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| {{Context|date=October 2009}}
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| '''Hybrid Theory''' for photon transport in tissue uses the advantages and eliminates the deficiencies of both the '''Monte Carlo''' method and the '''Diffusion Theory''' for photon transport to model photons traveling through tissue both accurately and efficiently.
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| ==MCML (Monte Carlo Modeling of Light Transportation in Multi-Layered Medium)==
| | Next - GEN Gallery is a full incorporated Image Gallery plugin for Word - Press which has a Flash slideshow option. Online available for hiring are most qualified, well knowledgeable and talented Wordpress developer India from offshore Wordpress development services company. Change the site's theme and you have essentially changed the site's personality. If you have any type of inquiries relating to where and ways to make use of [http://www.lmn3p.com//czb wordpress dropbox backup], you can contact us at our own page. After confirming the account, login with your username and password at Ad - Mob. In the most current edition you can customize your retailer layout and display hues and fonts similar to your site or blog. <br><br>Always remember that an effective linkwheel strategy strives to answer all the demands of popular search engines while reacting to the latest marketing number trends. Some of the Wordpress development services offered by us are:. Our Daily Deal Software plugin brings the simplicity of setting up a Word - Press blog to the daily deal space. Being able to help with your customers can make a change in how a great deal work, repeat online business, and referrals you'll be given. Aided by the completely foolproof j - Query color selector, you're able to change the colors of factors of your theme a the click on the screen, with very little previous web site design experience. <br><br>But before choosing any one of these, let's compare between the two. To sum up, ensure that the tactics are aiming to increase the ranking and attracting the maximum intended traffic in the major search engines. If Gandhi was empowered with a blogging system, every event in his life would have been minutely documented so that it could be recounted to the future generations. Every single Theme might be unique, providing several alternatives for webpage owners to reap the benefits of in an effort to instantaneously adjust their web page appear. " Thus working with a Word - Press powered web application, making any changes in the website design or website content is really easy and self explanatory. <br><br>The disadvantage is it requires a considerable amount of time to set every thing up. I didn't straight consider near it solon than one distance, I got the Popup Ascendancy plugin and it's up and lengthways, likely you make seen it today when you visited our blog, and I yet customize it to fit our Thesis Wound which gives it a rattling uncomparable visage and search than any different popup you know seen before on any added journal, I hump arrogated asset of one of it's quatern themes to make our own. re creating a Word - Press design yourself, the good news is there are tons of Word - Press themes to choose from. The most important plugins you will need are All-in-One SEO Pack, some social bookmarking plugin, a Feedburner plugin and an RSS sign up button. It does take time to come up having a website that gives you the much needed results hence the web developer must be ready to help you along the route. <br><br>Someone with a basic knowledge of setting up a website should be able to complete the process in a couple of minutes however even basic users should find they are able to complete the installation in around 20 minutes by following the step by step guide online. Here's a list of some exciting Word - Press features that have created waves in the web development industry:. While deciding couple should consider the expertise of the doctor,clinics success rate,the costs of fertility treatment,including fertility tests and IVF costs and overall ones own financial budget. And, it is better that you leave it on for the duration you are writing plugin code. Verify whether your company has a team of developers or programmers having hands-on experience and knowledge about all Word - Press concepts. |
| The [[Monte Carlo method for photon transport|MCML]] is a numerical way to simulate photon transport in biological tissue. Each photon packet follows a random walk with persistence, where the direction of each step dependent on the direction of the previous step. By averaging multiple independent random walks, MCML estimates the ensemble-averaged quantities such as reflectance, transmittance, absorption, and fluence.
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| Briefly, a packet of photon is first launched into the biological tissue. The parameters of photon transport, including the step size and deflection angle due to scattering, are determined by random sampling from probability distributions. A fraction of weight, determined by the scattering and absorption coefficients is deposited at the interaction site. The photon packet continues propagating until the weight left is smaller than a certain threshold. If this packet of photon hits the boundary during the propagation, it is either reflected or transmitted, determined by a pseudorandom number. Statistically sufficient numbers of photon packets must be simulated to obtain the expected values accurately.<ref name = Wang_BioMedBooK>{{cite book |author=LV Wang and HI Wu |title=Biomedical Optics|publisher=Wiley |year=2007|isbn=978-0-471-74304-0}}</ref>
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| '''Advantages and Disadvantages'''
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| This [[Monte Carlo method]] is rigorous and flexible. However, because of its statistical nature, this method requires tracking a large number of photon packets, making it computationally expensive.
