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| [[Image:step signal.png|thumb|right|452px|Examples of signals that may contain steps corrupted by noise. (a) [[Copy-number variation|DNA copy-number ratios]] from [[DNA microarray|microarray]] data, (b) [[cosmic ray]] intensity from a [[neutron monitor]], (c) rotation speed against time of [[Rhodobacter sphaeroides|R. Sphaeroides]] [[Molecular motors|flagellar motor]], and (d) red pixel intensity from a single scan line of a digital image.]]
| | Physicians and scientists from the Irvine university of California have lately discovered a new method of lowering blood pressure. To check up additional information, consider peeping at: [http://www.feedbooks.com/user/1296171/profile account]. This method is based on electroacupuncture, which appears to have a considerable effect in lowering blood pressure. The technique has been tested on rats, by inducing low electric stimulation at the front of their legs, and their blood"s pressure following the treatment was 40 percent lower than before(their blood pressure had been artificially improved prior to). This opens new doors for hypertension remedy, perhaps it will even replace the conventional medical remedies with this ancient strategy.<br><br>These are all the approaches that had been tested :<br><br>Needles had been inserted into:<br><br>-pericardium 5-6, and they were rotated every single ten to thirty minutes. Get additional resources on an affiliated site by clicking [http://www.dipity.com/urgentcarenoise257 Klinge Mayo]. While this procedure was performed, the rats" blood pressure was becoming raised by doctors.<br><br>-the rats" forelimbs, without any stimulation or twist, for 30 minutes.<br><br>Also, the pericardium five-6 was electrically stimulated with frequencies ranging from 2 to one hundred hertz.<br><br>Throughout these tests the alterations in blood pressure had been continuously monitored, and the outcomes cautiously recorded. The most productive in lowering blood pressure were these tests which involved manual and electrical acupuncture, which had critical effects in lowering blood pressure, lasting up to a single hour, and ranging from 33 to 36 percent. [http://www.iamsport.org/pg/bookmarks/walkincliniczak/read/26823093/most-of-us-need-these-vitamins-vitamin-b12-and-folacin Worth Reading] includes more about why to mull over this thing. The finest outcomes had been recorded at the rats which had been stimulated by electroacupuncture, specially at these treated at the electroacupuncture frequency of two hertz.<br><br>Nevertheless, the finest results were recorded at the rats stimulated at the heart (6-7) and stomach (36-37). Their blood pressure was lowered up to 44 percent for the heart stimulation, and 36 percent for the stomach.<br><br>An important observation that doctors made was that this electroacupuncture treatment can only lower blood pressure for the hypertensive individuals, it has no impact for healthful people.<br><br>We can only that these remedies involving acupuncture will soon be readily available to everyone, because they represent a very excellent way to lower blood pressure.<br><br>If you have any thoughts concerning wherever and how to use health books - [http://hungryspoof8873.jigsy.com just click the following web page] -, you can make contact with us at our own webpage. |
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| In [[statistics]] and [[signal processing]], '''step detection''' (also known as '''step smoothing''', '''step filtering''', '''shift detection''', '''jump detection''' or '''[[edge detection]]''') is the process of finding abrupt changes (steps, jumps, shifts) in the mean level of a [[time series]] or signal. It is usually considered as a special case of the statistical method known as [[change detection]] or change point detection. Often, the step is small and the time series is corrupted by some kind of [[noise]], and this makes the problem challenging because the step may be hidden by the noise. Therefore, statistical and/or signal processing algorithms are often required.
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| The step detection problem occurs in multiple scientific and engineering contexts, for example in [[statistical process control]]<ref name="Page1955">{{cite journal
| |
| | author=E.S. Page
| |
| | title=A test for a change in a parameter occurring at an unknown point
| |
| | journal=Biometrika
| |
| | volume=42
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| | year=1955
| |
| | pages=523−527
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| }}</ref> (the [[control chart]] being the most directly related method), in exploration [[geophysics]] (where the problem is to segment a [[Well logging|well-log]] recording into [[Stratigraphy|stratigraphic zones]]<ref name="Gill1970"/>), in [[genetics]] (the problem of separating [[microarray]] data into similar [[Copy-number variation|copy-number]] regimes<ref name="Snijders">{{cite journal
| |
| | first = A.M.
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| | last = Snijders
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| | coauthors = et al.
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| | year = 2001
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| | title = Assembly of microarrays for genome-wide measurement of DNA copy number
| |
| | journal = Nature Genetics
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| | volume = 29
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| | pages = 263–264
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| | doi = 10.1038/ng754
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| | issue=3
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| | pmid = 11687795
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| }}</ref>), and in [[biophysics]] (detecting state transitions in a [[molecular machine]] as recorded in time-position traces<ref name="">{{cite journal
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| | first = Y.
