Low impedance nature of 12 acupoints on the limbs,and the unexpected dependence on limb angle

INTRODUCTION

In recent years,complementary and alternative medicine has attracted more attention in clinical practice.One important type of complementary and alternative medicine is Traditional Chinese Medicine(TCM).As part of TCM,acupuncture is widely practiced worldwide,and the World Health Organization currently lists 43 diseases that can be treated or managed with acupuncture in 1979.1,2The actual physiological basis and working mechanism of channels and acupoints have become interesting topics for many researchers.The location and physical nature of channels and acupoints have been investigatedviaa variety of biophysical,biochemical,and molecular biological methods applied in clinical experiments.3-6Biophysical studies have been conducted to investigate thermal characteristics,7-12optical characteristics,13,14migration of isotopes along channels,15,16acoustic characteristics,17-22magnetic characteristics,23-25myoelectric activities,26and electrical characteristics.27-30Some specific results regarding research into the channels and acupoints include:acupuncture treatment results in high temperature lines that emerge along the channels;10research into the luminous biophysical properties of channels and acupoints identified 14 high luminous lines on the body surface,which matched well with the locations of 14 regular channels recorded in theHuang Di Nei Jing;13injecting the isotope99mTcO4-into one low hydraulic resistance point results in movement of the isotope along channel lines in minipigs.16These studies provide supporting evidence for the existence of channels and acupoints,and their locations match well to those reported in TCM theory.

Some interesting physical characteristics of the acupoints along the channels have also been revealed.Wanget al20evaluated the acoustic characteristics of acupoints and reported that the bidirectional conduction velocity was 6.2-10 cm/s,which is close to the velocity of propagated sensation along the channels.Most investigations into the magnetic characteristics of channels and acupoints have focused on functional magnetic resonance imaging technology.22Some studies showed that obvious myoelectric activity accompanied propagated sensation along the channels.26Early results on electrical characterization of channels and acupoints have demonstrated that channels and acupoints have low impedance and high capacitance.31-36However,other studies have not supported the low impedance nature of acupoints.27-30For example,Krameret al27recently measured the electrical impedance of 631 acupoints on the human body,and found that 25.9%of these acupoints showed low impedance,but 11.3%had higher impedance compared with non-acupoints in the surrounding area,and 62.8%showed no remarkable difference in impedance compared with the surrounding area.

These experimental results have led to varying theories on the actual nature and working mechanism of acupuncture.Yanget al37believed that the overlap between low impedance lines and regular channels in TCM was not incidental,and that the physiological basis of channels was the connective tissue,which had more interstitial fluid than the neighboring tissues.Fanet al38discovered that there were more gap junctions in the subcutaneous tissue of acupoints compared with that of non-acupoints,and suggested that the gap junction was the structure foundation of low impedance.

Despite all these developments in acupuncture studies,there is still controversy regarding the physical properties of channels and acupoints.In the present study,we investigated the impedances spectra(40-10 kHz)of more than ten acupoints on the hand and foot,and obtained detailed two-dimensional(2D)mapping of the impedance around acupoints.We also investigated whether the impedance at 12 original acupoints was dependent on limb position.

MATERIALS AND METHODS

We measured the skin electrical impedance in the frequency range from 40 to 10 kHz with the four-electrode method,using an Agilent 4294A Precision Impedance Analyzer(Agilent,Santa Clara,CA,USA).A 1.0 mm diameter probe was made with a copper wire,and a large reference electrode was made from a thick braided wire with a width of 2.0 cm.The reference electrode was firmly wrapped around the upper arm during investigation of acupoints on the hand(or the upper leg for acupoints on the foot),so that it caused a negligible amount of contact resistance during the measurements.Figures 1A and 1B show the tip of the testing probe,where the central part is the copper that was cleaned before each measurement,and the surrounding material was an insulator.Figure 1C shows the positions of the testing probe,the reference electrode,and the measurement circuit.

Figure 1 Photographs of the tip of the probe electrode and the experimental setup

A,B:the side view and the top view of the probe tip with a diameter of 1.0 mm,respectively;C:a schematic diagram of the experimental setting,including a precision impedance analyzer,a reference electrode,a probe,and an arm being tested.

