of g = 0.9, which is commonly used in tissue optics for light in the visible range (Jacques, 2013). Monte Carlo Plant Care Guide – Planting, Growing and Propagation Written by Michael in Home, Plants Monte Carlo is an aquatic plant that is relatively new to the fish keeping hobby. Our estimates of coral skeleton μs’ values suggest that the 3-D skeleton structure of a massive faviid coral can be compared to other low scattering structures such as bone (∼μs’ = 3.5 cm-1; Firbank et al., 1993). Corals are very efficient at using solar radiation, with photosynthetic quantum efficiencies approaching theoretical limits. 19, 879–888. Symbiont photosynthesis excretes O2 and carbohydrates supporting coral host metabolism and calcification, while the coral host provides a protected environment and metabolic waste products such as inorganic carbon and nutrients that fuel symbiont photosynthesis (Muscatine et al., 1981). doi: 10.1364/AO.49.005032, Falkowski, P. G., Dubinsky, Z., Muscatine, L., and Porter, J. W. (1984). Steve Poland Aquatics 6,217,305 views Squeeze the pot to push out the plant and rock wool. doi: 10.3354/meps117159, Lassen, C., Ploug, H., and Jørgensen, B. Bio-optical modeling of photosynthetic pigments in corals. doi: 10.1364/AO.22.002463, Hatcher, B. G. (1990). doi: 10.1364/AO.49.005032. J. Exp. Dubinsky, Z., and Falkowski, P. (2011). mcxyz.c, a 3D Monte Carlo Simulation of Heterogeneous Tissues. Finally, the 45° angle simulation was repeated, but with the skeleton properties changed to equal the coral tissue properties, as if there was no skeleton but just coral tissue. Biol. After experiments on the live coral, the tissue was removed with an air gun and experiments were repeated with the bare skeleton of the sample under otherwise identical underwater conditions; measurement spots were carefully selected to be similar to areas on the living coral. The idea behind Monte-Carlo techniques is to generate many possible solutions using random numbers and using these to look at the overall results. Future studies should aim at qualifying the simplifications, we have made here regarding the structural complexity of both tissue and skeleton, e.g., by employing non-invasive imaging techniques, such as optical coherence tomography that can gain high-resolution data of tissue structure and scattering properties (Levitz et al., 2004). and the simulations (in absolute units; W cm-2). Presented here is a model of a photon Monte Carlo method in a homogeneous infinite medium. B. Measurements were conducted on the coenosarc, which had a more even topography and less contractile tissue as compared with polyp tissue, thus allowing repeated measurements and more accurate estimates of horizontal light transfer. We will use three Cartesian coordinates to determine position, along with three direction cosines to determine the direction of propagation. Monte-Carlo Burnup Calculation Uncertainty Quantification and Propagation Determination Citation: M.R. The basic dimensions of the individual skeleton corallites were measured with a ruler and determined to be on average about 12 mm in diameter and about 8 mm in depth and with ∼3 mm wide skeletal walls (coenosteum). (A) The 2D distribution of relative 636 nm fluence rate ϕ (z,x) across the model coral (tissue and skeleton). Monte Carlo Simulations provide high accuracy even in strongly light absorbing media and have the advantage that in principle any source geometry can be modeled. 50, 1025–1032. HOWTO estimate parameter-errors using Monte Carlo ... for various real-world reasons you might be using a model-fitting scenario that breaks the chain of error-propagation in some way (might be e.g. The lateral light distribution was mapped along seven positions of increasing distance from the point of light delivery with the aid of a micromanipulator (Märtzhäuser GmbH, Wetzlar, Germany) to ensure accurate positioning of the fiber microprobe relative to the incident light spot. Here, we investigated potential mechanisms underlying such outstanding photosynthetic performance through extracting inherent optical properties of the living coral tissue and skeleton in a massive faviid coral. 51, 123–129. The corallite structure was modeled using a 3D Monte Carlo simulation software routine, termed ‘mcxyz.c’ (Jacques et al., 2013), which uses the basic algorithm underlying the well-known MCML (Monte Carlo multi-layer) program (Wang et al., 1995). PLoS ONE 8:e61492. Trends Ecol. Big Tanks, Big Fish, and Big Rich - Touring Ohio Fish Rescue - Duration: 19:42. The dashed red line indicates the region modeled by the Monte Carlo simulation. When contemplating the layout for our 8 gallon, we kicked around a few ideas on the look we wanted in a ground covering plant. doi: 10.1007/s00338-003-0291-8, Rickelt, L. F., Lichtenberg, M., Trampe, E., and Kühl, M. (2016). Plant Sci., 21 September 2016 (2014a) were used to feed the Monte Carlo simulation. The basic mechanism is initiation, propagation and arrest. The experimental measurements were recorded as measures of radially detected light relative to the 100% signal obtained when the sensor was directly within the beam (Wangpraseurt et al., 2014a). The high reduced scattering coefficient of coral tissue is comparable to the scattering of plant leaves (Ganapol et al., 1998) and human tissues such as muscle (μs’ = 9 cm-1) (Patterson et al., 1989). FIGURE 6. Note that the fluence rate within the living tissue is twice the delivered irradiance (1 cm-2). Featured on Meta Feature Preview: New Review Suspensions Mod UX Quantifying coral optical properties thus has important implications for understanding the ecophysiology of Symbiodinium in hospite. Copyright © 2016 Wangpraseurt, Jacques, Petrie and Kühl. This plant propagates by forming lateral shoots directly on its rhizomes, as well as sending out runners in the tank. And, the polar angle φ is generally assumed to be uniformly distributed between 0 and The in situ light microenvironment of corals. doi: 10.1007/s10661-015-4897-4, Hochberg, E. J., Apprill, A. M., Atkinson, M. J., and Bidigare, R. R. (2006). The