overview of electronic supplementary material (esm)10.1007/s00114-009-0569... · electronic...

Electronic Supplementary Material (ESM)

for the manuscript of Baumgartner et al.: „High-field 1H T1 and T2 NMR Relaxation Time Measurements of H2O in Homeopathic Preparations of Quartz, Sulfur, and Copper Sulfate“

ESM title page (Overview of all ESM)

Overview of Electronic Supplementary Material (ESM) ESM S1: Additional information concerning chapter 2 (Materials and Methods): detailed account of all

materials and methods used ESM S2: Flow-chart for sample preparation and measurement for the entire study ESM S3: Relaxation times T1 [s] at 600 MHz for homeopathic preparations of quartz, sulfur and copper

sulfate and corresponding controls as a function of production sequence (i.e. number of control or homeopathic dilution level)

ESM S4: Relaxation times T2 [s] at 600 MHz for homeopathic preparations of quartz, sulfur and copper sulfate and corresponding controls as a function of production sequence (i.e. number of control or homeopathic dilution level)

ESM S5: Descriptive statistics for correlations of relaxation times T1 or T2 [s] at 600 MHz between the three capillary subsets for homeopathic preparations of quartz, sulfur and copper sulfate and corresponding controls

ESM S6: Graphical representation of correlations of relaxation times T1 [s] at 600 MHz between the three capillary subsets for homeopathic preparations of quartz, sulfur and copper sulfate and corresponding controls

ESM S7: Graphical representation of correlations of relaxation times T2 [s] at 600 MHz between the three capillary subsets for homeopathic preparations of quartz, sulfur and copper sulfate and corresponding controls

ESM S8: Descriptive statistics for correlations of relaxation times between T1 and T2 [s] at 600 MHz, calculated separately for the three capillary subsets for homeopathic preparations of quartz, sulfur and copper sulfate and corresponding controls

ESM S9: Graphical representation of correlations of relaxation times between T1 and T2 [s] at 600 MHz, plotted separately for the three capillary subsets for homeopathic preparations of quartz, sulfur and copper sulfate and corresponding controls

ESM S10: Correlation of relaxation times T1 [s] between the three capillary subsets for homeopathic preparations of sulfur and corresponding controls (independent samples of analogously agitated potentisation medium) measured at 500 MHz in Zurich: graphics and descriptive statistics

ESM S11: T1 measurements of homeopathic sulfur preparations and controls (data set II): descriptive statistics for correlations between data from Tallahassee (600 MHz) and from Zurich (500 MHz)

ESM S12: Additional information concerning chapter 4 (Discussion): detailed discussion of possible factors influencing T1 and T2 in the chosen experimental set-up

ESM S13: Graphical representation of correlation of relaxation times T1 at 600 MHz and capillary filling level for the three capillary subsets for homeopathic preparations of quartz, sulfur and copper sulfate and corresponding controls

ESM S14: Graphical representation of correlation of relaxation times T2 at 600 MHz and capillary filling level for the three capillary subsets for homeopathic preparations of quartz, sulfur and copper sulfate and corresponding controls

ESM S15: Descriptive statistics for correlation of relaxation times T1 and T2 and capillary filling level for the three capillary subsets for homeopathic preparations of quartz and corresponding controls

ESM S16: Descriptive statistics for correlation of relaxation times T1 and T2 and capillary filling level for the three capillary subsets for homeopathic preparations of sulfur and corresponding controls

ESM S17: Descriptive statistics for correlation of relaxation times T1 and T2 and capillary filling level for the three capillary subsets for homeopathic preparations of copper sulfate and corresponding controls

Electronic Supplementary Material (ESM) S1


ESM S1, page 1 of 3

Electronic Supplementary Material (ESM) S1 Additional Information concerning chapter 2 (Materials and Methods) Since NMR relaxation is very sensitive to tiny amounts of impurities, our aim was to prepare homeopathic preparations that meet current standards of trace analytics as well as current legal regulation for homeopathic remedies (Anonymous 2004). Therefore, homeopathic preparations and controls were produced in a clean room using standard trace analytical procedures and equipment as well as standard homeopathic procedures.

2.1 Water preparation Water was prepared according to standard procedures in trace analytics. Deionised water (DI-water) was prepared from tap water using two ion exchange columns (Culligan, Northbrook IL, USA) for a first deionization and a subsequent Millipore system (Super-Q water purification system with four cartridges: 1. Super–C for organic removal, 2. Ion-Ex and 3. Ion-Ex for inorganic removal, and 4. Durapore for bacteria and particle removal), resulting in water of 18 MΩcm. Quartz distilled water (QD-water) was prepared by subsequent subboiling distillation of the DI-water (Seastar Chemicals Inc., Sidney BC, Canada).

2.2 Chemicals Hydrochloric acid (HCl) was subboiling double-distilled HCl, prepared from reagent grade HCl (certified ACS PLUS, normality 12.1, A 2005–212, from Fisher Scientific, Fairlawn NJ, USA). Nitric acid (HNO3) was twice two-bottle distilled HNO3, prepared from reagent grade HNO3 (certified ACS PLUS, normality 15.8, A 1445–212, from Fisher Scientific, Fairlawn NJ, USA). Ethanol used was Ethyl Alcohol USP, Absolute – 200 Proof (Aaper Alcohol and Chemical Co., Shelbyville, USA). Lactose (No 010924) was ordered from Dixa AG (St. Gallen, Switzerland), quartz powder (SiO2, No M1378-98, particle size < 63 µm) from Weleda AG (Schwäbisch Gmuend, Germany), copper sulfate (CuSO4·5H2O, No 532/99) from Weleda AG (Arlesheim, Switzerland), sublimed sulfur (S8, No Ch 3019912) from Phytomed AG, Hasle/Rüegsau, Switzerland. ICP-MS standards were obtained from High-Purity-Standards, Charleston SC, USA.

2.3 Clean room All samples were prepared in a metal-free class 100 HEPA (High Efficiency Particulate Air) filtered clean room. Clean flow boxes had class 5. All workers wore whole body protective suits.

2.4 Vessels Potentisation (dilution) vessels for all liquids were 500 ml narrow-necked bottles with conical shoulder, made from boro-silicate glass (DURAN, Schott, from VWR International, Dietikon, Switzerland). All 40 vessels used were numbered permanently in order to be able to retrace the use of every individual vessel during the entire study. After production of one series of homeopathic preparations and the corresponding controls, all vessels were cleaned (see below) and reused in randomized allocation for the next series. Trituratio (potentisation of solid compounds, see below) was performed with a porcelain mortar and pestle. For the ICP-MS measurement 4 ml polypropylene vials (Omni vials Polypropylene (PP), Cole-Parmer, Vernon Hills IL, USA) and for the NMR measurement micropipettes tubes (Wiretrol II, 1–5 µl) made of boro-silicate glass (Drummond Scientific Company, Broomall PA, USA) were used.