During each measurement process,a heavy load of 200 g was mounted on the probe to create a constant pressure on the skin of around 6 atm(i.e.,60 N/cm2)when the probe was pressed against the skin vertically.As a result,the skin at the location of the test points turned red(but did not bleed)and remained this way for a few hours(depending on individuals)after each measurement.This ensured that the repeat measurements were made at the same locations.

We obtained precise 2D maps of impedance distribution for the following eight acupoints:Zhongquan(EX-UE 3),Yangchi(TE 4),Yanglingquan(GB 34),Shangqiu(SP 5),Qiuxu(GB 40),Hegu(LI 4),Zhigou(TE 6),and Laogong(PC 8).We set a measurement matrix of 7×7(49 points)around each acupoint,where the spacing between each two neighboring measurement points was 2.0 or 3.0 mm,leading to a pixel density of 34 or 15 points/cm2.The original measurement results were calculated with a program written in Labview software(National Instruments,Austin,TX,USA),where the data for points between the testing points were calculated with a smooth interpolation algorithm.39,40

To limit the measurement error,we tested five different points within an area of 0.5 cm2at each acupoint and recorded the electrical impedance of each point.For each test point,the measurement was repeated three times,and the average was calculated.The lowest value among the five sets of testing data was taken as the representative impedance of the acupoint.

We also measured the angle dependence of electrical impedance for the following 12 original acupoints:Yangchi(TE 4),Hegu(LI 4),Taiyuan(LU 9),Shenmen(HT 7),Daling(PC 7),and Wangu(SI 4)near the wrist,and Qiuxu(GB 40),Taichong(LR 3),Taibai(SP 3),Taixi(KI 3),Chongyang(ST 42),and Jinggu(BL 64)around the ankle.We obtained the impedance data for the 12 original acupoints on both the left and right limbs.We defined the 0°position as that in which the arm(or leg)was in full extension,and defined the 90°position as that in which the distal arm(or leg)was flexed by 90°.Three different 0°and 90°positions were used for the acupoints on the hand,as shown in Figure 2.The positions shown in Figure 2A were applied for Hegu(LI 4)and Yangchi(TE 4),the positions shown in Figure 2B were used for Daling(PC 7),Taiyuan(LU 9),and Shenmen(HT 7),and the positions in Figure 2C were used for Wansu(SI 4).For the acupoints on the foot,we used similar positions to those shown in Figure 2B.For the acupoints Shenmen(HT 7),Taiyuan(LU 9),and Yangchi(TE 4)on both the left and right hands,we measured the change in the impedance spectrum by changing the bending angle of the front arm by 15°per step.

口罩[4]：外科口罩本来是用来预防外科感染的，但后来发现戴口罩可以在一定程度上滤过烟雾中的粒子，根据2003年等综述报道，外科烟雾由电外科器械所产生。

5 Jou NT and Ma SX.Responses of Nitric oxide-cGMP release in acupuncture point to electroacupuncture in human skinin vivousing dermal microdialysis.Microcirculation 2009;16(5):434-443.

RESULTS

Reliability and stability of the measurement system

We first checked the reliability and stability of our probe and measurement system.Using the measurement parameters and conditions described above,smooth measurement curves could be obtained for most testing points on dry skin.We found that maintaining constant pressure on the probe ensured repeatable measurement results.Figure 3 presents a set of typical experimental data taken from Delta at three acupoints:Qiangu(SI 2),Juque(CV 14),and Laogong(PC 8);the measurement was repeated three times for each acupoint,and thesethreedatacurvesare well-matched with each other.

In some cases,when the pressure on the testing point was changed a bit,a small jump in the measurement curve was recorded,but the relative change was small and the trend of the curve remained the same.As highlighted by the red circles in Figure 4,the measured impedance dropped by 20%when we increased the pressure on the right Jinggu(BL 64)(Figure 4A),but it increased by 17%when we reduced the pressure on Qiuxu(GB 40)(Figure 4B).

