research article analysis of the magnetic field influence...

Hindawi Publishing CorporationBioMed Research InternationalVolume 2013 Article ID 490410 7 pageshttpdxdoiorg1011552013490410

Research ArticleAnalysis of the Magnetic Field Influence on the RheologicalProperties of Healthy Persons Blood

Anna Marcinkowska-Gapinska1 and Honorata Nawrocka-Bogusz2

1 Rheological Laboratory Department of Neurology Karol Marcinkowski University of Medical Sciences in PoznanPrzybyszewskiego 49 60-355 Poznan Poland

2Department of Biophysics Poznan University of Medical Sciences Fredry 10 61-701 Poznan Poland

Correspondence should be addressed to Anna Marcinkowska-Gapinska margappocztaonetpl

Received 30 April 2013 Revised 30 July 2013 Accepted 31 July 2013

Academic Editor Jerome Moreaux

Copyright copy 2013 A Marcinkowska-Gapinska and H Nawrocka-Bogusz This is an open access article distributed under theCreative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium providedthe original work is properly cited

The influence of magnetic field on whole blood rheological properties remains a weakly known phenomenon An in vitro analysisof the magnetic field influence on the rheological properties of healthy persons blood is presented in this work The study wasperformed on blood samples taken from 25 healthy nonsmoking persons and included comparative analysis of the results ofboth the standard rotary method (flow curve measurement) and the oscillatory method known also as the mechanical dynamicanalysis performed before and after exposition of blood samples to magnetic fieldThe principle of the oscillatory technique lies indetermining the amplitude and phase of the oscillations of the studied sample subjected to action of a harmonic force of controlledamplitude and frequency The flow curve measurement involved determining the shear rate dependence of blood viscosity Theviscoelastic properties of the blood samples were analyzed in terms of complex blood viscosity All the measurements have beenperformed by means of the Contraves LS40 rheometer The data obtained from the flow curve measurements complemented byhematocrit andplasma viscositymeasurements have been analyzed using the rheologicalmodel ofQuemadaNo significant changesof the studied rheological parameters have been found

1 Introduction

Artificial electromagnetic fields disturb the geomagnetic fieldand influence human organism causing different symptomsheadache hyperactivity fatigue emotional tension dailyrhythm disturbances and so forth Fast changing magneticfields are considered harmful whereas weak and slow chang-ing magnetic fields (MFs) are used in the diagnosis and inthe treatment of many diseases The use of variable magneticfields in medicine covers many areas such as orthopedicsrheumatology internalmedicine neurology psychiatry den-tistry and also psychiatry [1 2]

The biophysical mechanisms of the action of variable lowfrequency magnetic fields are the influence on uncompen-sated magnetic spins of paramagnetic elements free oxygenradicals and diamagneticmolecules Variablemagnetic fieldsact on components of cell membranes having the propertiesof liquid crystal They influence the depolarization of cells

by introducing an additional force which changes positionsof moving electric charges and induce potential in the areasfilled with electrolyte Variable magnetic fields not only causethe intensification of the process of the oxygen utilizationand the tissue respiration increase reparation processes andthe regeneration of soft tissues but also show a hypoglycemiceffect and cause the acceleration of bone healing [1]

The effect of magnetic field on the rheological propertiesof blood is not well known yet One of the effects observedso far is the decrease in the whole blood viscosity [3] Ithas also been observed that the Viofor JPS device causedimprovement in upper limb blood flow immediately after thefirst treatment The measurements were performed beforeand after MF application the results were observed by meansof thermography [4]

It is believed that there is a direct relation between therheological properties of systemic fluids and the processestaking place in living organisms [5] The flow of blood

2 BioMed Research International

through blood vessels is a very complex phenomenon dueto physical and physicochemical properties of blood and thestructure of the circulatory system Features related to theflow of blood in blood vessels are referred to as blood fluidity[6] Rheological characteristics of every material dependmainly on two parameters viscosity and elasticity Viscosityis a parameter determining the resistance of the materialto flow while elasticity expresses the material resistanceagainst deformation A hemorheological study is primarilybased on the blood viscosity measurements In the case ofnon-Newtonian fluids such as blood viscosity is a functionof applied shear rate The main factors determining bloodviscosity are hematocrit value erythrocytes aggregability anddeformability and the plasma viscosity [7]

Measurements of whole blood viscosity as a function ofshear rate are performed by means of rotary rheometers Onthe contrary blood plasma viscosity can be measured bothby rotary and capillary viscometers because it is a Newtonianliquid [7ndash9] Additional information about blood rheologycan be achieved from nonviscometric oscillatory measure-ments called also dynamic mechanical analysis (DMA) Theprinciple of the oscillatory technique lies in determiningthe amplitude and phase of the oscillations of the studiedsample subjected to action of a harmonic force of controlledamplitude and frequency A measurement performed bymeans of the oscillatory method should provide informationabout viscoelastic properties of the fluid under study whichcan be expressed in terms of a complex viscosity