2.5 Cleaning To minimize ion release from the vessel walls, all vessels used for liquid sample preparation and measurement were pretreated as customary in inorganic trace analytics. Only the NMR measurement micropipettes tubes could not be cleaned with reasonable effort due to the tiny volume (≈17 µl). The treatment of the dilution (potentisation) vessels before the first use included: Rinse 3 x with DI-water, fill 1/4 of height with 1.2 N HCl (12.1 N, Fisher Scientific, 1:10 diluted with QD-water), put vessels on hot plate (125°C) for 8 hours in a clean flow box, remove HCl, rinse 3 x with DI-water, rinse 3 x with QD-water. Cleaning of the dilution vessels before sulfur sample preparation consisted of: Rinsing 3 x with QD-water. Potentisation vessels before copper sulfate sample preparation: Rinsing 3 x with DI-water and 3 x with QD-water. Vessels having contained homeopathic dilutions with concentrations higher than 10–10 were rinsed 6 x with DI-water and 3 x with QD-water. ICP-MS-vials and pipette tips: 24 h in 7.9 N HNO3 (15.8 N, Fisher Scientific, 1:1 diluted with QD-water) on hot plate (100°C), rinse 3 x DI-water, rinse 3 x QD-water. Mortar and pestle used for trituratio (see below) were rinsed with hot and cold tap water, then with distilled water, finally with ethanol (75%), and dried at 80°C.



ESM S1, page 2 of 3

2.6 Preparation of homeopathic preparations and controls Quartz and copper sulfate were prepared as so called “c-potencies” (centesimal potencies, 100fold dilution). Sulfur was diluted in decimal steps (10-fold dilution, so-called “x-potencies”). Liquid dilution medium was Quartz distilled water (QD-water) with 1% ethanol, mixed in our laboratory (ethanol was added because we originally aimed at measuring 1H relaxation also in ethanol). All homeopathic preparations and controls of a given set (quartz, sulfur or copper sulfate) were prepared from the same batch of QD-water with 1% ethanol. Solid “dilution” (mixing) medium was lactose (applied only for the first 3 dilution steps of quartz and the first 6 dilution steps of sulfur – see below). Trituratio (grinding and simultaneous “dilution” of insoluble solids in lactose, i.e. homeopathic “potentisation” of solid compounds) was performed by hand for 60 minutes according to standard homeopathic pharmaceutical procedures (prescription no. 6 of the German Homeopathic Pharmacopoeia (Anonymous 2004)). 1 g quartz powder was triturated with 99 g lactose with mortar and pestle to obtain quartz 1c. Quartz 2c and 3c were prepared analogously from quartz 1c or 2c, respectively. 10 g sulfur powder were triturated with 90 g lactose to obtain sulfur 1x. Sulfur 2x, 3x up to 6x were prepared analogously from sulfur 1x, 2x, up to 5x, respectively. Homeopathic “potentisation” (dilution and vigorous shaking) of liquids was performed by hand according to standard pharmaceutical procedures (Anonymous 2004) with the multiple glass method. For potentisation, the vessel was closed with its stopper and shaken horizontally back and forth for 4 minutes at a rate of about 2.7 Hz. For copper sulfate, the first dilution level (1c) was prepared by dissolving 2 g of copper sulfate in 200 ml QD-water with 1% ethanol and successive shaking. For the next dilution step, 2 ml of fluid were pipetted into another bottle filled with 198 ml QD-water with 1% ethanol; the content was shaken as described above. All further dilution levels were prepared analogously. For quartz, liquid potentisation started with the dissolution of 2 g quartz trituratio 3c in 200 ml QD-water with 1% ethanol. Shaking resulted in quartz 4c. All further liquid potentisation levels were prepared as described above for copper sulfate. For sulfur, liquid potentisation started with the dissolution of 10 g sulfur trituratio 6x in 100 ml QD-water with 1% ethanol. Shaking resulted in sulfur 7x. All further liquid potentisation levels were prepared analogously as described above, but with a dilution ratio of 1:9 (20 ml added to 180 ml dilution medium). For each set of homeopathic preparations (quartz, sulfur, or copper sulfate), 10 independent controls were prepared as follows: 1 glass bottle was filled with 200 ml QD-water with 1% ethanol and shaken equally to the homeopathic preparations. No lactose was added to the controls. The 10 controls were independent, i.e. there was no dilution from one control to another. This procedure resulted in a preparation called “agitated dilution medium”. This type of control accounts for all the unspecific physicochemical effects associated with agitation, e.g. ion release from the vessel walls, air suspension and dissolution with subsequent pH alteration, and radical formation as discussed in Baumgartner et al. (1998). 5 of the controls were prepared before the preparation of the homeopathic preparations, and 5 controls afterwards in order to control for a possible cross-contamination and other interference in the course of the production process. Randomization was effectuated through random allocation of the numbered potentisation vessels to the dilution levels or controls to be produced. Codes were kept secret until the end of the measurements and data reduction, with the exception of one control sample (for each series) that was measured several times. ESM S2 gives a flow chart of the sample preparation and measurements for the entire study.

2.7 ICP-MS measurements 3 ml samples of each homeopathic preparation and control were pipetted from the preparation vessels directly into ICP-MS-vials to which 15 µl internal standard (45Sc, 74Ge, 115In, 205Tl, 1ppb each) and 30 µl 15.8 N HNO3 were added. Samples were prepared in the clean room and sealed with a cap. Samples were transferred to the ICP-MS-autosampler and opened only under the protection hood of the sampler. For analysis, a Sector ICP-MS Finnigan MAT Element (Thermo Electron, Karlsruhe, Germany) with PFA inlet system, Teflon spray chamber, and PFA nebulizer with a flowrate of 100 µl/min was used. The system was run with guard electrode in operational mode. Analyzed elements were 7Li, 11B, 23Na, 24Mg, 27Al, 28Si, 44Ca, 48Ti, 56Fe, 65Cu, 66Zn, 85Rb, 88Sr, 133Cs, 137Ba, and 208Pb, measured either in low or medium resolution mode. Samples were measured in random order in runs of 10 samples. Blank and external standard samples (all analyzed elements in a concentration of about 1 ppb) were measured at the beginning, in the middle and at the end of each run. After measurement, data reduction was performed as follows. For each run, the slope of the corresponding calibration curve was calculated (difference between the means of the external standards and of the blanks (n=3 each [cps]), divided by the concentration of the standard [ppb]). The inverted calibration curve (according to Funk et al. (1985), p. 38) was used to calculate effective concentrations [ppb] for all samples. Errors (95% confidence limits, tDf=3=3.18) were calculated according to Funk et al. (1985), p. 43. Detection limit



ESM S1, page 3 of 3

determination was based upon the standard deviation of the blank (n=3) for alpha = beta = 5% (t Df=1=6.31) according to Funk et al. (1992), p. 25.