Precise 2D mapping of the impedance distribution around acupoints

Figure 2 Three sets of positions consisting of the 0°position and the 90°positon used during the measurement of the electrical impedance of various original acupoints on the hand

A1,A2:the positions used for Hegu(LI 4)andYangchi(TE 4);B1,B2:the positions used for Daling(PC 7),Taiyuan(LU 9),and Shenmen(HT 7);C1,C2:the positions used forWangu(SI 4).

Figure 3 Three sets of data measured from one study subject at right Qiangu(SI 2),Juque(CV 14),and Laogong(PC 8)

The black,red,and blue lines in each graph represent the impedance spectra of the first,second,and third measurements,respectively.A:Qiangu(SI 2);B:Juque(CV 14);C:Laogong(PC 8).

Figure 4 Influence of varying pressure on acupoint impedance

A:the impedance of right Jinggu(BL 64)decreased by 20%immediately after increasing the pressure applied on the skin;B:the impedance of left Qiuxu(GB 40)increased by 17%immediately after the pressure applied on the skin was alleviated.The red circles mark the moments that the pressure was changed.These data are from the study subject referred to as Beta.

Our measurement data for 2D mapping of the electrical impedance distribution around individual acupoints revealed that some acupoints showed clear low impedance while others did not.For example,the impedance measured at Zhongquan(EX-UE 3),Yangchi(TE 4),Yanglingquan(GB 34),Shangqiu(SP 5),and Qiuxu(GB 40)was markedly lower than that measured in the surrounding area by a factor of up to more than ten times at a low frequency range(f＜100 Hz).However,at other acupoints,such as Hegu(LI 4),Zhigou(TE 6),and Laogong(PC 8),there was less impedance difference between the acupoints and the surrounding area for the same frequency range.

4 Ma SX,Li XY,Smith BT,Jou NT.Changes in nitric oxide,cGMP,and nitrotyrosine concentrations over skin along the meridians in obese subjects.Obesity 2010;19(8):1560-1567.

这种模式是某些在线教育企业采用的模式。通过与名校名师合作，在线教育企业录制了大量的慕课视频，并配套建设相应的习题测试等教学资源，然后将该课程出售给相关学校使用。购买了课程的学校可以开展单纯的线上教学，也可与线下翻转课堂相结合开展混合式教学。其本质就是校内私播课加上商业化运作。由于很多学校同时使用，并有一定的灵活性，也可以达到慕课的大规模和开放性目标。

Figure 5A shows the 2D mapping result at 1.0 kHz for Yangchi(TE 4)on the right hand.This is a typical result showing the low impedance of the acupoint.To present the 2D map clearly,we have converted the impedance data Z(x,y)to conductance data σ(x,y),where σ(x,y)=1/Z(x,y)and x and y are the location coordinates of the testing point.The highest conductance at the peak was 8×10－6S,while the average conductance at the plane region was 5×10－7S,which was 16 times lower than the peak value.In contrast,there was no marked conductance peak in the 2D conductance map of Zhigou(TE 6)on the left arm,also measured at 1.0 kHz(Figure 5C).For some acupoints,like Yanglingquan(GB 34),the 2D mapping of conductance distribution showed several secondary peaks,which had a conductance of half the highest peak,but several times more than the plane region,1×10－6S(Figure 5B).

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From the peak result shown in Figure 5A,we obtained the full width at half maximum(FWHM)of the peak.The FWHM value represents the effective dimension of the area with low impedance,or high conductance.As shown in Figure 6,for the Yangchi(TE 4)of Alpha,the diameter of the acupoint area was 3.8 mm.We repeated the measurement of those acupoints with low impedance in the following days,and found that for the same acupoint the 2D mapping curves were similar,but the location of the central points for the lowest impedance(thus the highest conductance)either overlapped or shifted slightly by 2-4 mm.We concluded that,for such acupoints with obvious low impedance,the effective acupoint area in terms of electrical conductance was around 0.25 cm2,which is much smaller than recently reported.41

Limb angle-dependent impedance of 12 original acupoints

Typical results for the limb angle-dependence of the electrical impedance at the 12 original acupoints on both the left and right limbs in the 0°and 90°positions are shown in Figures 7-10.