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| | last = Sowa
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| | coauthors = Rowe, A. D., Leake, M. C., Yakushi, T., Homma, M., Ishijima, A., Berry, R. M.
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| | year = 2005
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| | title = Direct observation of steps in rotation of the bacterial flagellar motor
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| | journal = Nature
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| | volume = 437
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| | pages = 916–919
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| | doi = 10.1038/nature04003
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| | issue=7060
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| |bibcode = 2005Natur.437..916S
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| | pmid = 16208378 }}</ref>). For 2D signals, the related problem of [[edge detection]] has been studied intensively for [[image processing]].<ref name="Serra1982">{{cite book
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| | last = Serra
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| | first = J.P.
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| | title = Image analysis and mathematical morphology
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| | publisher = Academic Press
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| | location = London; New York
| |
| | year = 1982}}</ref>
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| == Algorithms ==
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| When the step detection must be performed as and when the data arrives, then [[online algorithm]]s are usually used,<ref>{{cite book
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| | last = Basseville
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| | first = M.
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| | coauthors = I.V. Nikiforov
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| | title = Detection of Abrupt Changes: Theory and Application
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| | publisher = Prentice Hall
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| | year = 1993}}</ref>
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| and it becomes a special case of [[sequential analysis]]. | |
| Such algorithms include the classical [[CUSUM]] method applied to changes in mean.
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| <ref>
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| Rodionov, S.N., 2005a: A brief overview of the regime shift detection methods. [http://www.beringclimate.noaa.gov/regimes/rodionov_overview.pdf link to PDF] In: Large-Scale Disturbances (Regime Shifts) and Recovery in Aquatic Ecosystems: Challenges for Management Toward Sustainability, V. Velikova and N. Chipev (Eds.), UNESCO-ROSTE/BAS Workshop on Regime Shifts, 14–16 June 2005, Varna, Bulgaria, 17-24.
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| </ref> | |
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| By contrast, ''offline'' algorithms are applied to the data potentially long after it has been received. Most offline algorithms for step detection in digital data can be categorised as ''top-down'', ''bottom-up'', ''sliding window'', or ''global'' methods.
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| === Top-down ===
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| These algorithms start with the assumption that there are no steps and introduce possible candidate steps one at a time, testing each candidate to find the one that minimizes some criteria (such as the least-squares fit of the estimated, underlying piecewise constant signal). An example is the ''stepwise jump placement'' algorithm, first studied in geophysical problems,<ref name="Gill1970">{{cite journal
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| | last = Gill
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| | first = D.
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| | year = 1970
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| | title = Application of a statistical zonation method to reservoir evaluation and digitized log analysis
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| | journal = American Association of Petroleum Geologists Bulletin
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| | volume = 54
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| | pages = 719−729}}</ref> that has found recent uses in modern biophysics.<ref name="Kers2006">{{cite journal
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| | last = Kerssemakers
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| | first = J.W.J.
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| | coauthors = Munteanu, E.L., Laan, L., Noetzel, T.L., Janson, M.E., Dogterom, M.
| |
| | year = 2006
| |
| | title = Assembly dynamics of microtubules at molecular resolution
| |
| | journal = Nature
| |
| | volume = 442
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| | doi = 10.1038/nature04928
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| | pages = 709−712
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| | issue=7103|bibcode = 2006Natur.442..709K }}</ref>
| |
| | |
| === Bottom-up ===
| |
| Bottom-up algorithms take the "opposite" approach to top-down methods, first assuming that there is a step in between every sample in the digital signal, and then successively merging steps based on some criteria tested for every candidate merge.
| |
| | |
| === Sliding window ===
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| By considering a small "window" of the signal, these algorithms look for evidence of a step occurring within the window. The window "slides" across the time series, one time step at a time. The evidence for a step is tested by statistical procedures, for example, by use of the two-sample [[Student's t-test]]. Alternatively, a [[nonlinear filter]] such as the [[median filter]] is applied to the signal. Filters such as these attempt to remove the noise whilst preserving the abrupt steps.
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| | |
| === Global ===
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| Global algorithms consider the entire signal in one go, and attempt to find the steps in the signal by some kind of optimization procedure. Algorithms include [[wavelet]] methods,<ref name="Mallat2009">{{cite journal
| |
| | last = Mallat
| |
| | first = S.