120578lowast

= 1205781015840

+ 11989412057810158401015840

(1)

where 120578lowast is the complex viscosity 1205781015840 is the viscous compo-nent and 12057810158401015840 is the elastic component

Additional information about erythrocytes propertiessimilar to that from direct measurements of red cells aggre-gability and deformability [7 8 10 11] can be achievedindirectly from amathematical analysis of the flow curvewiththe use of rheological models [7 12] In this work we use theQuemada model [13 14]

The aimof the present workwas a comprehensive analysisof the rheological properties of blood in a group of healthyobjects with the use of a rotary-oscillating rheometer Bothrotary and oscillatory measurements were performed in thisstudy We present the results of viscosity measurements ofboth whole blood and blood plasma (rotary method) andthe results of complex viscositymeasurementswith separatelycalculated viscous and elastic components of the blood com-plex viscosity The flow curves were analyzed with the helpof Quemada rheological model to estimate the parametersmeasuring red cells aggregability anddeformability in healthypatients before and after application of magnetic field

2 Material and Methods

Blood samples for the comprehensive rheological analysiswere taken from a group of 25 healthy nonsmoking patientsaged 21 to 51 with 19 men and 6 women The average ageof patients in the group was 31 Blood donors did not sufferfrom any chronic diseases and passed the standard tests

for blood donors The interval between the blood collectionand the viscosity measurement never exceeded 4 hours Thecomprehensive analysis was based on the measurements ofhematocrit value (Hct) whole blood viscosity (120578) at fourchosen shear rate (1205741015840) values (01 1 10 and 100 sminus1) plasmaviscosity (120578

119901) complex viscosity (120578lowast) and its elastic (12057810158401015840) and

viscous (1205781015840) components measured for four chosen ampli-tudes (1205741015840

0) of shear rate values (02 1 10 and 20 sminus1)The blood

samples were collected into BD Vacutainer Tubes containinglithium heparin (17 international unitsmL of blood) Thehematocrit value was determined using the standardmethodBlood plasma was obtained by centrifugation of whole bloodat 4000 rpm for 10 minutes and collection of the supernatantAll viscosity measurements were performed by means of arotary-oscillating rheometer Contraves LS40 at the temper-ature of 37∘C The measurement cell consisted of a steel cupdriven by a precise step motor and a steel bob suspended ona quartz thread which together formed a Couette cell with avolume of 18mL In the rotary measurements the motion ofthe cupwas unidirectional and the torsion angle of the threadwas taken as the measure of shear stress In the oscillatoryones the cup was moved in an oscillating way with a constantfrequency and both the amplitude of the thread torsion andthe phase difference of the cup and bob oscillations wereused to calculate the real and imaginary components of thecomplex viscosity

Whole blood viscosity was measured in the order of de-creasing shear rate in the range 100ndash001 sminus1 within 5 minutesafter short preshearing at 1205741015840 = 100 sminus1 [15 16] Plasma viscos-ity was estimated from a regression analysis of shear ratedependence of shear stress measured in the range of 1205741015840 = 10ndash100 sminus1 Oscillatory measurements of the viscous and elasticparts of the complex blood viscosity were performed at aconstant frequency of 05Hz and decreasing amplitude [9]Conclusions with regard to the red cells aggregability anddeformability were drawn indirectly from the analysis of theflow curves using the rheological model of Quemada ((2)and (3)) and comparing the values of the model parameters1198960 119896infin and 1205741015840

119888 This model has been formulated for a

suspension of aggregating particlesmdasha substance resemblingthe properties of real whole blood The parameters 119896

infinand

1198960in (2) have the meaning of a measure of red cells rigidity

and aggregability respectively Parameter 119896119876has the sense of

erythrocyte intrinsic viscosity which also takes into accountthe change of erythrocyte shape via the function 119896

119876(1205741015840

) in (3)The symbols 120591(1205741015840) 120578

119901 and Hct denote shear stress plasma

viscosity and hematocrit value respectively

119896119876=1198960+ 119896infin(1205741015840

1205741015840

119888)12

1 + (12057410158401205741015840119888)12

(2)

120591 (1205741015840

) = 120578119901[1 minus1

2119896119876sdotHct]

minus2

sdot 1205741015840

(3)

The values of 1198960 119896infin and 1205741015840

119888were determined from the

least squares fit of the model to the experimental flow curveusing Hct and 120578

119901as fixed parameters taken from direct

measurements

BioMed Research International 3

Table 1 The values of blood rheological parameters and Quemadarsquos model in the group of healthy patients before and after magnetic field

Rheological parameter GroupBefore magnetic field (119899 = 25) After magnetic field (119899 = 25)

