Cancer cell proliferation is inhibited by specific modulation frequencies

BACKGROUND: There is clinical evidence that very low and safe levels of amplitude-modulated electromagnetic fields administered via an intrabuccal spoon-shaped probe may elicit therapeutic responses in patients with cancer. However, there is no known mechanism explaining the anti-proliferative effect of very low intensity electromagnetic fields. METHODS: To understand the mechanism of this novel approach, hepatocellular carcinoma (HCC) cells were exposed to 27.12 MHz radiofrequency electromagnetic fields using in vitro exposure systems designed to replicate in vivo conditions. Cancer cells were exposed to tumour-specific modulation frequencies, previously identified by biofeedback methods in patients with a diagnosis of cancer. Control modulation frequencies consisted of randomly chosen modulation frequencies within the same 100 Hz-21 kHz range as cancer-specific frequencies. RESULTS: The growth of HCC and breast cancer cells was significantly decreased by HCC-specific and breast cancer-specific modulation frequencies, respectively. However, the same frequencies did not affect proliferation of nonmalignant hepatocytes or breast epithelial cells. Inhibition of HCC cell proliferation was associated with downregulation of XCL2 and PLP2. Furthermore, HCC-specific modulation frequencies disrupted the mitotic spindle. CONCLUSION: These findings uncover a novel mechanism controlling the growth of cancer cells at specific modulation frequencies without affecting normal tissues, which may have broad implications in oncology. British Journal of Cancer (2012) 106, 307-313. doi:10.1038/bjc.2011.523 www.bjcancer.com Published online 1 December 2011 (C) 2012 Cancer Research UK

Short-term efficacy of physical interventions in osteoarthritic knee pain. A systematic review and meta-analysis of randomised placebo-controlled trials

Abstract Background Treatment efficacy of physical agents in osteoarthritis of the knee (OAK) pain has been largely unknown, and this systematic review was aimed at assessing their short-term efficacies for pain relief. Methods Systematic review with meta-analysis of efficacy within 1–4 weeks and at follow up at 1–12 weeks after the end of treament. Results 36 randomised placebo-controlled trials (RCTs) were identified with 2434 patients where 1391 patients received active treatment. 33 trials satisfied three or more out of five methodological criteria (Jadad scale). The patient sample had a mean age of 65.1 years and mean baseline pain of 62.9 mm on a 100 mm visual analogue scale (VAS). Within 4 weeks of the commencement of treatment manual acupuncture, static magnets and ultrasound therapies did not offer statistically significant short-term pain relief over placebo. Pulsed electromagnetic fields offered a small reduction in pain of 6.9 mm [95% CI: 2.2 to 11.6] (n = 487). Transcutaneous electrical nerve stimulation (TENS, including interferential currents), electro-acupuncture (EA) and low level laser therapy (LLLT) offered clinically relevant pain relieving effects of 18.8 mm [95% CI: 9.6 to 28.1] (n = 414), 21.9 mm [95% CI: 17.3 to 26.5] (n = 73) and 17.7 mm [95% CI: 8.1 to 27.3] (n = 343) on VAS respectively versus placebo control. In a subgroup analysis of trials with assumed optimal doses, short-term efficacy increased to 22.2 mm [95% CI: 18.1 to 26.3] for TENS, and 24.2 mm [95% CI: 17.3 to 31.3] for LLLT on VAS. Follow-up data up to 12 weeks were sparse, but positive effects seemed to persist for at least 4 weeks after the course of LLLT, EA and TENS treatment was stopped. Conclusion TENS, EA and LLLT administered with optimal doses in an intensive 2–4 week treatment regimen, seem to offer clinically relevant short-term pain relief for OAK.