2.8 NMR measurements One aim of the NMR measurements was to achieve a low measurement error and a high reproducibility. During a pilot phase we examined and optimized various aspects of the measurement. In particular, the sample volume was adjusted to exclude radiation damping, and various delay times were tested to achieve a minimal error of measurement. Using a locking agent (D2O) increased the error of measurement considerably and was therefore not used. The water peak is high, which leads to a high signal to noise ratio and a low error of measurement. The resulting procedure is detailed below. We were not able to realize our original idea to measure 1H relaxation also in ethanol because the signal amplitude of the corresponding protons was too small. For each sample, 4–6 capillaries were filled with about 10 µl fluid by capillary action in the clean room. Capillaries were flame sealed at one end, optically checked by binocular for tight closure, centrifuged at 1400 rpm for 75 sec., flame sealed at the other end, and again checked by binocular. This procedure was done within few hours in order to minimize environmental influences (changing air pressure etc.). Filling level was measured for each capillary with a millimeter ruler. The NMR measurements at the NHMFL Florida were performed with an Oxford superconducting magnet at 600 MHz, 14.1T using a 5mm Varian NMR PFG probe and a Varian console (Varian unity plus). Data processing was done with a Sun Ultra 5 Sparc PC workstation, equipped with Varian VNMR 6.1 software (Version C). For each sample, three capillaries out of a total of 4–6 were randomly selected. Capillaries were placed in a standard 5mm NMR tube without centering. All samples (individual capillaries) were measured at 20±0.1 °C (controlled by automatic temperature control (VT)) after 10 minutes of temperature equilibration within the magnet. Shimming for all samples was checked and adjusted individually by gradient shimming and by hand (minimizing the line width). The line width was <3Hz. PW90 was measured for each sample and was in the order of 10µs. Samples were measured in random order. Measurements of an entire set (18–21 homeopathic preparations and 10 controls) were accomplished within 210–310 h after sealing, with about 100 h of net measurement time. Three sample sets were prepared for measurement: 1.) set I: quartz (21 dilution levels of quartz and 10 controls,), 2.) set II: sulfur (18 dilution levels of sulfur and 10 controls), and 3.) set III: copper sulfate (20 dilution levels of copper sulfate and 10 controls). For each sample set, we aimed at measuring three capillaries (#1, #2, #3). Within the sample set, all capillaries #1 were measured first, then all capillaries #2 and finally all capillaries #3. All data of capillaries #1 form the data subset #1; data subsets #2 and #3 are defined analogously. For every sample, T1 was measured by an inversion recovery sequence with 18 spectra (d2=18; 0.025; 12; 0.04; 7.5; 0.06; 5; 0.09; 4; 0.14; 3; 0.22; 2.5; 0.35; 2; 0.54; 1.2; 0.83s), T2 immediately thereafter with the Carr-Purcell-Meiboom-Gill sequence (standard CPMGt2 parameter set) using 19 spectra (bt= 0; 0.128; 0.256; 0.368; 0.496; 0.624; 0.752; 0.88; 1.008; 1.12; 1.248; 1.376; 1.504; 1.632; 1.744; 1.872; 2; 2.496; 3.008s). For both sequences we used the following parameters: D1=10.6s, NT=4 (cycling through all phases); LB=0.318Hz, AT=4.098s, NP=40960. Data was Fourier transformed, baseline corrected and phased. Integrals were calculated over the area of the peak to increase the signal-to-noise ratio. Relaxation times were obtained from the exponential data analysis provided by the VNMR 6.1 software. Due to restrictions in magnet time availability we could not measure all samples prepared in the quartz data set: no data are available for capillaries #2 and #3 for quartz 21c and control No 6. Data for capillary #3 of sulfur control No 1 were excluded a posteriori because of insufficient centrifugation, as well as capillary #1 of copper sulfate 18c and 19c because of tiny air bubbles. The NMR measurements at the ETH Zurich were performed on a Bruker AVANCE 500 spectrometer (500.133 MHz, 11.7467 T) equipped with a 5 mm broad-band probe with an actively shielded z-gradient coil. The capillaries were centered by means of Teflon rings in high precession 5mm NMR tubes. The temperature was 293 K, controlled with a nitrogen flow of 400 l h-1 to avoid temperature fluctuations of more than 0.1 K. T1 times have been obtained with the standard inversion-recovery [rd – p180H – id1 – p90H – acquisition]n (relaxation delay > 5T1) pulse sequence (Bruker pulse program t1ir). In each experiment a series of 8–16 spectra were collected with an FID resolution of 0.8 Hz. P1 was 10.25µs and id=30; 20; 15; 12.5; 10; 8; 6; 5; 4; 3; 2; 1; 0.5; 0.3; 0.1; 0.05s. After Fourier transformation and baseline correction, data processing by the SimFit algorithm in XWinNMR 3.5 was done. T1 was measured three times in series and averaged. Three capillaries were missing (broken) and not measured: capillary #2 of sulfur 22x and 28x, and capillary #3 of control No 3. Data for capillary #3 of sulfur control No 1 were excluded because of insufficient centrifugation.

– 5 bottles with water 1c each– 27 bottles: quartz 4c – 30c– 5 bottles with water 1c each

randomization

• chemical analysis by ICP-MS• UV-spectroscopy

• NMR relaxation time T1, T2

blinding and randomization

• chemical analysis by ICP-MS

– 40 bottles with water 1x each(succussion by hand for 4 min.)

40 borosilicate glass bottles (DURAN)

– rinsing 3 times with DI water– pretreatment with 1.2 M HCl for 7 h at 150°C

– rinsing 3 times with DI water– rinsing 3 times with QD-DI water

rinsing 3 times with QD-DI water

– 5 bottles with water 1x each– 24 bottles: sulfur 7x – 30x– 5 bottles with water 1x each



randomization


– 5 bottles with water 1x each– 30 bottles: copper sulfate 1c – 30c– 5 bottles with water 1x each




rinsing 3–6 times with DI waterand 3 times with QD-DI water

randomization

M

M

M

M

S

S

S

S

Flow-chart for sample preparation and measurement for the entire study.S: sample preparation, M: measurements.


for the manuscript of Baumgartner et al.: „High-field 1H T1 and T2 NMR Relaxation Time Measurements of H2O

in Homeopathic Preparations of Quartz, Sulfur, and Copper Sulfate“

ESM S2

2.85

2.90

2.95

3.00

3.05

3.10

3.15

3.20

0 1 2 3 4 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 5 6 7 8 9

T1 capillary subset #1



T1 [s]

Controls Homeopathic quartz preparations [dilution level 100–xx] Controls

a

2.92

2.96

3.00

3.04

3.08

0 1 2 3 4 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 5 6 7 8 9




T1 [s]

Controls Homeopathic sulfur preparations [dilution level 10–xx] Controls

b

2.86

2.88

2.90

2.92

2.94

2.96

2.98

3.00

3.02

0 1 2 3 4 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 5 6 7 8 9




T1 [s]

