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| {{refimprove|date=June 2010}}
| | Thin people can often find out if they have cellulite by pinching the skin in between the thumb and forefinger. We now need to put extra effort into keeping ourselves fit and active. Have you ever thought about having a cellulite treatment. Yet, the normal treatment time ranges between 30 to 90 minutes. However, these substances are mainly concentrated in the beneath comestible locations of the fruits, like, the axis of pineapple and the leaves of papaya. <br><br>Instead of fried meals, you'll be able to replace it with a grilled or baked preparation. Increasing water intake also helps in getting less cellulite around your legs. Once the damaged fat cells are there, you still have to burn them and no improvement really occurs. In their fight against breast cancer many women lost their life and many are still standing in front of this disease. However, there are a few proven ways to get rid of cellulite such as diet and exercise changes, as well as skin brushing. <br><br>Older skin, like older muscles, needs protein, especially soy protein with much less weight, for toning and firming. If you know that, it'll be easier to help you get rid of cellulite the vegetarian way. Water helps carry those toxins out of your body and the more water you drink the less likely your stool will be dry, hard and immovable. Luckily, that desire can be completely fulfilled with cellulite exercises. Normal water is beneficial because it improves metabolic rate and it's also good for the epidermis. <br><br>ALTA CARE Laboratoires is an independent multinational company founded by pharmacists and doctors working in the European Union. Benefits of home cellulite reduction are that treatments are generally inexpensive to administer and won’t cost as much as surgical treatments or spa treatments. No wonder, many people are turning to the Hydroxatone best anti aging products to rediscover radiant and glowing skin. Smoking is a terrible habit that can damage your health on various levels. However, below you will find some advice in this regard which will calm you down. <br><br>Actual reduction results vary from patient to patient, and are dependent on many factors, including but not limited to: the number and frequency of treatment sessions, area(s) being treated, amount body fat etc. To start off, you need to make a daily dietary menu to follow so you will consistently eat the right foods that will help you remove fat from your skin tissue. Flour, sugar, and foods high in carbohydrates contribute to cellulite more than most people realize. Well ladies, summer is nearly here which means it''. Certain devices such as vibrator and hot-packs have favorable results in reducing cellulite from the thighs.<br><br>Should you have just about any issues relating to in which as well as the best way to make use of [http://www.samfinds.info/sitemap/ can you get rid of cellulite], you possibly can call us from our website. |
| {{Distinguish|Goldman–Hodgkin–Katz flux equation}}
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| The '''Goldman–Hodgkin–Katz voltage equation''', more commonly known as the '''Goldman equation''', is used in cell membrane [[physiology]] to determine the [[reversal potential]] across a cell's membrane, taking into account all of the ions that are permeant through that membrane.
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| The discoverers of this are [[David E. Goldman]] of [[Columbia University]], and the English Nobel laureates [[Alan Lloyd Hodgkin]] and [[Bernard Katz]].