纳入标准：①经术前各种检查、临床表现及肿瘤切除术后病理诊断均提示直肠癌；②首次确诊为直肠癌且暂未接受任何治疗；③家属及患者本人均签订知情同意书；④依从性良好。排除标准：①手术绝对禁忌症；②术前及术中证实有远处转移者；③合并其它原发肿瘤的患者；④年龄大于75岁的患者；⑤精神病患者或有精神病史的患者。

Figure 7 presents the electrical impedance spectrum for 40-10 kHz at six original acupoints on the left hand of study subject Alpha.The black line plots the data for the 0°position,and the red line plots the data for the 90°position.For comparison,Figure 8 presents the

measurement data for the right hand of Alpha under similar measurement configurations.

Table 1 Changes in impedance at different frequencies after bending the limb to 90°at 12 original acupoints on the left and right limbs

Notes:the ratio of impedance,Zr(f),was defined as Zr(f)=Z90(f)/Z0(f),where Z0(f)and Z90(f)were the electrical impedance values at frequency f for the 0°and 90°positions,respectively.

Acupoint 10 kHz 1.1 0.6 0.9 1.3 0.8 1.0 1.0 1.2 0.5 1.1 1.1 0.7 Left Ratio of impedance Zr(f)10 kHz 1.0 0.8 1.0 1.0 1.2 2.6 2.6 1.0 2.2 1.1 1.0 0.5 Daling(PC 7)Yangchi(TE 4)Hegu(LI 4)Taiyuan(LU 9)Wangu(SI 4)Shenmen(HT 7)Chongyang(ST 42)Jinggu(BL 64)Taichong(LR 3)Qiuxu(GB 40)Taibai(SP 3)Taixi(KI 3)50 Hz 5.4 0.2 0.7 11.0 0.2 0.4 1.2 7.3 0.1 1.1 1.4 0.9 100 Hz 4.3 0.3 0.6 7.1 0.3 0.5 1.0 4.3 0.1 1.2 1.6 0.7 1 kHz 2.0 0.5 0.8 2.7 0.6 0.7 1.0 2.3 0.2 1.0 1.3 0.6 Right Ratio of impedance Zr(f)50 Hz 0.4 0.7 2.6 14.3 2.8 17.3 52.3 1.7 14.5 1.1 0.4 0.1 100 Hz 0.4 0.3 1.7 1.4 2.9 11.3 28.3 1.5 8.8 1.2 0.6 0.1 1 kHz 0.5 0.6 1.3 1.3 2.1 4.5 6.0 1.2 3.8 1.1 0.7 0.3

Figure 5 Comparison of the conductance distribution for rightYangchi(TE 4),rightYanglingquan(GB 34),and left Zhigou(TE 6)at 1000 Hz

TheX-Yplane represents the measured skin area,with a pixel pitch of 2.0 mm;and the vertical coordinate represents the conductance of the points being tested.A:there was a conductance peak at right Yangchi(TE 4),with 16 times conductance more than the surrounding area;B:the conductance distribution of right Yanglingquan(GB 34)had a highest peak and several secondary peaks;C:there was a relatively flat distribution of electrical impedance around left Zhigou(TE 6).

Figures 9 and 10 present the measurement data for six original acupoints on the left foot and right foot of Alpha,where the black lines and red lines plot the impedance spectra at the 0°and 90°positions of the leg,respectively.Four main trends were recognized.After bending the limb by 90º,the electrical impedance of Taiyuan(LU 9)and Jinggu(BL 64)increased in both the left and right limbs.After the same bending,the impedance of Yangchi(TE 4)and Taixi(KI 3)decreased in both the left and right limbs.For Qiuxu(GB 40),the change in limb position did not greatly change the impedance in both sides.For the remaining acupoints,the trend of the change in impedance relative to limb bending in the left limb did not match the trend in the right limb.

Figure 6 Side view of precise 2D mapping of conductance around right Yangchi(TE 4)with a full width at half maximum(FWHM)of 4 mm

TheXaxis represents the spacing between two adjacent points of 2.0 mm,and the vertical coordinate represents the conductance.