Controls Homeopathic copper sulfate preparations [dilution level 100–xx] Controls

c

0.45

0.46

0.47

0.48

0.49

0.50

0.51

0.52

0.53

0 1 2 3 4 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 5 6 7 8 9




T2 [s]

Controls Homeopathic quartz preparations [dilution level 100–xx] Controls

a

0.44

0.46

0.48

0.50

0.52

0.54

0.56

0 1 2 3 4 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 5 6 7 8 9




T2 [s]

Controls Homeopathic sulfur preparations [dilution level 10–xx] Controls

b

0.44

0.45

0.46

0.47

0.48

0.49

0.50

0 1 2 3 4 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 5 6 7 8 9




T2 [s]

Controls Homeopathic copper sulfate preparations [dilution level 100–xx] Controls

c



ESM S5

Hom. prep. Controls

Cap. subsets n r z p n r z p

Quartz T1 #1 and #2 20 0.421 0.449 0.064 9 0.659 0.791 0.053

#1 and #3 20 0.519 0.575 0.019 9 0.565 0.640 0.113

#2 and #3 20 0.345 0.360 0.136 9 0.661 0.795 0.052

mean 0.431 0.462 0.630 0.742

Quartz T2 #1 and #2 20 0.234 0.238 0.321 9 0.905 1.499 0.001

#1 and #3 20 0.446 0.480 0.049 9 0.953 1.861 0.001

#2 and #3 20 0.277 0.285 0.237 9 0.893 1.438 0.001

mean 0.322 0.334 0.922 1.599

Sulfur T1 #1 and #2 18 0.122 0.123 0.629 10 -0.480 -0.523 0.160

#1 and #3 18 -0.114 -0.115 0.652 9 0.287 0.295 0.454

#2 and #3 18 -0.025 -0.025 0.922 9 -0.004 -0.004 0.992

mean -0.006 -0.006 -0.077 -0.077

Sulfur T2 #1 and #2 18 0.395 0.418 0.105 10 0.562 0.636 0.091

#1 and #3 18 0.387 0.409 0.112 9 0.781 1.048 0.013

#2 and #3 18 0.030 0.030 0.905 9 0.391 0.413 0.298

mean 0.278 0.286 0.604 0.699

Copper sulfate T1 #1 and #2 18 -0.101 -0.101 0.691 10 0.245 0.250 0.496

#1 and #3 18 -0.145 -0.146 0.567 10 0.214 0.217 0.553

#2 and #3 20 0.417 0.444 0.067 10 -0.075 -0.075 0.838

mean 0.066 0.066 0.130 0.131

Copper sulfate T2 #1 and #2 18 0.161 0.163 0.522 10 0.218 0.221 0.546

#1 and #3 18 0.142 0.143 0.574 10 0.331 0.344 0.350

#2 and #3 20 0.278 0.285 0.236 10 0.190 0.192 0.600

mean 0.195 0.197 0.247 0.253

Correlation of relaxation times T1 or T2 [s] at 600 MHz between the three capillary subsets (#1, #2, #3) for homeopathic preparations of quartz, sulfur and copper sulfate and corresponding controls (independent samples of agitated potentisation medium). n = number of samples, r = correlation coefficient, z= z-transformed corr. coeff., p = p-value. Mean correlation coefficients were calculated based on z-transformed correlation coefficients. Corresponding graphics are plotted in ESM S3 and S4.

a

T1 cap. subset #2 as f(#1)


y = 0.60332 + 0.81427x R= 0.42133

y = 0.37435 + 0.92014x R= 0.51922

Quartz data set:Homeopathic preparations

2.85

2.90

2.95

3.00

3.05

3.10

3.15

3.20

2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20


y = 2.1387 + 0.31661x R= 0.34527

T1 [sec]

T1 [sec]

2.85

2.90

2.95

3.00

3.05

3.10

3.15

3.20

2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20


y = 0.98002 + 0.69432x R= 0.66141

T1 [sec]

T1 [sec]

d



y = -4.2781 + 2.4664x R= 0.65911

y = -3.4848 + 2.2181x R= 0.56467

Quartz data set:controls

2.90

2.95

3.00

3.05

3.10

2.90 2.95 3.00 3.05 3.10


y = 3.189 - 0.070228x R= 0.024711

T1 [sec]

T1 [sec]

b



y = 2.627 + 0.11211x R= 0.12215

y = 3.8563 - 0.29772x R= 0.11414

Sulfur data set:Homeopathic preparations

2.90

2.95

3.00

3.05

3.10

2.90 2.95 3.00 3.05 3.10


y = 2.9765 - 0.0044329x R= 0.0037781

T1 [sec]

T1 [sec]

e



y = 5.9143 - 1.0095x R= 0.48009

y = 0.92875 + 0.69189x R= 0.28699

Sulfur data set:Controls

2.85

2.90

2.95

3.00

2.85 2.90 2.95 3.00


y = 0.79353 + 0.7378x R= 0.41711

T1 [sec]

T1 [sec]

c



y = 3.2002 - 0.099937x R= 0.10073

y = 3.6605 - 0.2487x R= 0.14451

Copper sulfate data set:Homeopathic preparations

2.85

2.90

2.95

3.00

2.85 2.90 2.95 3.00


y = 3.2395 - 0.10337x R= 0.07455

T1 [sec]

T1 [sec]

f



y = 2.0282 + 0.30731x R= 0.24469

y = 1.8653 + 0.37203x R= 0.21364

Copper sulfate data set:Controls

0.44

0.46

0.48

0.50

0.52

0.44 0.46 0.48 0.50 0.52


y = 0.31972 + 0.33013x R= 0.2773

T2 [sec]

T2 [sec]



y = 0.39141 + 0.17389x R= 0.23402 y = 0.29025 + 0.39445x R= 0.4459


a

0.44

0.46

0.48

0.50

0.52

0.44 0.46 0.48 0.50 0.52


y = -0.25285 + 1.5355x R= 0.89326

T2 [sec]

T2 [sec]

d



y = 0.1672 + 0.65062x R= 0.905 y = -0.081039 + 1.1774x R= 0.95273


0.44

0.46

0.48

0.50

0.52

0.54

0.56

0.44 0.46 0.48 0.50 0.52 0.54 0.56


y = 0.48122 + 0.027385x R= 0.030411

T2 [sec]

T2 [sec]

b



y = 0.219 + 0.57746x R= 0.39517

y = 0.24917 + 0.5098x R= 0.38741


0.44

0.46

0.48

0.50

0.52

0.54

0.56

0.44 0.46 0.48 0.50 0.52 0.54 0.56


y = 0.33044 + 0.34775x R= 0.39104

T2 [sec]

T2 [sec]

e



y = -0.028423 + 1.0958x R= 0.56201 y = -0.15643 + 1.3731x R= 0.78099


0.44

0.45

0.46

0.47

0.48

0.49

0.44 0.45 0.46 0.47 0.48 0.49


y = 0.37542 + 0.19049x R= 0.27781

T2 [sec]