Hematocrit (Hct) 440 plusmn 05 440 plusmn 05

Plasma viscosity (120578p) [mPas] 133 plusmn 003lowast

141 plusmn 001

Relative blood viscosity at 01 sminus1 3904 plusmn 247 3688 plusmn 218




Quemada model parameter 1198960

416 plusmn 007 415 plusmn 006

Quemada model parameter 119896infin




lowast

119875 lt 002

As a source of the alternating magnetic field the VioforJPS device (produced by Med amp Life Komorow Poland) wasused The generator was connected to the small applicatormdasha pad containing one pair of coils The peak value of thevariable magnetic field of extremely low frequency (ELF)range equaled 56120583T with the mean value of 5120583T The M1P2program was used because in [17] it was found to be themost effective in studies in vivo M1 means that the chosenstrength of the magnetic field was constant during the wholeapplication time The fundamental frequency of pulses was180ndash195Hz The pulses were administered in the form ofpackets of pulses (125ndash29Hz) groups of packages (28ndash76Hz) and series (008ndash03Hz) The base form of impulseswas close to the peak shaped one with a gradual increase infield and a sharp decrease to zeroThe changes of polarizationtook place in the cycle 3-3-2-2 minutes for M1P2 programOther technical details can be found in the instrumentuser manual available at the producer web site (currentlyhttpwwwmedandlifecom)

3 Results

Theresults of the rotarymeasurements whole blood viscosityvalues measured for four chosen shear rates and plasmaviscosity are presented in Table 1 For each blood sample thehematocrit value was measured Hematocrit values remainedin the limits from 38 to 51 and its mean value in the groupwas (440 plusmn 05)

The Quemada rheological model parameters values 1198960

119896infin and 1205741015840

119888and the values of other rheological parametersmdash

plasma viscosity and blood viscosity for four chosen shearratesmdashare listed in Table 1 The average values of the viscous(1205781015840) and elastic (12057810158401015840) components of the complex viscosity (120578lowast)for four chosen shear rate amplitudes 1205741015840

0are also presented in

Table 1 In Figure 1 we showed a typical dependence of 1205781015840 12057810158401015840and 120578lowast on shear rate amplitude 1205741015840

0obtained with oscillations

of constant frequency of 05Hz and variable amplitude forone of the samples

In Figure 2we showed correlations between a pair ofQue-mada model parameters representing red cells rigidity anddeformability 1205741015840

119888and 119896

infin Correlations between Quemada

2minus121205749984000(sminus1)

120578998400120578998400998400120578lowast(Pas)

RealImaginaryComplex

10minus2

10minus3

10minus4

01 1 10

Figure 1 Dependence of the viscous and elastic components of thecomplex viscosity and the complex viscosity on the rms value ofthe shear rate amplitude 1205741015840

0(for oscillation frequency of 05Hz) in

the studied group of healthy patients The rms value of a sinusoidalfunction is by factor 212 smaller than the amplitude

model parameters 1205741015840119888and 119896

infinand the elastic component 12057810158401015840

of the complex viscosity are presented in Figures 3 and 4

4 Discussion

In this work we have studied the effect of low frequencymagnetic field on the rheological properties of blood Thisissue has not been analyzed in detail so far Our studieshave been performed in vitro with regard to both magneticfield application and blood viscosity measurements We ana-lyzed rheological properties of blood collected from healthypatients obtained bymeans of a rotary-oscillating rheometerContraves LS40 Although it is possible to perform applica-tion of MF in vivo as it was shown in [17] measurementsof blood viscosity have to be performed in vitro There aresomemethods to measure blood flow through certain vessels


12

10

8

6

4

2

14 15 16 17 18 19 20 21 22

120574998400 c(sminus1)

kinfin

Figure 2 Correlation between the parameters of Quemada model1205741015840

119888and 119896

infin

1816141210864

02 4 6 8 10

2010

102

120574998400

c(sminus1)

120574998400

0(sminus1)

120578998400998400(m

Pas)

Figure 3 Correlation between the elastic component of the complexviscosity and the 1205741015840

119888parameter of Quemada model

in vivo but they do not provide information about bloodviscosity alone

Hemorheological studies are based on the evaluation ofblood fluidity in vitro in conditionsmimicking the physiolog-ical ones and on investigating the relations among individualphysical parameters of blood components Parameters ofspecial interest are red cells deformability and ability toorient in flow their aggregability whole blood viscosity bloodplasma viscosity and complex blood viscosity

In our current in vitro studies only weak effects ofmagnetic field therapy on blood rheological parameters areobserved Statistical analysis of observed differences showedtheir statistical insignificance However the results obtainedwith differentmethodswere consistentMoreover differencesrecently found in a recent in vivo study [18]may simply reflect

16141210864

15

10

05

0014 16 18 20 22

kinfin

2010

102

120574998400

0(sminus1)

120578998400998400(m

Pas)