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| ==Equation for monovalent ions==
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| The GHK voltage equation for <math>M</math> monovalent positive [[ion]]ic species and <math>A</math> negative:
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| :<math>E_{m} = \frac{RT}{F} \ln{ \left( \frac{ \sum_{i}^{N} P_{M^{}_{i}}[M^{+}_{i}]_\mathrm{out} + \sum_{j}^{M} P_{A^{-}_{j}}[A^{-}_{j}]_\mathrm{in}}{ \sum_{i}^{N} P_{M^{+}_{i}}[M^{+}_{i}]_\mathrm{in} + \sum_{j}^{M} P_{A^{-}_{j}}[A^{-}_{j}]_\mathrm{out}} \right) }</math>
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| This results in the following if we consider a membrane separating two <math>\mathrm{K}_{x}\mathrm{Na}_{1-x}\mathrm{Cl}</math>-solutions:
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| :<math>E_{m, \mathrm{K}_{x}\mathrm{Na}_{1-x}\mathrm{Cl} } = \frac{RT}{F} \ln{ \left( \frac{ P_{Na^{+}}[Na^{+}]_\mathrm{out} + P_{K^{+}}[K^{+}]_\mathrm{out} + P_{Cl^{-}}[Cl^{-}]_\mathrm{in} }{ P_{Na^{+}}[Na^{+}]_\mathrm{in} + P_{K^{+}}[K^{+}]_{\mathrm{in}} + P_{Cl^{-}}[Cl^{-}]_\mathrm{out} } \right) }</math>
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| It is "[[Nernst]]-like" but has a term for each permeant ion:
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| :<math>E_{m,Na} = \frac{RT}{F} \ln{ \left( \frac{ P_{Na^{+}}[Na^{+}]_\mathrm{out}}{ P_{Na^{+}}[Na^{+}]_\mathrm{in}} \right) }=\frac{RT}{F} \ln{ \left( \frac{ [Na^{+}]_\mathrm{out}}{ [Na^{+}]_\mathrm{in}} \right) }</math>
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| *<math>E_{m}</math> = The membrane potential (in [[volt]]s, equivalent to [[joule]]s per [[coulomb]])
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| *<math>P_\mathrm{ion}</math> = the permeability for that ion (in meters per second)
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| *<math>[ion]_\mathrm{out}</math> = the extracellular concentration of that ion (in [[Mole (unit)|moles]] per cubic meter, to match the other [[SI]] units)
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| *<math>[ion]_\mathrm{in}</math> = the intracellular concentration of that ion (in moles per cubic meter)
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| *<math>R</math> = The [[ideal gas constant]] (joules per [[kelvin]] per mole)
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| *<math>T</math> = The temperature in kelvins
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| *<math>F</math> = [[Faraday constant|Faraday's constant]] (coulombs per mole)
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| The first term, before the parentheses, can be reduced to 61.5 mV for calculations at human body temperature (37 °C)
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| :<math>E_{X} = 61.5 \ \mathrm{mV} \log{ \left( \frac{ [X^{+}]_\mathrm{out}}{ [X^{+}]_\mathrm{in}} \right) } = -61.5 \ \mathrm{mV} \log{ \left( \frac{ [X^{-}]_\mathrm{out}}{ [X^{-}]_\mathrm{in}} \right) }</math>
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| Note that the ionic charge determines the sign of the membrane potential contribution.
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| === Calculating the first term ===
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| Using <math>R \approx \frac{8.3 \ \mathrm{J}}{\mathrm{K} \cdot \mathrm{mol}}</math>, <math>F \approx \frac{9.6 \times 10^4 \ \mathrm{J}}{\mathrm{mol} \cdot \mathrm{V}}</math>, (assuming body temperature) <math>T=37 \ ^\circ \mathrm{C}=310 \ \mathrm{K}</math> and the fact that one volt is equal to one joule of energy per coulomb of charge, the equation
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| :<math>E_X = \frac{RT}{zF} \ln \frac {X_o}{X_i}</math>
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| can be reduced to
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| :<math> \begin{align}
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| E_X & \approx \frac{.0267 \ \mathrm{ V}}{z} \ln \frac {X_o}{X_i} \\
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| & = \frac{26.7 \ \mathrm{ mV}}{z} \ln \frac {X_o}{X_i} \\
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| & \approx \frac{61.5 \ \mathrm{ mV} }{z} \log \frac {X_o}{X_i} & \text{ since } \ln 10 \approx 2.30 \end{align}</math>
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| ==Derivation==
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| Goldman's equation seeks to determine the [[voltage]] ''E''<sub>''m''</sub> across a membrane.<ref>{{cite book | author = Junge D | year = 1981 | title = Nerve and Muscle Excitation | edition = 2nd edition | publisher = Sinauer Associates | location = Sunderland, MA | isbn = 0-87893-410-3 | pages = 33–37}}</ref> A [[Cartesian coordinate system]] is used to describe the system, with the ''z'' direction being perpendicular to the membrane. Assuming that the system is symmetrical in the ''x'' and ''y'' directions (around and along the axon, respectively), only the ''z'' direction need be considered; thus, the voltage ''E''<sub>''m''</sub> is the [[integral]] of the ''z'' component of the [[electric field]] across the membrane.