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| ==Diffusion Theory==
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| The [[Radiative transfer equation and diffusion theory for photon transport in biological tissue|Diffusion Theory]] is an approximation of the radiative transfer equation (RTE), and an analytical way to simulate photon transport. As such, it has the ability to model photon propagation through tissue quickly.
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| As an example, one way to attain a solution for a pencil beam that is vertically incident on a semi-infinite homogeneous scattering medium is by taking three approximation steps as follows:
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| *The anisotropically scattering medium is converted to an isotropically scattering medium. That is, the scattering coefficient is scaled by <math>1-g</math>, where <math>g</math> is the anisotropy. The anisotropy <math>g</math> is then set to zero;
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| *The unit-power pencil beam is converted into an equivalent isotropic point source at a depth that is equal to the transport mean free path, with a power equal to the transport albedo;
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| *The boundary effect of the scattering medium is removed by adding an image source to satisfy the boundary condition.<ref name="Wang_BioMedBooK"/>
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| '''Advantages and Disadvantages'''
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| Diffusion Theory is more computationally efficient than MCML. However, it is also less accurate than MCML near the source and boundaries.
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| ==Hybrid Theory==
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| The Hybrid Theory combines the Diffusion Theory and the Monte Carlo method in order to increase accuracy near the source and boundaries while reducing computation time. In the previous example for the Diffusion Theory, a semi-infinite scattering medium with only one boundary was assumed. If the geometry is a slab, the second boundary must be taken into account. The fluence rate at the extrapolated boundaries must be approximately 0. Using an array of image sources fulfills this boundary condition. The extrapolated boundary is located at distance <math>z_b = 2C_RD</math>. The <math>z</math> coordinates for the source pairs are <math>z_{\pm i} = -z_b + 2i(d+2z_b)\pm(z'+z_b)</math> where <math>z^'</math> is the <math>z</math> coordinate for the point source and <math>d</math> is the slab thickness. Only 2-3 pairs are usually necessary to achieve good accuracy.
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| [[File:Hybrid Slab Geometry1.png|thumb|400 px|right|Figure 1: Slab geometry and Source pairs for Hybrid Theory]]
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| A Monte Carlo approach can be used to make up for the Diffusion Theory's inherently poor accuracy near the boundaries. As mentioned before, the Monte Carlo simulation is time consuming. When a photon packet is within a critical depth <math>z_c</math> the Monte Carlo simulation tracks all packets but within the center region the photon packet is transformed to an isotropic source and subsequently treated with Diffusion Theory. Just like in the Monte Carlo simulation, any photon packet that gets reemitted is added to the diffuse reflectance <math>R_{MC}</math>.
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| When a photon packet is scattered into the center zone <math>z_c \le z \le -z_c</math>, it is conditionally converted to an isotropic point source. The photon packet must still be in the center region after one transport mean free path <math>l_t'</math> along the direction of the photon packet propagation for it to be converted to a point source, otherwise the Monte Carlo simulation continues. Before the conversion to an isotropic point source, the photon packet reduces its weight due to its interaction with the scattering medium. The resulting weight is recorded as a source function <math>S(r, z)</math>. This is the accumulated weight distribution which can be converted to relative source density function <math>S_d</math> by:
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| :<math> S_d [i_r, i_z] = \frac{S[i_r, i_z]}{N\Delta V(i_r)}</math> where <math>\Delta V</math> is the grid volume and <math>N</math> is the number of photon packets.
