Journal of Electromyography and Kinesiology 20 (2010) 868–878

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Journal of Electromyography and Kinesiology

journal homepage: www.elsevier .com/locate / je lek in

Analysis of the peak-to-peak ratio of extracellular potentials in the proximityof excitable fibres

Javier Rodriguez a, Armando Malanda a, Luis Gila b, Ignacio Rodriguez a, Javier Navallas a,*

a Public University of Navarra, Dept. Electrical and Electronical Engineering, 31006 Pamplona, Spainb Virgen del Camino Hospital, Dept. Clinical Neurophysiology, 31008 Pamplona, Spain

a r t i c l e i n f o

Article history:Received 4 May 2009Received in revised form 28 July 2009Accepted 28 July 2009

Keywords:Single fibre action potentialSFAP modelingPeak-to-peak ratioIAP spatial profileFibre-electrode distance

1050-6411/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.jelekin.2009.07.008

* Corresponding author.E-mail addresses: javier.rodriguez.falces@gmail

(J. Navallas).

a b s t r a c t

In a previous work we studied the ratio between the amplitudes of the second and first phases (which wecall PPR, after peak-to-peak ratio) of the single fibre action potential (SFAP) for a collection of fibrillationpotentials (FPs) extracted from two pathological muscles. These FPs showed a wider PPR range than theDimitrov–Dimitrova (D–D) convolutional model could provide. We proposed a modification of the D–Dintracellular action potential (IAP) in order to obtain a range of PPRs comparable to that observed inour FPs. This paper extends that study to a large number of SFAPs extracted from the tibialis anteriormuscle of normal subjects. The estimation of the average PPR range of non-diseased muscles in non-fati-gued conditions is important since it can be used as a reference to establish a comparison with PPR rangesfrom muscles suffering some disorder or from fibres that are fatigued. Other aspects of the PPR, as its sen-sitivity with volume conductor parameters or to what extent changes in the SFAP PPR reflects changes inIAP spatial profile are also examined. We found that the PPR of experimental SFAPs ranges from 0.3 to 2.5in all subjects and that all PPR histograms contain a well-defined single peak around the PPR value 1.0.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

To analyse the features of the single fibre action potential(SFAP), many authors (Plonsey, 1974; Nandedkar and Stålberg,1983a; Dimitrov and Dimitrova, 1998) assume that the muscle fi-bre can be modeled as a time-shift invariant system. This allowsthe SFAP to be expressed as a convolution of two time dependentfunctions. In the Dimitrov–Dimitrova (D–D) SFAP model (Dimitrovand Dimitrova, 1998), the input signal is the first temporal deriva-tive of the intracellular action potential (IAP).

In terms of volume conductor theory (Plonsey, 1974; Andreas-sen and Rosenfalck, 1981; Miller-Larson, 1985), SFAPs are triphasicwaveforms, although biphasic SFAPs are often recorded experi-mentally (Ekstedt, 1964; Dumitru et al., 1994), especially withinthe 300 lm radius where they are usually detected. Occasionally,SFAPs with the amplitude of the first positive phase (V1) higherthan the negative one (V2) have been recorded, though usually V2

is higher (Ekstedt, 1964). The peak-to-peak ratio (PPR), defined asthe absolute value of the quotient of V2 over V1, was introducedby Rodriguez et al. (2006a) but was only studied for a collectionof fibrillation potentials.

ll rights reserved.

.com, malanda@unavarra.es

Traditionally, the IAP waveform has been divided into the depo-larization and repolarization portions (Dumitru et al., 1994; Rodri-guez et al., 2007). At short radial distances, it is generally acceptedthat the IAP depolarization portion generates the first and secondSFAP phases, whereas the IAP repolarization portion essentiallydetermines the third small phase of the SFAP (Dumitru et al.,1994; Arabadzhiev et al., 2008). However, according to the IAPdescriptions proposed by some authors (Nandedkar and Stålberg,1983a; Dimitrov and Dimitrova, 1998), SFAP PPR is largely inde-pendent from the IAP depolarization portion. A recent modificationof the IAP analytical expression proposed in the D–D model intro-duced a new parameter (A2b) in the IAP rising phase that permitscontrolled variation of SFAP PPR (Rodriguez et al., 2006a). Withthe inclusion of parameter A2b in the new IAP approach, SFAPPPR range was enlarged so that it comprises the PPRs observedin a collection of fibrillation potentials. However, many aspectsof SFAP PPR still remain open.

Measures of the PPR range of SFAPs recorded from non-diseasedmuscles in non-fatigue conditions are very valuable since they canbe used as a reference to establish a comparison with PPR rangesfrom muscles suffering some disorder or from fibres that arefatigued.

Information about the sensitivity of PPR with changes in the IAPrising phase is also of interest. Abnormal calcium accumulation inmyopathic muscle fibres can increase the IAP spike duration andnegative after potential (Bodensteine and Engel, 1978; Emery and

J. Rodriguez et al. / Journal of Electromyography and Kinesiology 20 (2010) 868–878 869

Burt, 1980; Bertorini et al., 1982). The slowing of the ionic pro-cesses observed in fatigued muscles (Lüttgau, 1965; Hanson andPersson, 1971; Lännergren and Westerblad, 1987; Balog et al.,1994) and the variations in potassium and sodium concentrationsobserved in dystrophy (Ludin, 1973) also produce changes in theIAP spatial profile. Some SFAP features such as the rise-time haveproved to be strongly sensitive to these processes (Arabadzhievet al., 2008). Then, it should be analysed whether SFAP PPR is ableto reflect the changes in the IAP spatial profile that follows thementioned conditions disorders so that it can be used for electro-diagnostic assessment of muscle fibres in disease.