T2 [sec]

c



y = 0.40334 + 0.13658x R= 0.16132 y = 0.42792 + 0.077788x R= 0.1422


0.44

0.45

0.46

0.47

0.48

0.49

0.44 0.45 0.46 0.47 0.48 0.49


y = 0.36864 + 0.21711x R= 0.18951

T2 [sec]

T2 [sec]

f



y = 0.40515 + 0.1194x R= 0.21778 y = 0.37229 + 0.20815x R= 0.33138




ESM S8

Hom. prep. Controls Cap. subsets n r p n r p Quartz #1 21 0.342 0.129 10 0.298 0.404 #2 20 -0.266 0.256 9 0.245 0.525 #3 20 0.104 0.664 9 0.358 0.344 Sulfur #1 18 -0.137 0.589 10 0.460 0.181 #2 18 -0.226 0.366 10 -0.272 0.448 #3 18 -0.793 0.001 9 -0.740 0.024 Copper sulfate #1 18 -0.540 0.021 10 -0.293 0.411 #2 20 -0.040 0.866 10 -0.665 0.036 #3 20 0.102 0.669 10 -0.112 0.759 Correlation of relaxation times between T1 and T2 [s] at 600 MHz, calculated separately for the three capillary subsets (#1, #2, #3) of the homeopathic preparations of quartz, sulfur and copper sulfate and of the corresponding controls (independent samples of agitated potentisation medium). n = number of samples, r = correlation coefficient, p = p-value. Corresponding graphics are plotted in ESM S9.

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y = 0.12519 + 0.11702x R= 0.3418 y = 0.57855 - 0.035007x R= 0.26648 y = 0.42139 + 0.017659x R= 0.10354

T2 [sec]

T1 [sec]


a

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d




y = -0.49641 + 0.32894x R= 0.29757 y = 0.32027 + 0.052036x R= 0.24514 y = 0.097287 + 0.12448x R= 0.35811

T2 [sec]

T1 [sec]


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b




y = 0.8585 - 0.12816x R= 0.13656 y = 1.4973 - 0.33825x R= 0.22638 y = 1.614 - 0.37538x R= 0.79288

T2 [sec]

T1 [sec]


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e




y = -1.1293 + 0.54786x R= 0.45979 y = 1.3838 - 0.30023x R= 0.27176 y = 2.3904 - 0.63659x R= 0.7369

T2 [sec]

T1 [sec]


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c




y = 1.3775 - 0.31699x R= 0.53969 y = 0.52488 - 0.020019x R= 0.040208 y = 0.4064 + 0.019686x R= 0.10199

T2 [sec]

T1 [sec]


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f




y = 1.2193 - 0.26235x R= 0.29342 y = 1.2163 - 0.25936x R= 0.66446

y = 0.57449 - 0.036041x R= 0.11175

T2 [sec]

T1 [sec]


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y = 1.9345 + 0.35294x R= 0.3879

T1 [sec]

T1 [sec]

a



y = 2.4102 + 0.19923x R= 0.41528 y = 2.6934 + 0.10135x R= 0.20426


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y = 1.1994 + 0.59681x R= 0.38659

T1 [sec]

T1 [sec]

b



y = 2.5827 + 0.12964x R= 0.26968

y = 2.489 + 0.1618x R= 0.41176

Sulfur data set:controls



ESM S11

T1 measurements of homeopathic sulfur preparations and controls (data set II) Correlation between data from Tallahassee (TLH, 600 MHz) and from Zurich (ZRH, 500 MHz) Legend T1_1_TLH Capillary subset #1 measured in TLH T1_2_TLH Capillary subset #2 measured in TLH T1_3_TLH Capillary subset #3 measured in TLH T1_TLH Mean value of 3 capillaries (TLH) T1_1_ZRH Capillary subset #1 measured in ZRH T1_2_ZRH Capillary subset #2 measured in ZRH T1_3_ZRH Capillary subset #3 measured in ZRH T1_ZRH Mean value of 3 capillaries (ZRH) r correlation coefficient p p-value n number of data points Controls only T1_1_ZRH T1_2_ZRH T1_3_ZRH T1_ZRH T1_1_TLH r = -0.17194 r = -0.12233 r = -0.02016 r = -0.22592 p = 0.635 p = 0.736 p = 0.962 p = 0.530 (n = 10) (n = 10) (n = 8) (n = 10) T1_2_TLH r = 0.03443 r = -0.14069 r = 0.15101 r = 0.00206 p = 0.925 p = 0.698 p = 0.721 p = 0.995 (n = 10) (n = 10) (n = 8) (n = 10) T1_3_TLH r = 0.3196 r = 0.77659 r = 0.57159 r = 0.63446 p = 0.402 p = 0.014 p = 0.139 p = 0.066 (n = 9) (n = 9) (n = 8) (n = 9) T1_TLH r = 0.22466 r = 0.43227 r = 0.48435 r = 0.40663 p = 0.533 p = 0.212 p = 0.224 p = 0.244 (n = 10) (n = 10) (n = 8) (n = 10) Hom. prep. only T1_1_ZRH T1_2_ZRH T1_3_ZRH T1_ZRH T1_1_TLH r = 0.25238 r = 0.34582 r = -0.11424 r = 0.21249 p = 0.312 p = 0.190 p = 0.652 p = 0.397 (n = 18) (n = 16) (n = 18) (n = 18) T1_2_TLH r = 0.11104 r = 0.34182 r = 0.43947 r = 0.31158 p = 0.661 p = 0.195 p = 0.068 p = 0.208 (n = 18) (n = 16) (n = 18) (n = 18) T1_3_TLH r = 0.1916 r = 0.01108 r = -0.08265 r = 0.08553 p = 0.446 p = 0.968 p = 0.744 p = 0.736 (n = 18) (n = 16) (n = 18) (n = 18) T1_TLH r = 0.29905 r = 0.23976 r = 0.02574 r = 0.25265 p = 0.228 p = 0.371 p = 0.919 p = 0.312 (n = 18) (n = 16) (n = 18) (n = 18) All data T1_1_ZRH T1_2_ZRH T1_3_ZRH T1_ZRH T1_1_TLH r = 0.11645 r = 0.10634 r = -0.09355 r = 0.05661 p = 0.555 p = 0.605 p = 0.649 p = 0.775 (n = 28) (n = 26) (n = 26) (n = 28) T1_2_TLH r = 0.10275 r = 0.2303 r = 0.36584 r = 0.24316 p = 0.603 p = 0.258 p = 0.066 p = 0.212 (n = 28) (n = 26) (n = 26) (n = 28) T1_3_TLH r = 0.2387 r = 0.30833 r = 0.10794 r = 0.29692 p = 0.231 p = 0.134 p = 0.600 p = 0.133 (n = 27) (n = 25) (n = 26) (n = 27) T1_TLH r = 0.29621 r = 0.41107 r = 0.2197 r = 0.38523 p = 0.126 p = 0.037 p = 0.281 p = 0.043 (n = 28) (n = 26) (n = 26) (n = 28)