Novel simulation methods for Coulomb and hydrodynamic interactions

This thesis presents new methods to simulate systems with hydrodynamic and electrostatic interactions. Part 1 is devoted to computer simulations of Brownian particles with hydrodynamic interactions. The main influence of the solvent on the dynamics of Brownian particles is that it mediates hydrodynamic interactions. In the method, this is simulated by numerical solution of the Navier--Stokes equation on a lattice. To this end, the Lattice--Boltzmann method is used, namely its D3Q19 version. This model is capable to simulate compressible flow. It gives us the advantage to treat dense systems, in particular away from thermal equilibrium. The Lattice--Boltzmann equation is coupled to the particles via a friction force. In addition to this force, acting on {it point} particles, we construct another coupling force, which comes from the pressure tensor. The coupling is purely local, i.~e. the algorithm scales linearly with the total number of particles. In order to be able to map the physical properties of the Lattice--Boltzmann fluid onto a Molecular Dynamics (MD) fluid, the case of an almost incompressible flow is considered. The Fluctuation--Dissipation theorem for the hybrid coupling is analyzed, and a geometric interpretation of the friction coefficient in terms of a Stokes radius is given. Part 2 is devoted to the simulation of charged particles. We present a novel method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic field. This algorithm scales linearly, too. We focus on the Molecular Dynamics version of the method and show that it is intimately related to the Car--Parrinello approach, while being equivalent to solving Maxwell's equations with freely adjustable speed of light. The Lagrangian formulation of the coupled particles--fields system is derived. The quasi--Hamiltonian dynamics of the system is studied in great detail. For implementation on the computer, the equations of motion are discretized with respect to both space and time. The discretization of the electromagnetic fields on a lattice, as well as the interpolation of the particle charges on the lattice is given. The algorithm is as local as possible: Only nearest neighbors sites of the lattice are interacting with a charged particle. Unphysical self--energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green's function. The method allows easy parallelization using standard domain decomposition. Some benchmarking results of the algorithm are presented and discussed.

Collective effects for the LHC injectors: non-ultrarelativistic approaches

The upgrade of the CERN accelerator complex has been planned in order to further increase the LHC performances in exploring new physics frontiers. One of the main limitations to the upgrade is represented by the collective instabilities. These are intensity dependent phenomena triggered by electromagnetic fields excited by the interaction of the beam with its surrounding. These fields are represented via wake fields in time domain or impedances in frequency domain. Impedances are usually studied assuming ultrarelativistic bunches while we mainly explored low and medium energy regimes in the LHC injector chain. In a non-ultrarelativistic framework we carried out a complete study of the impedance structure of the PSB which accelerates proton bunches up to 1.4 GeV. We measured the imaginary part of the impedance which creates betatron tune shift. We introduced a parabolic bunch model which together with dedicated measurements allowed us to point to the resistive wall impedance as the source of one of the main PSB instability. These results are particularly useful for the design of efficient transverse instability dampers. We developed a macroparticle code to study the effect of the space charge on intensity dependent instabilities. Carrying out the analysis of the bunch modes we proved that the damping effects caused by the space charge, which has been modelled with semi-analytical method and using symplectic high order schemes, can increase the bunch intensity threshold. Numerical libraries have been also developed in order to study, via numerical simulations of the bunches, the impedance of the whole CERN accelerator complex. On a different note, the experiment CNGS at CERN, requires high-intensity beams. We calculated the interpolating Hamiltonian of the beam for highly non-linear lattices. These calculations provide the ground for theoretical and numerical studies aiming to improve the CNGS beam extraction from the PS to the SPS.

Multiscale fabrication of functional materials for life sciences

Regenerative medicine claims for a better understanding of the cause-effect relation between cell behaviour and environment signals. The latter encompasses topographical, chemical and mechanical stimuli, electromagnetic fields, gradients of chemo-attractants and haptotaxis. In this perspective, a spatial control of the structures composing the environment is required. In this thesis I describe a novel approach for the multiscale patterning of biocompatible functional materials in order to provide systems able to accurately control cell adhesion and proliferation. The behaviour of different neural cell lines in response to several stimuli, specifically chemical, topographical and electrical gradients is presented. For each of the three kind of signals, I chose properly tailored materials and fabrication and characterization techniques. After a brief introduction on the state of art of nanotechnology, nanofabrication techniques and regenerative medicine in Chapter 1 and a detailed description of the main fabrication and characterization techniques employed in this work in Chapter 2, in Chapter 3 an easy route to obtain accurate control over cell proliferation close to 100% is described (chemical control). In Chapter 4 (topographical control) it is shown how the multiscale patterning of a well-established biocompatible material as titanium dioxide provides a versatile and robust method to study the effect of local topography on cell adhesion and growth. The third signal, viz. electric field, is investigated in Chapter 5 (electrical control), where the very early stages of neural cell adhesion are studied in the presence of modest steady electric fields. In Chapter 6 (appendix) a new patterning technique, called Lithographically Controlled Etching (LCE), is proposed. It is shown how LCE can provide at the same time the micro/nanostructuring and functionalization of a surface with nanosized objects, thus being suitable for applications both in regenerative medicine in biosensing.