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| | coauthors = Hwang, W.L.
| |
| | year = 1992
| |
| | title = Singularity detection and processing with wavelets
| |
| | journal = IEEE Transactions on Information Theory
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| | volume = 38
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| | pages = 617−643
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| | doi = 10.1109/18.119727
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| | issue = 2}}</ref> and [[total variation denoising]] which uses methods from [[convex optimization]]. Where the steps can be modelled as a [[Markov chain]], then [[Hidden Markov Models]] are also often used (a popular approach in the biophysics community<ref>{{cite doi | 10.1529/biophysj.106.082487 }}</ref>). When there are only a few unique values of the mean, then [[k-means clustering]] can also be used.
| |
| | |
| == Linear versus nonlinear signal processing methods for step detection ==
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| Because steps and (independent) noise have theoretically infinite [[Bandwidth (signal processing)|bandwidth]] and so overlap in the [[Fourier transform|Fourier basis]], [[signal processing]] approaches to step detection generally do not use classical smoothing techniques such as the [[low pass filter]]. Instead, most algorithms are explicitly nonlinear or time-varying.<ref name="Little2011">
| |
| {{Cite journal
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| | last = Little
| |
| | first = M.A.
| |
| | coauthors = Jones, N.S.
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| | title = Generalized Methods and Solvers for Piecewise Constant Signals: Part I
| |
| | journal = [[Proceedings of the Royal Society A]]
| |
| | url = http://web.media.mit.edu/~maxl/publications/pwc_filtering_arxiv.pdf
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| | year = 2011 }}</ref>
| |
| | |
| == Step detection and piecewise constant signals ==
| |
| Because the aim of step detection is to find a series of instantaneous jumps in the mean of a signal, the wanted, underlying, mean signal is [[piecewise constant]]. For this reason, step detection can be profitably viewed as the problem of recovering a piecewise constant signal corrupted by noise. There are two complementary models for piecewise constant signals: as [[spline (mathematics)|0-degree splines]] with a few knots, or as [[level set]]s with a few unique levels. Many algorithms for step detection are therefore best understood as either 0-degree spline fitting, or level set recovery, methods.
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| | |
| === Step detection as level set recovery ===
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| When there are only a few unique values of the mean, clustering techniques such as [[k-means clustering]] or [[mean-shift]] are appropriate. These techniques are best understood as methods for finding a level set description of the underlying piecewise constant signal.
| |
| | |
| === Step detection as 0-degree spline fitting ===
| |
| Many algorithms explicitly fit 0-degree splines to the noisy signal in order to detect steps (including stepwise jump placement methods<ref name="Gill1970"/><ref name="Kers2006"/>), but there are other popular algorithms that can also be seen to be spline fitting methods after some transformation, for example [[total variation denoising]].<ref name="Chan">
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| {{cite journal
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| | last = Chan
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| | first = D.
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| | coauthors = T. Chan
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| | year = 2003
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| | title = Edge-preserving and scale-dependent properties of total variation regularization
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| | journal = Inverse Problems
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| | volume = 19
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| | pages = S165–S187
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| | bibcode = 2003InvPr..19S.165S
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| | doi = 10.1088/0266-5611/19/6/059
| |
| | issue = 6}}
| |
| </ref>
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| | |
| === Generalized step detection by piecewise constant denoising ===
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| All the algorithms mentioned above have certain advantages and disadvantages in particular circumstances, yet, a surprisingly large number of these step detection algorithms are special cases of a more general algorithm.<ref name="Little2011"/> This algorithm involves the minimization of a global functional:<ref name="Mrazek">
| |
| {{Cite conference
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| | first = P.
| |
| | last = Mrazek
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| | coauthors = Weickert, J., Bruhn, A.