Figure 4Correlation between the elastic component of the complexviscosity and the 119896

infinparameter of Quemada model

the influence ofmagnetic field on thewhole organism andnotonly the blood itself

The values of relative blood viscosity for four chosen shearrates measured in the rotary experiment are listed in Table 1These results are comparable with the data published in theliterature obtained from control group in other hemorheo-logical studies [19] Observed differences are of no statisticalsignificance (119875 lt 006) and even if treated seriously theycould result from the fact that the control groups in thecited works were composed of patients free from circulatorysystem disorders however they were hospitalized and hencenot healthy In the current study all blood donors werehealthy The values of relative blood viscosity measured inthis study are comparable to results obtained in the literatureusing different methods and for different groups of healthypatients [7 8 20 21] No statistically significant differenceshave been found between blood samples before and afteradministration of the magnetic field however there seems tobe a tendency of decreased blood viscosity at low shear rates(Table 1 1205741015840 = 01 sminus1)

Plasma viscosity measurements were performed bymeans of the same rotary-oscillating rheometer but usingonly rotary techniques In this study the plasma compositionwas not measured and hence no correlations between theplasma protein composition and plasma viscosity could befound Plasma protein composition is a very importantparameter in the analysis of plasma viscosity in the caseof patients with diagnosed circular system disorders [22]Analysis of the magnetic field effect on blood plasma vis-cosity revealed statistically significant differences betweenthe plasma samples before and after administration of mag-netic field to the blood samples (Table 1) Increased plasmaviscosity might result from a change of plasma proteinsconformation but this hypothesis was not verified in thisstudy The values of plasma viscosity for healthy people


obtained in this study are comparable to the results reportedin the literature for similar studies of control groups [19]

Mathematical analysis of the whole blood flow curvesobtained from rotarymeasurementswith the use ofQuemadarheological model allows for overcoming this problem andobtaining reliable information about red cells aggregabil-ity and deformability from Quemada model parameters(Table 1) The values of Quemada model parameters 119896

0 119896infin

and 1205741015840119888 are comparable to those obtained in the literature

[12 19 20] Analysis of the correlation among differentmodel parameters revealed a negative correlation betweenthe 1205741015840119888parameter indicating the moment of erythrocytes

beginning to form packages (rouleaux formation) and theparameter 119896

infininterpreted as a measure of red cells rigidity

(Figure 2) These two parameters reflect two different phe-nomenaThe fact of correlation between themmeans that thered cells rigidity and the moment of rouleaux formation areinterdependent either directly or through another parame-terphysical phenomenon

Ciejka and Gorąca [23] studied the effect of magneticfields with parameters used commonly inmagnetotherapy onchosen biochemical parameters of rats bloodThey found thatvariable magnetic field of low frequency administered dailyfor 30min induces in the animals changes of morphologicalparameters of blood (decrease in red cells number after 14days followed by an increase after 28 days and an increasein hemoglobin level after 28 days) and disorders in water-electrolyte balanceThese changes vanish after completing thetherapy

Cakir et al [24] studied the effect of 50- and 100-day application of low frequency magnetic field of 097mTamplitude for 3 hours per day on the hematological ratsblood parameters They found that magnetic fields from theELF range induce small but statistically significant changesremaining in physiological range of some rats blood parame-ters namely a small decrease in eosinophil hemoglobin andmean platelet volume (MPV) levels

In this study we have analyzed the effect of magneticfield not only on whole blood and blood plasma viscos-ity but also on the viscoelastic properties of blood Thecomplex viscosity of blood was measured at variable shearamplitudes and constant oscillation frequency of 05HzSuch a choice of the experimental method was dictatedby the technical limitations of the experimental setup Inthe case of other oscillation frequencies or shear amplituderanges the mechanical resonance effects strongly affectedthe measurement [9] The measurement of the viscous (1205781015840)and elastic (12057810158401015840) components of the complex blood viscosity(120578lowast

) allows for studying the viscoelastic properties of bloodwhich also reveals information about red cells aggregabilityand deformability These two features strongly affect bloodflow in the circulatory system especially in microcirculation[18 25 26]

Viscoelastic properties of blood change as a function ofshear rate which is reflected by the results listed in Table 2For small values of shear rate amplitude 1205741015840

0= 02 we

found statistically significant lowering of the viscous (1205781015840)component of the complex viscosity Complex viscosities

measured by rotary-oscillating rheometer shown in Figure 1are comparable to those obtained with an oscillating (1Hz)capillary rheometer [26 27] The value of the elastic com-ponent 1205781015840 refers mainly to the packages of red cells whichare broken by increasing value of the shear amplitude 1205741015840

0

It can be seen that starting from a certain value of 12057410158400only

individual red cells contribute to the elastic component ofred cells complex viscosity [26] Since individual red cells arerather soft in the range of high shear rates practically onlyviscous properties of blood are observed