Campi elettromagnetici pulsanti nella terapia dell'artrosi del cane

The aim of this study is to evaluate the effects of the pulsed electromagnetic fields (PEMFS) on pain relief and functional capacity of dogs with osteoarthritis by which a single centre study prospective clinical trial. PEMFs are non ionized, athermic and time varying electromagnetic fields that has been successfully used for the treatment of osteoarthritis in human thanks to their chondroprotective, antinflammatory and analgesic property. 20 dogs were treated with PEMFs , 3 times per week for a total of 20 sessions.We found beneficial effects on pain relief and lameness in the absence of adverse effect. The decrease of pain impacted positively on the health-dogs related quality of life and the grade of satisfaction of their owner was very high. The benefits were obvious at half therapy and lasted for a medium long time. This is the first published report concerning PEMFs treatment on canine osteoarthtitis. The result of this study proves that PEMFs is a non –invasive remedy, lacking in adverse effect , easy to employ and useful for controlling pain and inflammation associated with osteoarthritis.

Valutazione sperimentale della rigenerazione cartilaginea articolare dopo stimolazione biofisica con campi elettromagnetici pulsati in associazione a trattamenti chirurgici

Diverse tecniche di ingegneria tessutale sono state sviluppate per promuovere la riparazione delle lesioni della cartilagine articolare. Nonostante i buoni risultati clinici a breve termine, il tessuto rigenerato fallisce nel tempo poiché non possiede le caratteristiche meccaniche e funzionali della cartilagine articolare nativa. La stimolazione con campi elettromagnetici pulsati (CEMP) rappresenta un approccio terapeutico innovativo. I CEMP aumentano l’attività anabolica dei condrociti con conseguente incremento della sintesi della matrice, e limitano l’effetto catabolico delle citochine pro-infiammatorie riducendo la degradazione della cartilagine nel microambiente articolare. I CEMP agiscono mediante l’up-regolazione dei recettori adenosinici A2A potenziando il loro affetto anti-infiammatorio. Lo scopo di questo studio è stato quello di valutare l’effetto della stimolazione con CEMP sulla guarigione di difetti osteocondrali in un modello sperimentale nel coniglio. Un difetto osteocondrale del diametro di 4mm è stato eseguito nel condilo femorale mediale di entrambe le ginocchia di 20 conigli. A destra la lesione è stata lasciata a guarigione spontanea mentre a sinistra e stata trattata mediante inserimento di scaffold collagenico o trapianto di cellule mesenchimali midollari sul medesimo scaffold precedentemente prelevate dalla cresta iliaca. In base al trattamento eseguito 10 animali sono stati stimolati con CEMP 4 ore/die per 40 giorni mentre altri 10 hanno ricevuto stimolatori placebo. Dopo il sacrificio a 40 giorni, sono state eseguite analisi istologiche mediante un punteggio di O’Driscoll modificato. Confrontando le lesioni lasciate a guarigione spontanea, la stimolazione con CEMP ha migliorato significativamente il punteggio (p=0.021). Lo stesso risultato si è osservato nel confronto tra lesioni trattate mediante trapianto di cellule mesenchimali midollari (p=0.032). Nessuna differenza è stata osservata tra animali stimolati e placebo quando la lesione è stata trattata con il solo scaffold (p=0.413). La stimolazione con CEMP è risultata efficace nel promuovere la guarigione di difetti osteocartilaginei in associazione a tecniche chirurgiche di ingegneria tessutale.

Vector meson photoproduction in ultra-peripheral heavy ion collisions with ALICE at the LHC

Ultra-relativistic heavy ions generate strong electromagnetic fields which offer the possibility to study γ-γ and γ-nucleus processes at the LHC in the so called ultra-peripheral collisions (UPC). The photoproduction of J/ψ vector mesons in UPC is sensitive to the gluon distribution of the interacting nuclei. In this thesis the study of coherent and incoherent J/ψ production in Pb-Pb collisions at √sNN = 2.76 TeV is described. The J/ψ has been measured via its leptonic decay in the rapidity range -0.9 < y < 0.9. The cross section for coherent and incoherent J/ψ are given. The results are compared to theoretical models for J/ψ production and the coherent cross section is found to be in good agreement with those models which include nuclear gluon shadowing consistent with EPS09 parametrization. In addition the cross section for the process γ γ→ e+e− has been measured and found to be in agreement with the STARLIGHT Monte Carlo predictions. The analysis has been published by the ALICE Collaboration in the European Physical Journal C, with one of its main plot depicted on the cover-front of the November 2013 issue.