ESM S12, page 1 of 3

Electronic Supplementary Material (ESM) S12 Additional Information concerning chapter 4 (Discussion) What are factors that influence T1 and T2 relaxation times and that might furnish an explanation of the phenomena observed? First, one has to carefully consider all types of unintended side effects such as: 1. Contamination with dust; 2. Leached substances from the dilution vessel walls; 3. Varying ethanol content; 4. Leached substances from the measurement vessel walls (capillaries); 5. Microorganisms growing in the solutions; 6. Contamination with flame gases; 7. Differences in pH; 8. Traces of the substance diluted; 9. Paramagnetic oxygen (O2); and 10. Other paramagnetic substances. If all these factors can be ruled out, one may discuss specific physicochemical explana-tions involving 11. Dipolar 1H spin coupling and 12. Scalar spin-spin-coupling (quadrupole relaxation can be ruled out since 1H has no electric quadrupole moment). In the following we discuss all possible explanations in detail.

1.) Contamination with dust. Sample preparation (dilution and succussion) was effectuated with great care under standardized clean room condi-tions; all material used was cleaned as customary in trace analytics (see Materials and Methods). In addition, chemi-cal analysis with ICP-MS yielded no evidence for contamination during sample preparation: none of the samples exceeded the concentration of 10 ppb for any of the elements measured. Some of the elements measured by ICP-MS (e.g. Na, Al, Fe) are good tracers for most kind of airborne environmental particles (“dust”); we therefore conclude that a contamination with dust during sample preparation is highly improbable. A weak point, however, is the use of capillaries as NMR measurement vessels, which could not be cleaned with reasonable effort. Since the capillaries are also manufactured for medical purposes, a heavy dust load is quite improbable. In addition, a systematic differ-ence between control samples and homeopathic preparations seems improbable for the following reasons: 1. all samples (homeopathic potencies and controls) of one sample set (quartz, sulfur, and copper sulfate) were prepared with capillaries from the same lot; 2. samples were processed in random order; 3. four to six capillaries were pre-pared for each sample, from which three capillaries were randomly selected for measurement.

2.) Leached substances from the dilution vessel walls. It is well known that pure water as used in our investigation leaches many ions from the glass vessel walls used for dilution and preparation of the homeopathic solutions and controls. Leaching was minimized due to the careful cleaning and acid pre-treatment of the dilution vessels (see ESM S1). No outliers were observed in the preceding water control run, and no systematic differences between homeopathic preparations and controls were observed in the ICP-MS analysis (Table 1). A systematic difference between control samples and homeopathic preparations also seems improbable due to the random allocation of the dilution vessels used.

3.) Varying ethanol content. Compared to pure water, the addition of 1% ethanol leads to a reduction of T1 of about 3% (from about 3.1 sec to about 3 sec) and a much stronger reduction of T2 of about 75% (from about 2.2 sec to about 0.5 sec). The decrease in T1 is comparable to literature data, see e.g. Clifford and Pethica (1965) or von Goldammer and Zeidler (1969); we did not find any data in literature for T2 of water-ethanol mixtures. During sample preparation, errors can be intro-duced by mistakes in pipetting or by unequal evaporation (e.g. by unevenly closed stoppers or differences in time during the capillary sealing process). Again, a systematic difference between control samples and homeopathic preparations is improbable due to the blinded random allocation of the vessels used. For the same reasons, differ-ences in ethanol concentration due to unequal capillary filling levels (leading to unequal evaporation of ethanol into the capillary void and subsequently to differences in ethanol content) are improbable. The general increase of T1 in the course of time (Fig. 1) cannot be due to evaporating ethanol into the capillary void, because the corresponding effect in T2 is much smaller.

4.) Leached substances from the measurement vessel walls (capillaries). Even though the capillaries were also made of highly resistant boro-silicate glass, leaching within the capillaries will be stronger than in the dilution vessels due to the higher ratio of surface to volume. Due to the small sample amount (≈ 10 µl), analysis of the elementary composition after the NMR measurement was not possible. Referring to the main constituents of the boro-silicate glass used, we would expect release of Si, B, Al, K, Na, Ca, and Mg. Engel and Hertz (1968) investigated the influence of the latter three ions on the proton relaxation rate (1/T1) in water. In all three cases, T1 decreased with increasing concentration. 1 m (molale, mol/kg) solutions led to maximal decrease of 33%. A change in T1 of 1% thus would require concentrations in the order of 1:1000. This is far beyond what can be expected as release from the capillary vessel walls. We found no comparable data for Si, B, K, and Al and thus can-not estimate their effects on T1 or T2. Si might be present not only as dissolved Si(OH)4, but also as polysilicid acid or colloidal silica (Iler 1979). Also here, we did not find any data to estimate the effects of silica hydrogel formation on proton T1 and T2. Thus a possible influence of this process cannot be excluded. However, a systematic difference between control samples and homeopathic sulfur preparations due to some systematic differences between capillar-ies again seems improbable due to the blinded and random allocation of the capillaries used.




On the other hand one could raise the quite unconventional, but easily testable hypothesis, that homeopathic sulfur preparations influence leaching and/or silica hydrogel formation. One hint in this direction can be found in the in-vestigation of Demangeat et al. (2004) who measured a 10% excess of Si in homeopathic preparations of SiO2 com-pared to potentised dilution medium. In this context we also want to discuss the observation that different correla-tions were in many cases higher (better) for the control samples than for the homeopathic preparations. The correla-tion between the relaxation time data for the three different capillary subsets yields some information about the ratio of the signal of the dilution vessels compared to the signal of the capillaries. If the influence of the capillaries is negligible, correlation coefficients should be around unity; if the influence of the capillaries is very strong (e.g. by leaching), correlation would be expected to be zero. Thus the systematically lower correlation coefficients for all homeopathic preparations (cf. ESM S5) at least do not contradict the hypothesis that homeopathic preparations in-teract with the leaching process. Most probably, enhanced leaching would lead to a decrease in T1 and T2 since out of the main capillary glass composition (Si, B, Al, K, Na, Ca, and Mg), only K is known as structure breaker (Marcus 1985). Thus, in the sulfur preparations with a higher T1 leaching would be reduced (compared to the con-trols).

5.) Microorganisms growing in the solutions Since the samples were not prepared under sterile conditions it is not possible to exclude a microbial contamination, consequences of which for T1 and T2 are difficult to estimate. Again, blinding and the various randomization proce-dures applied should exclude a systematic difference between homeopathic preparations and controls. The lactose concentration in the most concentrated sulfur preparation (13x) was 0.1 ppm and correspondingly lower for all other dilutions. This concentration seems to be too small to induce relevant effects compared to the controls (without lactose).

6.) Contamination with flame gases During the sealing process flame gases might enter the capillary and modify T1 and T2 in an unknown direction. Blinding and the various randomization procedures applied should exclude a systematic difference between homeo-pathic preparations and controls.