Table 1 summarizes the exact values for the relative changes in impedance at different frequencies at the 12 original acupoints after bending the limb from the 0°position to the 90°position.We defined Z0(f)and Z90(f)as the electrical impedance at frequency f for the 0°and 90°positions,respectively,and the relative change in impedance,Zr(f),by Zr(f)=Z90(f)/Z0(f).All the data in Table 1 are taken from the measurement data shown in Figures 7-10.A Zr(f)value＞1 indicates that the impedance increased after bending;a Zr(f)value＜1 indicates that the impedance decreased after bending.It is interesting to note that,for some acupoints tested on study subject Alpha,the electrical impedance changed by a factor of more than ten times the original impedance value.

We further tested three of the 12 original acupoints[(Yangchi(TE 4),Taiyuan(LU 9),and Shenmen(HT 7)],by bending the limb at smaller angles.Instead of bending the limb by 90°in one step as shown in Figure 2,we performed the bending process in six uniform steps,each by 15°.Figure 11A plots the original measurement data of electrical impedance for Shenmen(HT 7)on the right hand of Alpha.Figure 11B shows the limb angle-dependent data extracted from Figure 11A at frequencies of 50,100,200,500 Hz,1,2,5,and 10 kHz.The curves were smooth,and an increasing trend occurred at each frequency.There was no crossover of the measurement curves in Figures 11A and 11B.

The phenomenon in which the impedance of the 12 original acupoints changed with the position of the limb was also found in other subjects besides Alpha,except for Delta who dropped out of the study due topersonal reason(Table 2).For all three subjects who were tested,the impedances of Yangchi(TE 4),Hegu(LI 4),Wansu(SI 4),and Shenmen(HT 7)on the left,and the impedances of Daling(PC 7),Yangchi(TE 4),and Qiuxu(GB 40)on the right decreased when the limb was bent at 90°(Zr≤ 1.0);these values are typed in blue color in Table 2.In contrast,the impedances of Taiyuan(LU 9),Jinggu(BL 64),Qiuxu(GB 40),and Taibai(SP 3)on the left,and the impedance of Hegu(LI 4),Taiyuan(LU 9),Chongyang(ST 42),Jinggu(BL 64),and Taichong(LR 3)on the right increased when the limb was bent at 90°(Zr≥ 1.0);these values are typed in green color in Table 2.

Table 2 Changes in acupoint impedance at 200 Hz after bending the limb to 90°

Notes:12 original acupoints in three study subjects(Alpha,Beta,and Gamma)on the left and right limbs were measured.Ratio of impedance,Zr,is defined as Zr=Z90/Z0,where Z0and Z90are the electrical impedances of the acupoint at 200 Hz for the 0°and 90°positions,respectively.

Gamma 0.8 0.6 0.9 1.4 0.9 0.8 0.4 1.5 0.8 1.2 1.3 7.7 Acupoint Left Ratio of impedance Zrat 200 Hz Right Ratio of impedance Zrat 200 Hz Daling(PC 7)Yangchi(TE 4)Hegu(LI 4)Taiyuan(LU 9)Wangu(SI 4)Shenmen(HT 7)Chongyang(ST 42)Jinggu(BL 64)Taichong(LR 3)Qiuxu(GB 40)Taibai(SP 3)Taixi(KI 3)Alpha 3.3 0.4 0.7 4.0 0.4 0.6 1.0 3.9 0.1 1.0 1.4 0.6 Beta 0.8 0.2 0.1 1.9 1.0 0.9 1.3 1.2 2.8 11.0 1.0 1.1 Alpha 0.4 0.4 1.6 1.3 2.5 7.2 16.3 1.4 6.2 0.9 0.6 0.2 Beta 0.9 0.7 30.9 2.0 1.2 0.9 1.8 1.0 29.2 1.0 1.3 1.8 Gamma 0.5 0.1 1.4 6.0 0.7 0.4 7.1 1.0 1.0 0.3 0.8 1.4

Figure 7 Impedance changes at six original acupoints on the left hand after bending the left arm to 90º

The black and red lines show the acupoint impedance spectra at the 0°position and the 90°position,respectively.A,B,C,D,E,and F represent the results of Daling(PC 7),Yangchi(TE 4),Hegu(LI 4),Taiyuan(LU 9),Wansu(SI 4),and Shenmen(HT 7)on the left hand,respectively.