Stimolazione precoce della consolidazione ossea in pazienti con frattura di gamba attraverso campi elettromagnetici pulsati basata su un algoritmo predittivo del rischio diritardo di consolidazione ossea (ARRCO – Algoritmo Rischio Ritardo Consolidazione Ossea – IGEA®).

E' stato sviluppato un algoritmo predittivo del rischio di consolidazione ossea (ARRCO – Algoritmo Rischio Ritardo Consolidazione Ossea - IGEA, Carpi, Italy) che combina diversi fattori correlati al rischio di ritardata o mancata guarigione di una frattura. Questo algoritmo ha permesso di idntificare una popolazione di pazienti affetti da fratture con aumentato rischio di ritardo di consolidazione o mancata guarigione. Questi pazienti sono stati sottoposti precocemente a stimolazione biofisica precoce mediante Campi Elettromagnetici Pulsati a bassa frequenza (CEMP), ottenendo la guarigione della frattura nella maggior parte dei casi e in tempi considerati fisiologici. Pertanto in un gruppo selezionato di pazienti, il trattamento può essere indirizzato all'applicazione precoce di CEMP, al fine di promuovere la consolidazione ossea di una frattura "a richio", il cui trattamento richiederebbe altrimenti tempi più prolungati e un costo virtuale maggiore dell'intero trattamento sanitario.

Implicazioni teoriche e sperimentali della sincronizzazione assoluta nella teoria della relatività speciale

Sono indagate le implicazioni teoriche e sperimentali derivanti dall'assunzione, nella teoria della relatività speciale, di un criterio di sincronizzazione (detta assoluta) diverso da quello standard. La scelta della sincronizzazione assoluta è giustificata da alcune considerazioni di carattere epistemologico sullo status di fenomeni quali la contrazione delle lunghezze e la dilatazione del tempo. Oltre che a fornire una diversa interpretazione, la sincronizzazione assoluta rappresenta una estensione del campo di applicazione della relatività speciale in quanto può essere attuata anche in sistemi di riferimento accelerati. Questa estensione consente di trattare in maniera unitaria i fenomeni sia in sistemi di riferimento inerziali che accelerati. L'introduzione della sincronizzazione assoluta implica una modifica delle trasformazioni di Lorentz. Una caratteristica di queste nuove trasformazioni (dette inerziali) è che la trasformazione del tempo è indipendente dalle coordinate spaziali. Le trasformazioni inerziali sono ottenute nel caso generale tra due sistemi di riferimento aventi velocità (assolute) u1 e u2 comunque orientate. Viene mostrato che le trasformazioni inerziali possono formare un gruppo pur di prendere in considerazione anche riferimenti non fisicamente realizzabili perché superluminali. È analizzato il moto rigido secondo Born di un corpo esteso considerando la sincronizzazione assoluta. Sulla base delle trasformazioni inerziali si derivano le trasformazioni per i campi elettromagnetici e le equazioni di questi campi (che sostituiscono le equazioni di Maxwell). Si mostra che queste equazioni contengono soluzioni in assenza di cariche che si propagano nello spazio come onde generalmente anisotrope in accordo con quanto previsto dalle trasformazioni inerziali. L'applicazione di questa teoria elettromagnetica a sistemi accelerati mostra l'esistenza di fenomeni mai osservati che, pur non essendo in contraddizione con la relatività standard, ne forzano l'interpretazione. Viene proposto e descritto un esperimento in cui uno di questi fenomeni è misurabile.