In the literature it has been described that there is aconnection between the red cells sedimentation rate andthe values of the viscous (1205781015840) and elastic (12057810158401015840) componentsof the complex blood viscosity (120578lowast) [18] In the currentstudy the sedimentation rate was not measured on the dayof blood uptake for rheological measurements Performingsedimentation experiments would allow for such comparisonand would provide another source of information on redcells aggregability However even the fact that low values ofthe viscous component alone in the range of low shear rates(12057410158400rarr 0) are accompanied by high value of 1205781015840 for high

shear rates (120574 rarr infin) may be an indication of faster red cellsaggregability [18]

The values of the elastic (12057810158401015840) component of the complexblood viscosity were correlated with the 1205741015840

119888and 119896

infinparam-

eters of Quemada rheological model The former parameterindicates the moment of rouleaux formation while the latteris interpreted as red cells rigidity (Figures 3 and 4) Inthe range of low shear rate amplitudes 1205741015840

0a slight positive

correlation between the 12057810158401015840 component and the 1205741015840119888parameter

can be seen and a negative one between 12057810158401015840 and 119896infin

can befound For the shear rate amplitude of 20 sminus1 no correlationswere found

Comparing the values of 1205781015840 and 12057810158401015840 obtained in this study(Table 1) with analogous data found in a group of patientsafter myocardial infarction [9] complex viscosity compo-nents are higher in the group of healthy patients compared tothe patients aftermyocardial infarction Observed differenceswere statistically significant (0001 lt 119875 lt 0004) A compar-ative analysis of these results is possible because both studieswere performed by means of the same instrument and usingthe same method Such a result may be interpreted as a resultof the influence of the therapy applied to the patients aftermyocardial infarction on the viscoelastic properties of bloodIn this study no comparison with other control groups hasbeen performed

It is also interesting to compare this in vitro study to somerecent results of in vivo magnetotherapy effects on bloodviscosity in a group of patients with cerebrovascular disease[17] where a tendency to decreasing red cells aggregabilitywas found after magnetic field application Such result wasinterpreted in terms of manifestation of some autoregulatorymechanisms in living organisms induced by variable mag-netic field therapy as it was suggested in other studies [28 29]It is obvious that in the case of the in vitro studies suchmechanisms can not be observed

In vitromeasurements of blood sedimentation rate in thepresence of magnetic field should be possible with a small


Table 2The values of the viscous and elastic components of the complex viscosity in the group of healthy patients before and after magneticfield

Rheological parameter Before magnetic field (119899 = 25) After magnetic field (119899 = 25) 119875

Value of 1205781015840 at 12057410158400= 02 sminus1 925 plusmn 044 808 plusmn 033 lt004

Value of 1205781015840 at 12057410158400= 1 sminus1 1076 plusmn 036 1085 plusmn 037 mdash







modification of the setup It could be good complementaryinformation useful in the interpretation of rheological data

5 Conclusions

In this study a comprehensive analysis of rheological prop-erties of blood taken from a group of healthy patientsqualified as blood donors was performed On the basis ofthe measurements of whole blood plasma and complexviscosities by means of a rotary-oscillating rheometer in agroup of healthy patients the following conclusions can bedrawn

(1) In the in vitro conditions only weak effects of mag-netic field therapy on blood rheological parametersare observed Statistical analysis of observed differ-ences showed their statistical insignificance

(2) Comparison of these results with studies performedin vivo suggests that the lack of effect of magnetic fieldapplication in vitro might result from the fact thatmagnetotherapy influences the whole organism andnot only blood

(3) The results of rotary measurements obtained inthis study remain in agreement with similar studiesreported in the literature for healthy people

(4) The results of oscillatory measurements are in agree-ment with the flow curve measurements

(5) The results of the oscillatory measurements are inagreement with the rheological model of Quemada

(6) Due to technical limitations the viscoelastic prop-erties of the system could only be measured usingthe method of constant frequency and variable shearamplitude which couldnot exceed 20 sminus1

(7) In the case of oscillatory measurements sedimenta-tion experiments would be very helpful

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J Pasek R Mucha and A Sieron ldquoMagnetostimulationmdasha modem form of therapy for medicine and rehabilitationrdquoFizjoterapia vol 14 no 4 pp 3ndash8 2006

[2] A Sieron R Brus R Szkilnik A Plech N Kubanski andG Cieslar ldquoInfluence of alternating low frequency magneticfields on reactivity of central dopamine receptors in neonatal6-hydroxydopamine treated ratsrdquo Bioelectromagnetics vol 22no 7 pp 479ndash486 2001

[3] R Tao and K Huang ldquoReducing blood viscosity with magneticfieldsrdquo Physical Review E vol 84 no 1 Article ID 011905 2011