Figure 8 Impedance changes at six original acupoints on the right hand after bending the right arm to 90º

The black and red lines show the acupoint impedance spectra at the 0°position and the 90°position,respectively.A,B,C,D,E,and F represent the results of Daling(PC 7),Yangchi(TE 4),Hegu(LI 4),Taiyuan(LU 9),Wansu(SI 4),and Shenmen(HT 7)on the right hand,respectively.

In particular,the three acupoints located close to each other on the medial aspect of the wrist[Daling(PC 7),Taiyuan(LU 9),and Shenmen(HT 7)]showed very different trends in the change of impedance under the same process of arm bending(Figure 12).The distances from these three acupoints to the reference electrode(fixed on the upper arm)were almost the same.However,they showed different initial impedances,which were 1×105Ω for Daling(PC 7),3.5×105Ω for Taiyuan(LU 9),and 7×105Ω,for Shenmen(HT 7),at f=100 Hz.In addition,when the arm was bent from the 0°position to the 90°position,the impedances for Daling(PC 7)and Taiyuan(LU 9)increased by 400%and 500%,respectively,while the impedance for Shenmen(HT 7)decreased by 50%.

Figure 9 Impedance changes at six original acupoints on the left leg after bending the left leg to 90º

The black and red lines show the acupoint impedance spectra at the 0°position and the 90°position,respectively.A,B,C,D,E,and F represent the results of Chongyang(ST 42),Jinggu(BL 64),Taichong(LR 3),Qiuxu(GB 40),Taibai(SP 3),and Taixi(KI 3)on the left leg,respectively.

Figure 1 0 Impedance changes at six original acupoints on the right leg after bending the right leg to 90º

The black and red lines show the acupoint impedance spectra at the 0°position and the 90°position,respectively.A,B,C,D,E,and F represent the results of Chongyang(ST 42),Jinggu(BL 64),Taichong(LR 3),Qiuxu(GB 40),Taibai(SP 3),and Taixi(KI 3)on the right leg,respectively.

DISCUSSION

These 12 original acupoints are considered important acupoints for the corresponding 12 channels in the diagnosis and therapy of visceral disease in clinical practice.The waxing and waning ofQiand blood,and the function of the viscera can be detected by sensitive changes at the related original acupoints.42-44That is the reason we chose them as the targets.

Low impedance characteristics of acupoints

Our 2D mapping results of the electrical impedance around various acupoints are consistent with previous reports in which some acupoints showed clear low impedance,while others did not.27-30As shown in Figure 4,the electrical impedance was affected by the pressure applied on the skin at the testing point,which was also consistent with previous reports.45,46This indicates that the contact resistance of the probe tip and the skin was sensitive to this pressure.However,the measured change induced by the pressure was only a small portion of the average measured value.

矿石中黄铜矿多以不规则状嵌布于脉石矿物裂隙、粒间（见图1），有的呈微粒浸染于脉石矿物中。黄铜矿与其他硫化矿物关系不密切，少量的黄铜矿与黄铁矿嵌布在脉石矿物中（见图2）。

Figure 1 1 Relationship between acupoint impedance,frequency,and arm angle for Shenmen(HT 7)on the right hand

A:acupoint impedance increased as the angle of the arm increased.B:degree of change in acupoint impedance increased as the frequency decreased.

Figure 1 2 Comparison of the changes in impedance at Daling(PC 7),Shenmen(HT 7),and Taiyuan(LU 9)after bending the limb from 0°to 90°

A:this photograph shows the relative locations of the three acupoints and the distance from each acupoint to the reference electrode,the bending of the arm from 0°to 90°,and the channels of the pericardium,lung,and heart(as represented by the black,red,and blue lines,respectively).B:the acupoint impedances of the three acupoints with the arm in the 0°and 90°positions.The tendencies of impedance changes at Daling(PC 7),Shenmen(HT 7),andTaiyuan(LU 9)are indicated with the black,red,and blue arrows,respectively.