Mobi - kids - rischio di tumori cerebrali ed esposizione a campi a radiofrequenza nei bambini e negli adolescenti

Introduzione. Il rapido e globale incremento dell’utilizzo dei telefoni cellulari da parte degli adolescenti e dei bambini ha generato un considerevole interesse circa i possibili effetti sulla salute dell’esposizione a campi elettromagnetici a radiofrequenza. Perciò è stato avviato lo studio internazionale caso-controllo Mobi-kids, all’interno del quale si colloca quello italiano condotto in 4 Regioni (Piemonte, Lombardia, Toscana, Emilia-Romagna). Obiettivi. Lo studio ha come obiettivo quello di valutare la stima del rischio degli effetti potenzialmente avversi di queste esposizioni sul sistema nervoso centrale nei bambini e negli adolescenti. Materiali e Metodi. La popolazione include tutte le persone di età compresa tra 10 e 24 anni residenti nelle 4 Regioni, con una diagnosi confermata di neoplasia cerebrale primitiva, diagnosticata durante il periodo di studio (3 anni). Sono stati selezionati due controlli - ospedalizzati per appendicite acuta - per ciascun caso. I controlli sono stati appaiati individualmente a ciascun caso per età, sesso e residenza del caso. Risultati. In Italia sono stati intervistati a Giugno 2014, 106 casi e 191 controlli. In Emilia-Romagna i casi reclutati sono stati fino ad ora 21 e i controlli 20, con una rispondenza del’81% e dell’65% rispettivamente. Dei 41 soggetti totali, il 61% era di sesso maschile con un’età media generale pari a 16,5 (±4,5) anni. Inoltre il 44% degli intervistati proveniva dalla classe di età più giovane (10-14). In merito allo stato di appaiamento, nella nostra Regione sono state effettuate 7 triplette (33%) - 1 caso e 2 controlli - e 6 doppiette (29%) - 1 caso ed 1 controllo. Conclusioni. Nonostante le varie difficoltà affrontate data la natura del progetto, l’esperienza maturata fin ad ora ha comunque portato alla fattibilità dello studio e porterà probabilmente a risultati che contribuiranno alla comprensione dei potenziali rischi di neoplasie cerebrali associati all'uso di telefoni cellulari tra i giovani.

Direct and inverse transient eddy current problems

Die vorliegende Arbeit behandelt Vorwärts- sowie Rückwärtstheorie transienter Wirbelstromprobleme. Transiente Anregungsströme induzieren elektromagnetische Felder, welche sogenannte Wirbelströme in leitfähigen Objekten erzeugen. Im Falle von sich langsam ändernden Feldern kann diese Wechselwirkung durch die Wirbelstromgleichung, einer Approximation an die Maxwell-Gleichungen, beschrieben werden. Diese ist eine lineare partielle Differentialgleichung mit nicht-glatten Koeffizientenfunktionen von gemischt parabolisch-elliptischem Typ. Das Vorwärtsproblem besteht darin, zu gegebener Anregung sowie den umgebungsbeschreibenden Koeffizientenfunktionen das elektrische Feld als distributionelle Lösung der Gleichung zu bestimmen. Umgekehrt können die Felder mit Messspulen gemessen werden. Das Ziel des Rückwärtsproblems ist es, aus diesen Messungen Informationen über leitfähige Objekte, also über die Koeffizientenfunktion, die diese beschreibt, zu gewinnen. In dieser Arbeit wird eine variationelle Lösungstheorie vorgestellt und die Wohlgestelltheit der Gleichung diskutiert. Darauf aufbauend wird das Verhalten der Lösung für verschwindende Leitfähigkeit studiert und die Linearisierbarkeit der Gleichung ohne leitfähiges Objekt in Richtung des Auftauchens eines leitfähigen Objektes gezeigt. Zur Regularisierung der Gleichung werden Modifikationen vorgeschlagen, welche ein voll parabolisches bzw. elliptisches Problem liefern. Diese werden verifiziert, indem die Konvergenz der Lösungen gezeigt wird. Zuletzt wird gezeigt, dass unter der Annahme von sonst homogenen Umgebungsparametern leitfähige Objekte eindeutig durch die Messungen lokalisiert werden können. Hierzu werden die Linear Sampling Methode sowie die Faktorisierungsmethode angewendet.