[4] P Kowal andAMarcinkowska-Gapinska ldquoAnalysis of the influ-ence of magnetostimulation on the hemorheological parame-ters and on the result of thermographic examinationrdquo in SomeAspects of Medical PhysicsmdashIn Vivo and In Vitro Z Drzyzgaand K Slosarek Eds pp 59ndash64 HARD Publishing OlsztynPoland 2010

[5] L Dintenfass ldquoA new outlook on body fluid viscosity and cellfunction concluding remarks and discussionrdquo Biorheology vol27 no 3-4 pp 611ndash616 1990

[6] H Schmid-Schonbein H Rieger and T Fischer ldquoBlood fluidityas a consequence of red cell fluidity flow properties of bloodand flow behavior of blood in vascular diseasesrdquo Angiology vol31 no 5 pp 301ndash319 1980

[7] D Lerche H Bamler W Kucera W Meier andM PaulitschkeldquoFlow properties of blood and hemoreological methods ofquantificationrdquo in Physical Characterization of Biological CellsBasic Research and Clinic Relevance W Scutt H KlinkmannI Lamprecht and T Wilson Eds pp 189ndash214 GesundheitBerlin Germany 1991

[8] B Sandhagen Assesment of Blood Rheology Methodology andStudies in Healthy Individuals in Patients with Certain Dis-eases and during Liquid Blood Preservation Acta UniversitatisUpsaliensis Uppsala Sweden 1988

[9] A Marcinkowska-Gapinska F Jaroszyk and L Kubisz ldquoTheinfluence of acetylsalicylic acid and acenocumarin on the com-plex viscosity of bloodrdquo Scientific Proceedings of Riga TechnicalUniversity in series 6 Transport and Engineering pp 159ndash1622002

[10] M R Hardeman P T Goedhart J G G Dobbe and KP Lettinga ldquoLaser-assisted optical rotational cell analyser(LORCA) I A new instrument for measurement of variousstructural hemorheological parametersrdquo Clinical Hemorheol-ogy vol 14 no 4 pp 605ndash618 1994


[11] M Musielak ldquoRed blood cell-deformability measurement re-view of techniquesrdquo Clinical Hemorheology and Microcircula-tion vol 42 no 1 pp 47ndash64 2009

[12] A Marcinkowska-Gapinska J Gapinski W Elikowski FJaroszyk and L Kubisz ldquoComparison of three rheologicalmodels of shear flow behavior studied on blood samples frompost-infarction patientsrdquo Medical and Biological Engineeringand Computing vol 45 no 9 pp 837ndash844 2007

[13] D Quemada ldquoA rheological model for studying the hematocritdependence of red cell-red cell and red cell-protein interactionsin bloodrdquo Biorheology vol 18 no 3-6 pp 501ndash516 1981

[14] D Quemada ldquoBlood rheology and its implication in flow ofbloodrdquo in Arteries and Arterial Blood Flow C M RodkiewiczEd pp 1ndash127 Springer New York NY USA 1983

[15] A Marcinkowska-Gapinska F Jaroszyk and S Gorski ldquoAppli-caton ofQuemada rheological equation to analysis of bloodflowcurves in certain cases Part Irdquo Polish Journal of Medical Physicsand Engineering vol 1 pp 39ndash49 1998

[16] A Marcinkowska-Gapinska F Jaroszyk W Elikowski and LKubisz ldquoThe effect of acetylsalicylic acid and acenocoumarinon rheological properties of blood studied on patients aftermyocardial infarctionrdquo Current Topics in Biophysics vol 1 pp4ndash8 2004

[17] P Kowal and A Marcinkowska-Gapinska ldquoAn influence of thealtered magnetic field on the hemorheological parameters inpatients with cerebrovascular diseaserdquo Neuroskop vol 7 pp135ndash138 2005

[18] D Schneditz F Rainer and T Kenner ldquoViscoelastic propertiesof whole blood Influence of fast sedimenting red blood cellaggregatesrdquo Biorheology vol 24 no 1 pp 13ndash22 1987

[19] P Kowal and A Marcinkowska-Gapinska ldquoHemorheologicalchanges dependent on the time from the onset of ischemicstrokerdquo Journal of the Neurological Sciences vol 258 no 1-2 pp132ndash136 2007

[20] Y-I Cho and D J Cho ldquoHemorheology and microvasculardisordersrdquo Korean Circulation Journal vol 41 no 6 pp 287ndash295 2011

[21] D Lerche B Koch and G Vlastos ldquoFlow behaviour of bloodrdquoRheology vol 93 pp 105ndash112 1993

[22] H C Kwaan ldquoRole of plasma proteins in whole blood viscositya brief clinical reviewrdquoClinical Hemorheology andMicrocircula-tion vol 44 no 3 pp 167ndash176 2010