Figure 6 shows that some acupoints had a smaller impedance at the central point(which is supposed to be the acupoint)than the average plane value by a factor of up to more than ten times.This phenomenon could not be induced by fluctuation of the pressure on testing points during the measurement procedure.Furthermore,the effective area of such acupoints is very small,with a dimension of a few millimeters.These results confirm unambiguously that acupoints really exist on human skin,although the physical basis and tissue structures responsible for the markedly low impedance at acupoints are still unclarified.

30 Pearson S,Colbert AP,Mcnames J,Baumgartner M,Hammerschlag R.Electrical skin impedance at acupuncture points.J Altern Complement Med 2007;13(4):409-418.

We also observed acupoints that had a lesser degree of low impedance or no obvious difference in impedance from the surrounding skin(Figures 5B,5C).This may be explained by an ancient model that states that the acupoint is the opening of the superficial collateral,and the depth of such superficial collaterals relative to the skin surface varies with individual acupoints.Zhanget al47reviewed this theory from theHuang Di Nei Jingand showed it schematically in a figure.Figure 13,modified from this previous work47presents the correlations between the main channel,branch channel,superficial collateral,and acupoint.In our work,we used a sharp probe with a diameter of 1.0 mm and a high pressure(6 atm)on the testing points,so the tip of the probe was indeed a few millimeters lower than the normal skin surface during the measurement.As shown in Figure 13,when the opening of the superficial collateral is close to the skin surface,the testing probe could touch the opening and therefore recorded very low impedance,as highlighted by a red arrow and the letter"A".For acupoints located deep under the skin,as highlighted by a blue arrow and the letter"B",the measured impedance was relatively higher,or did not show any difference compared with the non-acupoints around the nominal acupoint marked on the skin surface.Figure 13 also explains why a greater degree of pressure applied on the testing point could result in smaller impedance,as the greater pressure causes a deep tip position of the probe,which is closer to the opening of the superficial collateral.

Figure 1 3 Schematic diagram illustrating the positional relationships of the channels,branch channels,superficial collateral,and acupoints(modified from a previous study)47

The red arrow marked with"A"indicates an acupoint at a position where the opening of the superficial collateral is superficial,while the blue arrow highlighted with“B”indicates an acupoint at a position where the opening of the superficial collateral is deep under the skin surface.

Dependence of acupoint impedance on limb angle

The limb angle dependence of acupoint impedance revealed in the present study offers unique information for understanding the physical property of channels and acupoints.The data presented in Figures 7-10 were taken from one study subject(Alpha);therefore,we could not perform a statistical analysis.However,the measured relative change in impedance was one or two orders of magnitude higher than the measurement error of our system,indicating that the results were reliable.

The degree of change in impedance at acupoints varied a little between the individual study subjects and with their physical status,but the dependence of acupoint impedance on limb angle was observed in every study subject.Furthermore,the same trend for the change in acupoint impedance was found in the three study subjects at 16 of the 24 original acupoints;the different change trend seen at the other acupoints might be due to the limited number of subjects.These are primary study results,and it would be more valuable to investigate the relationship between acupoint impedance and limb angle over a long time period in a specific case in clinical practice.Furthermore,according to traditional Chinese acupuncture theory,Daling(PC 7),Taiyuan(LU 9)and Shenmen(HT 7)belong to the meridians of the pericardium,lung,and heart,respectively(Figure 12A).Despite the measurement errors,the huge differences in initial impedance and in the trend of limb angle dependence both imply that each of the three channels might have an independent main electrical conductance channel inside the arm.The actual channel paths might have complicated three-dimensional structures.For instance,they might be located in interstitial positions among the muscle tissues.