Pacemakers and magnetic resonance imaging: Current status and survey in Switzerland

Electromagnetic fields arising from magnetic resonance imaging (MRI) can cause various clinically relevant functional disturbances in patients with cardiac pacemakers. Consequently, an implanted pacemaker is generally considered a contraindication for an MRI scan. With approximately 60 million MRI scans performed worldwide per year, MRI may be indicated for an estimated majority of pacemaker patients during the lifetime of their pacemakers. The availability of MR conditional pacemakers with CE labelling is of particular advantage since they allow the safe use of pacemakers in MRI. In this article the current state of knowledge on pacemakers and MR imaging is discussed. We present the results of a survey conducted among Swiss radiologists to assess current practice in patients with pacemakers.

A Computational Analysis of the Collision-Induced Dissociation Mechanisms of the Dipeptide Glycine-Serine Under Mass Spectrometry

Collision-induced dissociation (CID) of peptides using tandem mass spectrometry (MS) has been used to determine the identity of peptides and other large biological molecules. Mass spectrometry (MS) is a useful tool for determining the identity of molecules based on their interaction with electromagnetic fields. If coupled with another method like infrared (IR) vibrational spectroscopy, MS can provide structural information, but in its own right, MS can only provide the mass-to-charge (m/z) ratio of the fragments produced, which may not be enough information to determine the mechanism of the collision-induced dissociation (CID) of the molecule. In this case, theoretical calculations provide a useful companion for MS data and yield clues about the energetics of the dissociation. In this study, negative ion electrospray tandem MS was used to study the CID of the deprotonated dipeptide glycine-serine (Gly-Ser). Though negative ion MS is not as popular a choice as positive ion MS, studies by Bowie et al. show that it yields unique clues about molecular structure which complement positive ion spectroscopy, such as characteristic fragmentations like the loss of formaldehyde from the serine residue.2 The increase in the collision energy in the mass spectrometer alters the flexibility of the dipeptide backbone, enabling isomerizations (reactions not resulting in a fragment loss) and dissociations to take place. The mechanism of the CID of Gly-Ser was studied using two computational methods, B3LYP/6-311+G* and M06-2X/6-311++G**. The main pathway for molecular dissociation was analyzed in 5 conformers in an attempt to verify the initial mechanism proposed by Dr. James Swan after examination of the MS data. The results suggest that the loss of formaldehyde from serine, which Bowie et al. indicates is a characteristic of the presence of serine in a protein residue, is an endothermic reaction that is made possible by the conversion of the translational energy of the ion into internal energy as the ion collides with the inert collision gas. It has also been determined that the M06-2X functional¿s improved description of medium and long-range correlation makes it more effective than the B3LYP functional at finding elusive transition states. M06-2X also more accurately predicts the energy of those transition states than does B3LYP. A second CID mechanism, which passes through intermediates with the same m/z ratio as the main pathway for molecular dissociation, but different structures, including a diketopiperazine intermediate, was also studied. This pathway for molecular dissociation was analyzed with 3 conformers and the M06-2X functional, due to its previously determined effectiveness. The results suggest that the latter pathway, which meets the same intermediate masses as the first mechanism, is lower in overall energy and therefore a more likely pathway of dissociation than the first mechanism.

Differences in Median Ultraviolet Light Transmissions of Serial Homeopathic Dilutions of Copper Sulfate, Hypericum perforatum, and Sulfur

Homeopathic remedies are produced by potentising, that is, the serial logarithmic dilution and succussion of a mother tincture. Techniques like ultraviolet spectroscopy, nuclear magnetic resonance, calorimetry, or thermoluminescence have been used to investigate their physical properties. In this study, homeopathic centesimal (c) potencies (6c to 30c) of copper sulfate, Hypericum perforatum, and sulfur as well as succussed water controls were prepared. Samples of these preparations were exposed to external physical factors like heat, pressure, ultraviolet radiation, or electromagnetic fields to mimic possible everyday storage conditions. The median transmissions from 190nm to 340nm and 220nm to 340nm were determined by ultraviolet light spectroscopy on five measurement days distributed over several months. Transmissions of controls and potencies of sulfur differed significantly on two of five measurement days and after exposure to physical factors. Transmissions of potencies exposed to ultraviolet light and unexposed potencies of copper sulfate and Hypericum perforatum differed significantly. Potency levels 6c to 30c were also compared, and wavelike patterns of higher and lower transmissions were found. The Kruskal-Wallis test yielded significant differences for the potency levels of all three substances. Aiming at understanding the physical properties of homeopathic preparations, this study confirmed and expanded the findings of previous studies.