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| According to Goldman's model, only two factors influence the motion of ions across a permeable membrane: the average electric field and the difference in ionic [[concentration]] from one side of the membrane to the other. The electric field is assumed to be constant across the membrane, so that it can be set equal to ''E''<sub>''m''</sub>/''L'', where ''L'' is the thickness of the membrane. For a given ion denoted A with valence ''n''<sub>A</sub>, its [[flux]] ''j''<sub>A</sub>—in other words, the number of ions crossing per time and per area of the membrane—is given by the formula
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| :<math>
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| j_{\mathrm{A}} = -D_{\mathrm{A}}
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| \left( \frac{d\left[ \mathrm{A}\right]}{dz} - \frac{n_{\mathrm{A}}F}{RT} \frac{E_{m}}{L} \left[ \mathrm{A}\right] \right)
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| </math>
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| The first term corresponds to [[Fick's law of diffusion]], which gives the flux due to [[diffusion]] down the [[concentration]] gradient, i.e., from high to low concentration. The constant ''D''<sub>A</sub> is the [[diffusion constant]] of the ion A. The second term reflects the [[flux]] due to the electric field, which increases linearly with the electric field; this is a [[Einstein relation (kinetic theory)|Stokes-Einstein relation]] applied to [[electrophoresis|electrophoretic mobility]]. The constants here are the [[electric charge|charge]] [[valence (chemistry)|valence]] ''n''<sub>A</sub> of the ion A (e.g., +1 for K<sup>+</sup>, +2 for Ca<sup>2+</sup> and −1 for Cl<sup>−</sup>), the [[temperature]] ''T'' (in [[kelvin]]s), the molar [[gas constant]] ''R'', and the [[Faraday (unit)|faraday]] ''F'', which is the total charge of a mole of [[electron]]s.
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| Using the mathematical technique of [[separation of variables]], the equation may be separated
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| :<math>
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| \frac{d\left[ \mathrm{A}\right]}{-\frac{j_{\mathrm{A}}}{D_{\mathrm{A}}} + \frac{n_{\mathrm{A}}FE_{m}}{RTL} \left[ \mathrm{A}\right]} = dz
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| </math>
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| Integrating both sides from ''z''=0 (inside the membrane) to ''z''=''L'' (outside the membrane) yields the solution
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| :<math>
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| j_{\mathrm{A}} = \mu n_{\mathrm{A}} P_{\mathrm{A}}
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| \frac{\left[ \mathrm{A}\right]_{\mathrm{out}} - \left[ \mathrm{A}\right]_{\mathrm{in}} e^{n_{}\mu} }{1 - e^{n_{}\mu }}
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| </math>
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| where μ is a dimensionless number
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| :<math>
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| \mu = \frac{F E_{m}}{RT}
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| </math>
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| and ''P''<sub>A</sub> is the ionic permeability, defined here as
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| :<math>
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| P_{\mathrm{A}} = \frac{D_{\mathrm{A}}}{L}
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| </math>
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| The [[electric current]] [[current density|density]] ''J''<sub>A</sub> equals the charge ''q''<sub>A</sub> of the ion multiplied by the flux ''j''<sub>A</sub>
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| :<math>
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| J_{A} = q_{\mathrm{A}} j_{\mathrm{A}}
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| </math>
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| There is such a current associated with every type of ion that can cross the membrane. By assumption, at the Goldman voltage ''E''<sub>''m''</sub>, the total current density is zero
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| :<math>
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| J_{tot} = \sum_{A} J_{A} = 0
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| </math>
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| If all the ions are monovalent—that is, if all the ''n''<sub>A</sub> equal either +1 or -1—this equation can be written
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| :<math>
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| w - v e^{\mu} = 0
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| </math>
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| whose solution is the Goldman equation
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| :<math>
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| \frac{F E_{m}}{RT} = \mu = \ln \frac{w}{v}
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| </math> | |
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| where
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| :<math>
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| w = \sum_{\mathrm{cations\ C}} P_{\mathrm{C}} \left[ \mathrm{C}^{+} \right]_{\mathrm{out}} +
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| \sum_{\mathrm{anions\ A}} P_{\mathrm{A}} \left[ \mathrm{A}^{-} \right]_{\mathrm{in}}
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| </math>
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| :<math>
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| v = \sum_{\mathrm{cations\ C}} P_{\mathrm{C}} \left[ \mathrm{C}^{+} \right]_{\mathrm{in}} +
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| \sum_{\mathrm{anions\ A}} P_{\mathrm{A}} \left[ \mathrm{A}^{-} \right]_{\mathrm{out}}
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| </math>
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| If divalent ions such as [[calcium]] are considered, terms such as ''e''<sup>2μ</sup> appear, which is the [[square (algebra)|square]] of ''e''<sup>μ</sup>; in this case, the formula for the Goldman equation can be solved using the [[quadratic formula]].