The electrical impedance may be related not only to the depth of the acupoint,but also to many other factors such as the physical condition of the study subjects during testing,the material,shape,and size of the electrodes,and even the particular testing time over the course of a day.Many questions remain unanswered,and further studies with a larger sample are required.Further research may focus on the detailed relationship between the depth of individual acupoints(referred to as the opening of superficial collaterals in the present study)and the acupoint impedance,and on the impact of limb posture on the acupoint impedance as well as related medical effects.

In conclusion,not all acupoints tested show the property of low impedance,which might be related to the varied depth of the openings of superficial collaterals.However,our findings strongly support the TCM theory that each channel takes an independent path in the body.The sensitive reaction of acupoint impedance to the limb angle suggests that these channel paths have complicated and independent three-dimensional structures.The paths are likely to be located in the interstitial structures of the limbs.

The dependency of acupoint impedance on limb posture implies that it might be possible to find an optimized limb posture for each particular treatment process in clinical practice.Further studies are required to confirm the present findings.

含VSC-HVDC的交直流电网最优潮流计算中，一般以降低网损或发电成本作为优化目标。这里采用机组发电成本之和最小作为目标函数，即：

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Similar phenomena were found in each subject.Due to limited space,we chose to present the data from three acupoints from one subject(Alpha)to demonstrate the three typical kinds of 2D mapping of impedance distribution around acupoints,and its good space resolution of 2 mm.

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谈到少数政府机关工作的弊病，我们最常听到的一句话就是形式主义。所谓形式主义，就是只讲形式，不求实效。一些老百姓内心想脱贫，但与少数干部接触一段时间之后又烦扶贫，烦的也是形式主义。形式主义对发号施令的人没什么，他反正是坐在空调房里、电脑桌旁，事情再多，也不要他去做。但群众就不一样了。你随便做个决定很容易，群众要实施这个决定，也许就忙得不可开交。正因为如此，任何时代，群众都是最反感形式主义的，只是有时他们表现了出来，有时他们放在心里。

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以标准化思维和手段助力“河长制”。采取群众评议等形式，或参照国内外相关政务服务标准的方式，了解公众在水环境治理中对政府的期望，尽快理顺管理体制，及时研究制定出台“河长制”标准化实施细则，以进一步规范化、常态化、精细化落实“河长制”。按照“简约化、统一化”原则，依托政府政务信息平台，将“河长制”工作性质统一定义，相关组织、人员、职责、监督、管理等事项条例性列出，进行有效信息匹配。通过大数据分析与云计算系统，分解量化各项指标，为水环境治理提供技术支撑。

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新课标指导下编写的教材，大多是模块式、主题式，一个单元就是一个主题或话题，所以教师在备课时要进行单元备课，整体安排，上课时也要从单元的高度导入新课，将各部分知识纳入单元的整体建构中。

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公路养护管理部门还要增强养护人员的专业技能，改变原有的公路养护理念，让养护人员更加清晰地了解自身工作性质，充分认识到做好公路大中修养护工作对公路安全运行的重要性。从公路养护管理人员自身角度来分析，要树立长远工作目标，正确看待公路大中修工程养护工作，并定期总结工作经验，对于结构不同的公路，应当采取不同的公路养护方法，并加强检修力度，提升公路预防性养护水平，保证公路能够可靠运行。

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另外，该词调还出现了集句作品。集句，即选取前代一位或数位诗人的诗词句，组织辑合为一首新诗或新词，是诗词创作的方式之一。两宋期间的《卜算子》也先后出现两首集句词，分别是杨冠卿的《卜算子·秋晚集杜句吊贾傅》和赵彦端的《卜算子·集句》。

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为了得到足够视野亮度，必须用强光源并开大光栅，使充足的光源进入物镜。同样条件下，物镜头放大倍数越大，镜口率越高，进入光线越少。因此，转换物镜头时应注意调整光线强度，使用油镜头时一定要添加香柏油。聚光镜抬高接近物镜头可以增加亮度，如果亮度已经足够甚至过剩，可以缩小光圈，或者下调聚光镜，但一般不降低底座光源强度，因为会使光源的颜色由白变黄，失去自然光属性，改变物像的颜色。下调聚光镜不仅可以降低亮度，还可以增加物像的对比度，使物像层次清晰。

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