7.) Differences in pH Unequal shaking or unequal capillary void volumes could infer different amounts of CO2 dissolved in the tested solutions with corresponding consequences for pH. According to Meiboom (1961), pH alterations only influence T2 and leave T1 unchanged. Thus, pH changes can explain neither the general increase in T1 data in the course of time nor the elevated T1 values for the homeopathic sulfur preparations, nor the partially negative correlation of T2 and T1.

8.) Traces of the substance diluted Dilution was effectuated with great care using multiple vessels. Thus, a cross-contamination can be excluded with high certainty. Sulfur (S) is ubiquitary at a level of about 10–12 (Hopff 1991). Therefore, all homeopathic sulfur preparations and also the corresponding controls measured in our study are expected to have comparable material sulfur content. The same holds true for the quartz and copper sulfate preparations. Thus the observed increase in T1 for the sulfur preparations cannot be due to trace amounts of sulfur.

9.) Paramagnetic oxygen (O2) Oxygen (O2) – known as a strong relaxant as summarized by Glasel (1973) – might be responsible for the general increase in T1. Due to the heating during the sealing of the capillaries most probably a lower pressure develops within the capillaries. This would consequently lead to an evaporation of O2 into the capillary void and to an in-crease in T1 and T2 (Glasel 1973). One might also expect that such an effect would be dependent on the capillary filling level. This is indeed the case: T1 is positively correlated to the capillary filling height, and this correlation increases in the course of time (see ESM S13–S17). Thus it is probable that the general increase in course of time is due to evaporation of O2 into the capillary void. Interestingly, T2 is not consistently correlated to the capillary filling height; most probably, the effect of ethanol dominates the effect of O2 (see also points 3 and 12). As aforemen-tioned, there were no statistically significant differences in capillary filling volume between the homeopathic prepa-rations and the corresponding controls. Thus, randomization was successful, and differences in capillary filling height and consequent O2 degassing cannot be responsible for the differences in T1 between homeopathic sulfur preparations and controls.

10.) Other paramagnetic substances Paramagnetic ions (e.g. ions of Cr, Mn, Cu, and Ni) strongly influence relaxation times as described by Bloembergen and Morgan (1961). Systematic errors due to a contamination with such ions are quite improbable, for reasons discussed above in points 1, 2 and 4.




11.) Dipolar 1H spin coupling As elaborated by Bloembergen et al. (1948), the most efficient relaxation mechanism for proton T1 relaxation in water is dipolar spin-spin coupling of intra- and intermolecular nature. Since the water molecules are in constant motion within the fluid, their movement strongly influences T1 relaxation. The variation of dipolar coupling in the interior of a molecule arises mostly from the rotation of the molecule, while the interaction between molecules is mainly influenced by their relative translation. After introduction of correlation functions with a corresponding cor-relation time tc (characterizing the stochastic rotational motion), the quantum mechanical treatment of the problem (Abragam 1961) yields for the intramolecular (rotational) contribution to T1 of protons under the (justified) assump-tion of ωtc << 1 (“extreme narrowing”)

!

1

T1

"

# $

%

& ' rot

=3

2

( 4h2

b6)c

(1)

with b = spin-spin distance, γ = gyromagnetic ratio and

!

h = Planck’s constant. An analogous treatment of the intermolecular (translational) contribution to T1 of protons is given by Abragam (1961):

!

1

T1

"

# $

%

& ' trans

=(

5

N) 4h2

aD

(2)

with N = density of spins/cm3, a = radius of the hard sphere approximating the water molecule in Stokes formula, and D = self diffusion coefficient of water. The rotational contribution to 1/T1 is approximately three times the translational one. If one wants to explain the T1 increase for homeopathic sulfur preparations in the context of dipolar 1H spin coupling, i.e. by the two equations above, we see in principle the following free parameters: i) the rotational correlation time tc, ii) the intramolecular spin-spin distance b, iii) the density of spins N, and iv) the self diffusion coefficient of water D. In order to get an increase in T1 for homeopathic sulfur preparations, one needs a decrease in tc or N, or an increase in b or D (of all parameters, the intramolecular spin-spin distance b has the strongest influence on T1 because it enters the formula in the 6th potency). This would essentially correspond to an increase in molecular rotational or translational motion, or a decrease in density. According to Abragam (1961) T2 is expected to be equal to T1 for relaxation due to dipolar spin coupling in the case of “extreme narrowing”. Thus, no additional information can be extracted from the T2 data. The reduction of T2 to 0.5 sec through addition of ethanol must be due to another relaxation mechanism.

12.) Scalar spin-spin coupling. As discussed by Abragam (1961), scalar spin-spin-coupling is only relevant for relaxation in case of unlike spins (e.g. I, S). In this case, the longitudinal and the transverse relaxation times are given by

!

1

T1

=2A

2

3

"e

1+ #I$#

S( )2

"e

2S S +1( ) (3)

and

!

1

T2

=A2

3"e

+"e

1+ #I$#

S( )2

"e

2

%

& ' '

(

) * * S S +1( ) (4)

where A = scalar coupling constant, τe = chemical exchange time constant, and ωI and ωS = Larmor frequency of spin I and S, respectively. Since (wI–wS)te is not vanishingly small, T1 and T2 may be field dependent, and T2 may be considerably smaller than T1. Such a coupling is made responsible for the dependence of T2 as a function of pH (Meiboom 1961), and for the strong decrease of T2 in solutions of Mn++ (Bloembergen and Morgan 1961). Zeidler (1973) reports on the possibility of a chemical exchange between the protons of the alcohol hydroxyl group and the water. We thus assume that a corresponding coupling is responsible i) for the strong decrease in T2 after addition of ethanol and ii) for the partially observed negative correlation of T2 and T1 (which establishes as soon as the deriva-tive of T1 changes sign, see equations 3 and 4).