fit between experiment and simulation of the coral skeleton was then only based on the best choice of μs’ of the skeleton, which was 3.4 cm-1. Browse other questions tagged monte-carlo uncertainty error-propagation or ask your own question. is the absorption coefficient. We use a well-established method developed in medical tissue optics and apply it to the study of coral optical properties. Light as a source of information and energy in zooxanthellate corals. (2010) developed a Monte Carlo simulation to show that the in vivo light field of Symbiodinium increases exponentially when a coral is bleaching, i.e., expelling the light absorbing elements. doi: 10.1111/j.1365-2486.1996.tb00063.x, Groenhuis, R. A. J., Ferwerda, H. A., and Ten Bosch, J. J. The Monte Carlo is also known as the “New Large Pearl Grass”, it is a light green plant with … (A) The diffuse backscattering properties of skeletons from the coral Porites branneri have been measured and it was shown that the skeleton was highly reflective with an almost isotropic distribution of the backscattered light. Sci. Monte Carlo simulations were run for 5 μa values, assuming μs’ = 0.6 (A), 3.2 (B), and 17.8 cm-1 (C). - Compare the average and uncertainty for the Monte Carlo method with the traditional method. The present study provides a more detailed mechanistic understanding of the recent observations on light propagation in massive thick-tissued corals (Wangpraseurt et al., 2012, 2014a,b) and has important implications for the ecophysiology of corals and Symbiodinium photosynthesis in vivo. Monte Carlo simulations were run for the 5 μs’ values (colored numbers) and for a constant μa = 0.01 cm-1. - The uncertainty in the predicted velocity is rather large. Oceanogr. It was shown that the skeleton of the coral Porites branneri was diffusely backscattering and that such backscattered light can enhance the local irradiance exposure of Symbiodinium (Enriquez et al., 2005). The results suggested that coral tissue was able to scatter light and that such tissue light scattering was found to affect coral photosynthesis at remote areas from the incident light beam (Wangpraseurt et al., 2014a). is a random number and Appl. doi: 10.1364/AO.45.001062, Patterson, M. S., Chance, B., and Wilson, B. C. (1989). A comprehensive physical model for light reflection. 10, 1746–1752. (B) The axial profile down the center of the coral coenosteum ϕ (z) at x = 0 mm. The cnidarian cnidocyte, a hightech cellular weaponry. Image Sci. We present an estimation of the inherent optical properties of intact faviid coral tissues that enables a simulation of light propagation through a simplified coral skeleton and tissue model. (1983). Light transport in biological tissues is described by the radiative transfer equation (RTE), which simplifies Maxwell’s equations as it does not include non-linear properties of light such as interference, polarization and diffraction (Welch and van Gemert, 2011). Further studies on coral skeleton optics have highlighted the role of skeleton scattering in coral bleaching susceptibility. a Lateral light transfer ensures efficient resource distribution in symbiont-bearing corals. This normalization allowed comparison of the data, despite the differences in units between the experimental data (in relative units; a.u.) 25, 175–186. "Conv—convolution for responses to a finite diameter photon beam incident on multi-layered tissues", "Monte Carlo modeling of light transport in tissues", "Optimized radial and angular positions in Monte Carlo modeling", "Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration", "Monte Carlo Simulation of Photon Migration in 3D Turbid Media Accelerated by Graphics Processing Units", "Online object oriented Monte Carlo computational tool for the needs of biomedical optics", https://en.wikipedia.org/w/index.php?title=Monte_Carlo_method_for_photon_transport&oldid=941883703, Creative Commons Attribution-ShareAlike License, This page was last edited on 21 February 2020, at 06:47. Coral Reefs Ecosyst. 49, 5032–5042. The fiber-optic microprobes and laser diode were each mounted on a different micromanipulator (Pyro-Science, Aachen, Germany, and Märtzhäuser, Wetzlar, Germany) and aligned parallel to each other perpendicularly to the coral surface. The weight fraction can then be recorded in an array if an absorption distribution is of interest for the particular study. doi: 10.1111/php.12560, Rodriguez-Roman, A., Hernandez-Pech, X., Thome, P. E., Enriquez, S., and Iglesias-Prieto, R. (2006). Methods Programs 47, 131–146. Bellingham, WA: SPIE Press. Coral reef bleaching: facts, hypotheses and implications. Corals as light collectors: an integrating sphere approach. {"}Authors are permitted to share their accepted manuscripts on a departmental website, personal website (including Facebook), and/or an institutional or subject repository (including ResearchGate) after an embargo period of 12 months. doi: 10.1046/j.1365-3040.1998.00345.x, Kahng, S. E., Hochberg, E. J., Apprill, A., Wagner, D., Luck, D. G., Perez, D., et al. Based on the coral optical properties obtained from the Monte Carlo simulations, the relative fluence rate was modeled at 636 nm within the tissue during mid-day under vertically incident sunlight. Without the intricate coral skeleton elevated temperature in the uppermost tissue depths Zheng,,... That generates the measured lateral attenuation of the skeleton was about three times lower ( ’... Simulate photon transport beginning to understand fish, and Muscatine, L. ( 1993 ) possible solutions using random and! Deep within tissue top of the skeleton thus apparently enabled low but still significant amounts of light to! The fluence rate within the living coral scenario, light penetrated the tissue, our approach relies on estimates the., Porter, J., and most prominently in Argentina use a global coordinate system in tissues Front. Is not exactly correct, the polar angle φ is generally assumed be. The aim of this paper is to provide estimates of the page Moss dwarf. 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