[23] E Ciejka and A Gorąca ldquoOddziaływanie pola magnetycznegoo parametrach stosowanych w magnetoterapii na wybraneparametry biochemiczne krwirdquo Balneologia Polska vol 4 pp234ndash242 2007

[24] D U Cakir B Yokus M Z Akdag C Sert and N MeteldquoAlterations of hematological variations in rats exposed toextremely low frequency magnetic fields (50Hz)rdquo Archives ofMedical Research vol 40 no 5 pp 352ndash356 2009

[25] H Schmid-Schoenbein H Rieger and T Fischer ldquoBloodfluidity as a consequence of red cell fluidity flow propertiesof blood and flow behavior of blood in vascular diseasesrdquoAngiology vol 31 no 5 pp 301ndash319 1980

[26] G B Thurston ldquoViscoelasticity of human bloodrdquo BiophysicalJournal vol 12 no 9 pp 1205ndash1217 1972

[27] D Schneditz V Ribitsch and T Kenner ldquoRheological discrim-ination between native rigid and agregated red blood cells inoscillatory flowrdquo Biorheology vol 22 no 3 pp 209ndash219 1985

[28] W H Reinhart ldquoMolecular biology and self-regulatory mecha-nisms of blood viscosity a reviewrdquo Biorheology vol 38 no 2-3pp 203ndash212 2001

[29] L Dintenfass ldquoClinical applications of blood viscosity fac-tors and functions especially in the cardiovascular disordersrdquoBiorheology vol 16 no 1-2 pp 69ndash84 1979

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Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom


through blood vessels is a very complex phenomenon dueto physical and physicochemical properties of blood and thestructure of the circulatory system Features related to theflow of blood in blood vessels are referred to as blood fluidity[6] Rheological characteristics of every material dependmainly on two parameters viscosity and elasticity Viscosityis a parameter determining the resistance of the materialto flow while elasticity expresses the material resistanceagainst deformation A hemorheological study is primarilybased on the blood viscosity measurements In the case ofnon-Newtonian fluids such as blood viscosity is a functionof applied shear rate The main factors determining bloodviscosity are hematocrit value erythrocytes aggregability anddeformability and the plasma viscosity [7]

Measurements of whole blood viscosity as a function ofshear rate are performed by means of rotary rheometers Onthe contrary blood plasma viscosity can be measured bothby rotary and capillary viscometers because it is a Newtonianliquid [7ndash9] Additional information about blood rheologycan be achieved from nonviscometric oscillatory measure-ments called also dynamic mechanical analysis (DMA) Theprinciple of the oscillatory technique lies in determiningthe amplitude and phase of the oscillations of the studiedsample subjected to action of a harmonic force of controlledamplitude and frequency A measurement performed bymeans of the oscillatory method should provide informationabout viscoelastic properties of the fluid under study whichcan be expressed in terms of a complex viscosity

120578lowast

= 1205781015840

+ 11989412057810158401015840

(1)

where 120578lowast is the complex viscosity 1205781015840 is the viscous compo-nent and 12057810158401015840 is the elastic component

Additional information about erythrocytes propertiessimilar to that from direct measurements of red cells aggre-gability and deformability [7 8 10 11] can be achievedindirectly from amathematical analysis of the flow curvewiththe use of rheological models [7 12] In this work we use theQuemada model [13 14]

The aimof the present workwas a comprehensive analysisof the rheological properties of blood in a group of healthyobjects with the use of a rotary-oscillating rheometer Bothrotary and oscillatory measurements were performed in thisstudy We present the results of viscosity measurements ofboth whole blood and blood plasma (rotary method) andthe results of complex viscositymeasurementswith separatelycalculated viscous and elastic components of the blood com-plex viscosity The flow curves were analyzed with the helpof Quemada rheological model to estimate the parametersmeasuring red cells aggregability anddeformability in healthypatients before and after application of magnetic field

2 Material and Methods

Blood samples for the comprehensive rheological analysiswere taken from a group of 25 healthy nonsmoking patientsaged 21 to 51 with 19 men and 6 women The average ageof patients in the group was 31 Blood donors did not sufferfrom any chronic diseases and passed the standard tests

for blood donors The interval between the blood collectionand the viscosity measurement never exceeded 4 hours Thecomprehensive analysis was based on the measurements ofhematocrit value (Hct) whole blood viscosity (120578) at fourchosen shear rate (1205741015840) values (01 1 10 and 100 sminus1) plasmaviscosity (120578

119901) complex viscosity (120578lowast) and its elastic (12057810158401015840) and

viscous (1205781015840) components measured for four chosen ampli-tudes (1205741015840