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| ==See also==
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| * [[Bioelectronics]]
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| * [[Cable theory]]
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| * [[GHK current equation]]
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| * [[Hindmarsh-Rose model]]
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| * [[Hodgkin-Huxley model]]
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| * [[Morris-Lecar model]]
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| * [[Nernst equation]]
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| * [[Saltatory conduction]]
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| ==References==
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| {{reflist|1}}
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| ==External links==
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| * [http://www.nernstgoldman.physiology.arizona.edu/ Nernst/Goldman Equation Simulator]
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| * [http://www.physiologyweb.com/calculators/ghk_equation_calculator.html Goldman-Hodgkin-Katz Equation Calculator]
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| * [http://thevirtualheart.org/GHKindex.html Nernst/Goldman interactive Java applet] The membrane voltage is calculated interactively as the number of ions are changed between the inside and outside of the cell.
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| * [http://jgp.rupress.org/content/27/1/37.full.pdf+html Potential, Impedance, and Rectification in Membranes by Goldman (1949)]
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| [[Category:Physical chemistry]]
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| [[Category:Electrochemical equations]]
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Thin people can often find out if they have cellulite by pinching the skin in between the thumb and forefinger. We now need to put extra effort into keeping ourselves fit and active. Have you ever thought about having a cellulite treatment. Yet, the normal treatment time ranges between 30 to 90 minutes. However, these substances are mainly concentrated in the beneath comestible locations of the fruits, like, the axis of pineapple and the leaves of papaya.
Instead of fried meals, you'll be able to replace it with a grilled or baked preparation. Increasing water intake also helps in getting less cellulite around your legs. Once the damaged fat cells are there, you still have to burn them and no improvement really occurs. In their fight against breast cancer many women lost their life and many are still standing in front of this disease. However, there are a few proven ways to get rid of cellulite such as diet and exercise changes, as well as skin brushing.
Older skin, like older muscles, needs protein, especially soy protein with much less weight, for toning and firming. If you know that, it'll be easier to help you get rid of cellulite the vegetarian way. Water helps carry those toxins out of your body and the more water you drink the less likely your stool will be dry, hard and immovable. Luckily, that desire can be completely fulfilled with cellulite exercises. Normal water is beneficial because it improves metabolic rate and it's also good for the epidermis.
ALTA CARE Laboratoires is an independent multinational company founded by pharmacists and doctors working in the European Union. Benefits of home cellulite reduction are that treatments are generally inexpensive to administer and won’t cost as much as surgical treatments or spa treatments. No wonder, many people are turning to the Hydroxatone best anti aging products to rediscover radiant and glowing skin. Smoking is a terrible habit that can damage your health on various levels. However, below you will find some advice in this regard which will calm you down.
Actual reduction results vary from patient to patient, and are dependent on many factors, including but not limited to: the number and frequency of treatment sessions, area(s) being treated, amount body fat etc. To start off, you need to make a daily dietary menu to follow so you will consistently eat the right foods that will help you remove fat from your skin tissue. Flour, sugar, and foods high in carbohydrates contribute to cellulite more than most people realize. Well ladies, summer is nearly here which means it. Certain devices such as vibrator and hot-packs have favorable results in reducing cellulite from the thighs.
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