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y = 2.8397 + 0.0019654x R= 0.35541

y = 2.8673 + 0.0024956x R= 0.28934

y = 2.822 + 0.0047476x R= 0.75031

T1 [sec]

Filling level capillaries [mm]


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y = 2.9159 + 0.00070429x R= 0.36948 y = 2.6469 + 0.007105x R= 0.63558

y = 2.7118 + 0.0063731x R= 0.70044

T1 [sec]



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y = 2.9417 - 5.8096e-05x R= 0.027254 y = 2.9234 + 0.00072418x R= 0.30084 y = 2.9103 + 0.0014285x R= 0.24313

T1 [sec]



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y = 2.9381 + 4.4122e-05x R= 0.039236 y = 2.9298 + 0.00033404x R= 0.096825

y = 2.8034 + 0.0035043x R= 0.88881

T1 [sec]



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y = 2.845 + 0.00075874x R= 0.26737 y = 2.8397 + 0.0013136x R= 0.53519

y = 2.79 + 0.0027307x R= 0.55266

T1 [sec]



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y = 2.8011 + 0.0014468x R= 0.70611

y = 2.9208 - 0.00011523x R= 0.035159 y = 2.7929 + 0.0025857x R= 0.45924

T1 [sec]



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y = 0.46244 + 0.00014308x R= 0.075576 y = 0.45363 + 0.00035041x R= 0.30926 y = 0.46677 + 0.00016236x R= 0.15045

T2 [sec]



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y = 0.41392 + 0.0011108x R= 0.52717

y = 0.486 - 0.00017607x R= 0.074199

y = 0.47145 + 0.00014354x R= 0.045386

T2 [sec]



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y = 0.53868 - 0.001098x R= 0.54887 y = 0.59472 - 0.0021311x R= 0.59253

y = 0.53803 - 0.00086772x R= 0.31194

T2 [sec]



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y = 0.52932 - 0.00094872x R= 0.70804 y = 0.59913 - 0.0022237x R= 0.57779 y = 0.60821 - 0.0022845x R= 0.67073

T2 [sec]



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y = 0.50836 - 0.00083307x R= 0.4998

y = 0.47328 - 0.0001227x R= 0.10041 y = 0.46833 - 7.2664e-05x R= 0.076193

T2 [sec]



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y = 0.5036 - 0.00071375x R= 0.3896 y = 0.48745 - 0.00049222x R= 0.38477 y = 0.43208 + 0.00064979x R= 0.35783

T2 [sec]





ESM S15

T1 and T2 measurements of homeopathic quartz preparations and controls (data set I): Correlation between capillary filling level heighth and T1 and T2 Statistics for ESM S13a, S13d, S14a, S14d (quartz preparations and controls) Legend T1_TLH T1 measured in Tallahassee (600 MHz) T2_TLH T2 measured in Tallahassee (600 MHz) r correlation coefficient p p-value n number of data points Controls only T1_TLH T2_TLH Capillary #1 r = 0.36948 r = 0.52717 p = 0.293 p = 0.117 (n = 10) (n = 10) Capillary #2 r = 0.63558 r = -0.0742 p = 0.066 p = 0.850 (n = 9) (n = 9) Capillary #3 r = 0.70044 r = 0.04539 p = 0.036 p = 0.908 (n = 9) (n = 9) Hom. prep. only T1_TLH T2_TLH Capillary #1 r = 0.35541 r = 0.07558 p = 0.114 p = 0.745 (n = 21) (n = 21) Capillary #2 r = 0.28934 r = 0.30926 p = 0.216 p = 0.185 (n = 20) (n = 20) Capillary #3 r = 0.75031 r = 0.15045 p = 0.001 p = 0.527 (n = 20) (n = 20) All data T1_TLH T2_TLH Capillary #1 r = 0.30792 r = 0.29246 p = 0.092 p = 0.110 (n = 31) (n = 31) Capillary #2 r = 0.33906 r = 0.04902 p = 0.072 p = 0.801 (n = 29) (n = 29) Capillary #3 r = 0.71354 r = 0.08232 p = 0.001 p = 0.671 (n = 29) (n = 29)



ESM S16

T1 and T2 measurements of homeopathic sulfur preparations and controls (data set II): Correlation between capillary filling level heighth and T1 and T2 Statistics for ESM S13b, S13e, S14b, S14e (sulfur preparations and controls) Legend T1_TLH T1 measured in Tallahassee (600 MHz) T2_TLH T2 measured in Tallahassee (600 MHz) T1_ZRH T1 measured in Zurich (500 MHz) r correlation coefficient p p-value n number of data points Controls only T1_TLH T2_TLH T1_ZRH Capillary #1 r = 0.03923 r = -0.70804 r = 0.74185 p = 0.914 p = 0.022 p = 0.014 (n = 10) (n = 10) (n = 10) Capillary #2 r = 0.09682 r = -0.57779 r = 0.87702 p = 0.804 p = 0.103 p = 0.002 (n = 9) (n = 9) (n = 9) Capillary #3 r = 0.88881 r = -0.67073 r = 0.67492 p = 0.001 p = 0.048 p = 0.066 (n = 9) (n = 9) (n = 8) Hom. prep. only T1_TLH T2_TLH T1_ZRH Capillary #1 r = -0.02725 r = -0.54887 r = 0.79827 p = 0.915 p = 0.018 p = 0.001 (n = 18) (n = 18) (n = 18) Capillary #2 r = 0.30084 r = -0.59253 r = 0.28689 p = 0.225 p = 0.010 p = 0.281 (n = 18) (n = 18) (n = 16) Capillary #3 r = 0.24313 r = -0.31194 r = 0.28044 p = 0.331 p = 0.208 p = 0.260 (n = 18) (n = 18) (n = 18) All data T1_TLH T2_TLH T1_ZRH Capillary #1 r = -0.00828 r = -0.60157 r = 0.7648 p = 0.967 p = 0.001 p = 0.001 (n = 28) (n = 28) (n = 28) Capillary #2 r = 0.19846 r = -0.58633 r = 0.39429 p = 0.321 p = 0.001 p = 0.051 (n = 27) (n = 27) (n = 25) Capillary #3 r = 0.46205 r = -0.49424 r = 0.43839 p = 0.015 p = 0.009 p = 0.025 (n = 27) (n = 27) (n = 26)



ESM S17

T1 and T2 measurements of homeopathic copper sulfate preparations and controls (data set III): Correlation between capillary filling level heighth and T1 and T2 Statistics for ESM S13c, S13f, S14c, S14f (copper sulfate preparations and controls) Legend T1_TLH T1 measured in Tallahassee (600 MHz) T2_TLH T2 measured in Tallahassee (600 MHz) r correlation coefficient p p-value n number of data points Controls only T1_TLH T2_TLH Capillary #1 r = 0.70611 r = -0.3896 p = 0.022 p = 0.266 (n = 10) (n = 10) Capillary #2 r = -0.03516 r = -0.38477 p = 0.923 p = 0.272 (n = 10) (n = 10) Capillary #3 r = 0.45924 r = 0.35783 p = 0.182 p = 0.310 (n = 10) (n = 10) Hom. prep. only T1_TLH T2_TLH Capillary #1 r = 0.26737 r = -0.4998 p = 0.283 p = 0.035 (n = 18) (n = 18) Capillary #2 r = 0.53519 r = -0.10041 p = 0.015 p = 0.674 (n = 20) (n = 20) Capillary #3 r = 0.55266 r = -0.07619 p = 0.012 p = 0.750 (n = 20) (n = 20) All data T1_TLH T2_TLH Capillary #1 r = 0.44821 r = -0.42322 p = 0.017 p = 0.025 (n = 28) (n = 28) Capillary #2 r = 0.27615 r = -0.21236 p = 0.140 p = 0.260 (n = 30) (n = 30) Capillary #3 r = 0.50824 r = 0.15329 p = 0.004 p = 0.419 (n = 30) (n = 30)

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