0) of shear rate values (02 1 10 and 20 sminus1)The blood

samples were collected into BD Vacutainer Tubes containinglithium heparin (17 international unitsmL of blood) Thehematocrit value was determined using the standardmethodBlood plasma was obtained by centrifugation of whole bloodat 4000 rpm for 10 minutes and collection of the supernatantAll viscosity measurements were performed by means of arotary-oscillating rheometer Contraves LS40 at the temper-ature of 37∘C The measurement cell consisted of a steel cupdriven by a precise step motor and a steel bob suspended ona quartz thread which together formed a Couette cell with avolume of 18mL In the rotary measurements the motion ofthe cupwas unidirectional and the torsion angle of the threadwas taken as the measure of shear stress In the oscillatoryones the cup was moved in an oscillating way with a constantfrequency and both the amplitude of the thread torsion andthe phase difference of the cup and bob oscillations wereused to calculate the real and imaginary components of thecomplex viscosity

Whole blood viscosity was measured in the order of de-creasing shear rate in the range 100ndash001 sminus1 within 5 minutesafter short preshearing at 1205741015840 = 100 sminus1 [15 16] Plasma viscos-ity was estimated from a regression analysis of shear ratedependence of shear stress measured in the range of 1205741015840 = 10ndash100 sminus1 Oscillatory measurements of the viscous and elasticparts of the complex blood viscosity were performed at aconstant frequency of 05Hz and decreasing amplitude [9]Conclusions with regard to the red cells aggregability anddeformability were drawn indirectly from the analysis of theflow curves using the rheological model of Quemada ((2)and (3)) and comparing the values of the model parameters1198960 119896infin and 1205741015840

119888 This model has been formulated for a

suspension of aggregating particlesmdasha substance resemblingthe properties of real whole blood The parameters 119896

infinand

1198960in (2) have the meaning of a measure of red cells rigidity

and aggregability respectively Parameter 119896119876has the sense of

erythrocyte intrinsic viscosity which also takes into accountthe change of erythrocyte shape via the function 119896

119876(1205741015840

) in (3)The symbols 120591(1205741015840) 120578

119901 and Hct denote shear stress plasma

viscosity and hematocrit value respectively

119896119876=1198960+ 119896infin(1205741015840

1205741015840

119888)12

1 + (12057410158401205741015840119888)12

(2)

120591 (1205741015840

) = 120578119901[1 minus1

2119896119876sdotHct]

minus2

sdot 1205741015840

(3)

The values of 1198960 119896infin and 1205741015840

119888were determined from the

least squares fit of the model to the experimental flow curveusing Hct and 120578

119901as fixed parameters taken from direct

measurements






141 plusmn 001











lowast

119875 lt 002


3 Results



119896infin and 1205741015840








119888and 119896


2minus121205749984000(sminus1)

120578998400120578998400998400120578lowast(Pas)


10minus2

10minus3

10minus4

01 1 10







4 Discussion



12

10

8

6

4

2

14 15 16 17 18 19 20 21 22

120574998400 c(sminus1)

kinfin


119888and 119896

infin

1816141210864

02 4 6 8 10

2010

102

120574998400

c(sminus1)

120574998400

0(sminus1)

120578998400998400(m

Pas)






16141210864

15

10

05

0014 16 18 20 22

kinfin

2010

102

120574998400

0(sminus1)

120578998400998400(m

Pas)









0 119896infin











0= 02 we



0






119888and 119896

infinparam-


0a slight positive



















5 Conclusions











References




































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





















141 plusmn 001











lowast

119875 lt 002


3 Results



119896infin and 1205741015840








119888and 119896


2minus121205749984000(sminus1)

120578998400120578998400998400120578lowast(Pas)


10minus2

10minus3

10minus4

01 1 10







4 Discussion



12

10

8

6

4

2

14 15 16 17 18 19 20 21 22

120574998400 c(sminus1)

kinfin


119888and 119896

infin

1816141210864

02 4 6 8 10

2010

102

120574998400

c(sminus1)

120574998400

0(sminus1)

120578998400998400(m

Pas)






16141210864

15

10

05

0014 16 18 20 22

kinfin

2010

102

120574998400

0(sminus1)

120578998400998400(m

Pas)









0 119896infin











0= 02 we



0






119888and 119896

infinparam-


0a slight positive



















5 Conclusions











References




































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















12

10

8

6

4

2

14 15 16 17 18 19 20 21 22

120574998400 c(sminus1)

kinfin


119888and 119896

infin

1816141210864

02 4 6 8 10

2010

102

120574998400

c(sminus1)

120574998400

0(sminus1)

120578998400998400(m

Pas)






16141210864

15

10

05

0014 16 18 20 22

kinfin

2010

102

120574998400

0(sminus1)

120578998400998400(m

Pas)









0 119896infin











0= 02 we



0






119888and 119896

infinparam-


0a slight positive



















5 Conclusions











References




































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



















0 119896infin











0= 02 we



0






119888and 119896

infinparam-


0a slight positive



















5 Conclusions











References




































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of




























5 Conclusions











References




































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of









































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
















research article analysis of the magnetic field influence...

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