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| The additional diffuse reflectance <math>R_{DT}</math> from the sources is calculated as:
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| :<math>R_{DT}(r) = \int_{0}^{\infty}\int_{0}^{\infty}\int_{0}^{2\pi}S_d(r',z')R(r,0,0;r',\phi',z')r'd\phi'dr'dz'</math> where <math>R</math> is from the diffusion theory approximation for a slab and <math>\phi</math> is the azimuthal angle. The total diffuse reflectance would be <math>R_{DT}</math> and <math>R_{MC}</math> added together.<ref name="Wang_BioMedBooK"/>
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| ===Advantages over Diffusion Theory and MCML===
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| A trade-off between simulation speed and accuracy exists; choosing a critical depth <math>z_c</math> becomes the deciding factor for simulation speed with a deeper critical depth resulting in slower times due to packets needing to be tracked for a longer distance before the transition to diffusion theory.<ref name=Hybrid_Theory>{{cite journal |doi=10.1364/AO.39.002235 |author=Alexandrakis G., Farrell TJ., and Patterson MS. |title=Monte Carlo diffusion hybrid model for photon migration in a two-layer turbid medium in the frequency domain|journal=[[Applied Optics]]|volume=39 |issue=13|pages=2235–2244|year=2000}}</ref>
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| Advantages
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| *More accurate than the Diffusion Theory, especially near the source
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| *Faster than the Monte Carlo method
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| {|style="margin: 1em auto 1em auto"| class="wikitable" border="1"| style="margin: 1em auto 1em auto"
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| |+ User times for Monte Carlo (MC) method and Hybrid model (H) using IBM ThinkPad T43 with 1.86 GHz processor and 1.5 GB RAM
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| |-
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| ! <math>n_{rel}</math>
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| ! <math>d(cm)</math>
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| ! <math>\mu_{a}(cm^{-1})</math>
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| ! <math>T_{MC}(s)</math>
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| ! <math>T_H(s)</math>
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| ! <math>T_{MC}(s)/T_H(s)</math>
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| |-
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| | width="100pt" |1.37
| |
| | width="100pt"|3
| |
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| |
| | width="100pt"|7537
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| | 1.37
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| | 4924
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| | 25
| |
| | 189
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| | 2600
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| | 104
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| | 91
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| | 1051
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| | 41
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| |-
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| |}
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| <center>Where <math>n_{rel}</math> is the relative refraction coefficient, <math>d</math> is the slab thickness, <math>\mu_a</math> is the absorption coefficient, and <math>T</math> is the user time.</center>
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| ===Comparisons Between Theories===
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| <gallery widths="300px" heights="300px" align=center>
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| Image:Hb11.jpg|Comparisons between the Diffusion Theory and the Monte Carlo method in terms of the fluence in response to an isotropic point source.
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| Image:Hb22.jpg|Relative errors between the Diffusion Theory and the Monte Carlo method.
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| </gallery> | |
| <gallery widths="300px" heights="300px" align=center> | |
| Image:Hb33.JPG|Comparisons between the pure Monte Carlo method and the Hybrid Model in terms of the diffuse reflectance in response to a pencil beam.
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| Image:Hb4.JPG|Relative errors between the pure Monte Carlo method and the Hybrid Model. </gallery>
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| <gallery widths="300px" heights="300px" align=center>
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| Image:Hb55.jpg|Diffuse reflectance of the Hybrid Model in response to a pencil beam when the critical depth is set to 0.01 cm, 0.03 cm, 0.05 cm and 0.1 cm.
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| Image:Hb7.JPG|Relative errors with different critical depths for the Hybrid Model.
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| </gallery>
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| <gallery widths="300px" heights="300px" align=center>
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| Image:Hb7.jpg|Comparisons between the Monte Carlo method and the Hybrid Model in terms of diffuse reflectance in response to a pencil beam when the critical depth is set to 0.1 cm. The absorption coefficient <math>\mu_a</math> varies among 0.1, 1, and 10 <math>cm^{-1}</math>.
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| </gallery>
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| ==References==
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| {{reflist}}
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| [[Category:Scientific simulation software]]
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| [[Category:Optical software]]
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Next - GEN Gallery is a full incorporated Image Gallery plugin for Word - Press which has a Flash slideshow option. Online available for hiring are most qualified, well knowledgeable and talented Wordpress developer India from offshore Wordpress development services company. Change the site's theme and you have essentially changed the site's personality. If you have any type of inquiries relating to where and ways to make use of wordpress dropbox backup, you can contact us at our own page. After confirming the account, login with your username and password at Ad - Mob. In the most current edition you can customize your retailer layout and display hues and fonts similar to your site or blog.
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