| |
| | title = On robust estimation and smoothing with spatial and tonal kernels
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| | booktitle = Geometric properties for incomplete data
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| | publisher = Springer
| |
| | location = Berlin, Germany
| |
| | year = 2006 }}</ref>
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| | |
| {{NumBlk|:|<math>H[m]=\sum_{i=1}^N\sum_{j=1}^N \Lambda(x_i-m_j,m_i-m_j,x_i-x_j,i-j)</math>|{{EquationRef|1}}}}
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| | |
| Here, ''x''<sub>''i''</sub> for ''i'' = 1, ...., ''N'' is the input discrete-time input signal of length ''N'', and ''m''<sub>''i''</sub> is the signal output from the algorithm. The goal is to minimize ''H''[''m''] with respect to the output signal ''m''. The form of the function <math>\scriptstyle \Lambda</math> determines the particular algorithm. For example, choosing:
| |
| | |
| :<math>\Lambda = \frac12 \left|x_i-m_j\right|^2 I(i-j=0) + \gamma\left|m_i-m_j\right| I(i-j=1)</math>
| |
| | |
| where ''I''(''S'') = 0 if the condition ''S'' is false, and one otherwise, obtains the [[total variation denoising]] algorithm with regularization parameter <math>\gamma</math>. Similarly:
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| | |
| :<math>\Lambda=\min \left\{\frac12 \left|m_i-m_j\right|^2,W\right\}</math>
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| | |
| leads to the [[mean shift]] algorithm, when using an adaptive step size Euler integrator initialized with the input signal ''x''.<ref name="Mrazek"/> Here ''W'' > 0 is a parameter that determines the support of the mean shift kernel. Another example is:
| |
| | |
| :<math>\Lambda = \frac{1-\exp(-\beta|m_i-m_j|^2/2)}{\beta} \cdot I(|i-j|\le W)</math>
| |
| | |
| leading to the [[bilateral filter]], where <math>\scriptstyle \beta>0</math> is the tonal kernel parameter, and ''W'' is the spatial kernel support. Yet another special case is:
| |
| | |
| :<math>\Lambda= \frac12 \left|x_i-m_j\right|^2 I(i-j=0) + \gamma \left|m_i-m_j\right|^0 I(i-j=1)</math>
| |
| | |
| specifying a group of algorithms that attempt to greedily fit 0-degree splines to the signal.<ref name="Gill1970"/><ref name="Kers2006"/> Here, <math>\scriptstyle \left|x\right|^0</math> is defined as zero if ''x'' = 0, and one otherwise.
| |
| | |
| Many of the functionals in equation ({{EquationNote|1}}) defined by the particular choice of <math>\scriptstyle \Lambda</math> are [[Convex function|convex]]: they can be minimized using methods from [[convex optimization]]. Still others are non-convex but a range of algorithms for minimizing these functionals have been devised.<ref name="Mrazek"/>
| |
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| == References ==
| |
| {{Reflist}}
| |
| | |
| == External links ==
| |
| *[http://www.maxlittle.net/software/ PWCTools: Flexible Matlab software for step detection by piecewise constant denoising]
| |
| | |
| {{DEFAULTSORT:Step Detection}}
| |
| [[Category:Change detection]]
| |
| [[Category:Nonlinear filters]]
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| [[Category:Signal processing]]
| |
| [[Category:Feature detection]]
| |
| [[Category:Time series analysis]]
| |
Physicians and scientists from the Irvine university of California have lately discovered a new method of lowering blood pressure. To check up additional information, consider peeping at: account. This method is based on electroacupuncture, which appears to have a considerable effect in lowering blood pressure. The technique has been tested on rats, by inducing low electric stimulation at the front of their legs, and their blood"s pressure following the treatment was 40 percent lower than before(their blood pressure had been artificially improved prior to). This opens new doors for hypertension remedy, perhaps it will even replace the conventional medical remedies with this ancient strategy.
These are all the approaches that had been tested :
Needles had been inserted into:
-pericardium 5-6, and they were rotated every single ten to thirty minutes. Get additional resources on an affiliated site by clicking Klinge Mayo. While this procedure was performed, the rats" blood pressure was becoming raised by doctors.
-the rats" forelimbs, without any stimulation or twist, for 30 minutes.
Also, the pericardium five-6 was electrically stimulated with frequencies ranging from 2 to one hundred hertz.
Throughout these tests the alterations in blood pressure had been continuously monitored, and the outcomes cautiously recorded. The most productive in lowering blood pressure were these tests which involved manual and electrical acupuncture, which had critical effects in lowering blood pressure, lasting up to a single hour, and ranging from 33 to 36 percent. Worth Reading includes more about why to mull over this thing. The finest outcomes had been recorded at the rats which had been stimulated by electroacupuncture, specially at these treated at the electroacupuncture frequency of two hertz.
Nevertheless, the finest results were recorded at the rats stimulated at the heart (6-7) and stomach (36-37). Their blood pressure was lowered up to 44 percent for the heart stimulation, and 36 percent for the stomach.
An important observation that doctors made was that this electroacupuncture treatment can only lower blood pressure for the hypertensive individuals, it has no impact for healthful people.
We can only that these remedies involving acupuncture will soon be readily available to everyone, because they represent a very excellent way to lower blood pressure.
If you have any thoughts concerning wherever and how to use health books - just click the following web page -, you can make contact with us at our own webpage.