Experimental studies (Håkansson, 1957) and also simulations(Nandedkar and Stålberg, 1983a; Dimitrov and Dimitrova, 1989;Dimitrova and Dimitrov, 2006; Arabadzhiev et al., 2008) haveshown that, at distances very close to the fibre, some SFAP proper-ties such as the rise-time are relatively independent of the fibre-electrode distance (radial distance). However, several authors havestudied the dependence of SFAP amplitudes V1, V2 and V3 on radialdistance (Ekstedt, 1964; Miller-Larson, 1985). Then, it must beexamined to what extent changes in radial distance are accompa-nied by changes in SFAP PPR. Some insight as to how SFAP PPRchanges with radial distance was obtained by simulations usingthe D–D model (Rodriguez et al., 2006a). This should be checkedexperimentally with SFAPs recorded under intentional needlemovement.

The first goal of the present study was to calculate and comparethe PPR histograms of SFAPs recorded from various subjects andtest whether the new IAP description is able to generate the rangeof PPRs observed in the recorded data. The second objective was toanalyse the PPR dependence on radial distance using various setsof SFAPs recorded with controlled movement of the recordingneedle.

2. Electrodes, recording system and experimental signals

SF-EMG signals were recorded from the right tibialis anteriormuscle of four subjects (of 28, 30, 33 and 41 years). No musculardisease was previously reported from these subjects. The studywas approved by the clinical investigation ethics committee ofNavarra. Informed consent was obtained from all subjects.

Experimental signals were recorded with an electromyograph(Counterpoint, Dantec Co., Skovlunde, Denmark) using a SF elec-trode (core diameter of 25 lm, needle diameter of 0.46 mm, needlelength of 37 mm; Viasys Neurocare). The core-platinum recordingsurface of the SF electrode was 3.5 mm from the needle tip. Thebandwidth of the EMG recording system was 2 Hz–10 kHz. Record-ings were stored digitally after sampling at a rate of 50 kHz anddigitization at 16 bits per sample.

The SF electrode was inserted in the muscle between 10 and17 cm away from the centre of the patella and between 1 and3 cm away from the tibia. SFAPs were extracted from differentinsertion points in each subject. For each insertion point, the posi-tion of the SF electrode was changed several times in order to lo-cate SFAPs. To reduce the number of activated motor units,signals were generated at the 10% of the maximal voluntarycontraction.

Up to 100 consecutive discharges of each SFAP were extractedduring a low voluntary contraction of the patient. From now on,we call each collection of discharges a SFAP set (or SFAP series).In most cases, each SFAP set contained only one SFAP waveform,although in some SFAP series two or three different SFAP wave-forms appeared. For each subject, we recorded 50 SFAP sets. Oncea SFAP was found, the electromyographist tried to keep the needleas steady as possible so that consecutive SFAPs were recorded withsimilar peak-to-peak amplitudes (Vpp). In a few cases, the electr-

omyographist moved the needle intentionally in order to obtainthe maximum variation range of Vpp.

The criteria used to accept a recorded SFAP set for further studywere: (1) the SFAPs have biphasic or triphasic morphology, (2) con-tinuous monitoring of the discharges shows a consistent SFAPshape, (3) there is no other potentials overlapping the SFAP, (4)the rise-time does not exceed 1 ms, and (5) the amount of noiseis not so high as to make measurements of SFAP rise-timeunreliable.

3. Analysis of PPR in the Dimitrov and Dimitrova SFAP model

3.1. Dimitrov and Dimitrova SFAP convolutional model

We perform simulations of SFAPs using the model proposed byDimitrov and Dimitrova (1998). In this model the fibre is consid-ered as a time-shift invariant system and SFAPs can be expressedas a convolution of the input signal and impulse response of thecorresponding system (1):

SFAPðtÞ ¼ Can �@IAPðtÞ@t

� IRDDðtÞ ð1Þ

where Can is a coefficient of proportionality. The input signal wasthe IAP first temporal derivative, d(IAP(t))/dt. The impulse response(IRDD) is computed as the potential produced by two current dipolespropagating along the fibre in opposite directions from the endplatetoward the fibre ends and detected by a single fibre (SF) electrode.In these conditions, the analytic expression of the impulse responsein the D–D model (Dimitrov and Dimitrova, 1998) can be computedas

IRDDðtÞ ¼v � ðz0 � vtÞ

½ðz0 � vtÞ2 þ kan � r2�ð2Þ

where v is the propagation velocity, r the radial distance, z0 the axialdistance and Kan the constant of anisotropy. In (2) only the sourcepropagating to the right is considered. A frequently used mathemat-ical relationship (Nandedkar and Stålberg, 1983a,b; Nandedkar andSanders, 1988) between the propagation velocity, v (in m/s), and thefibre diameter, d (in mm) is

v ¼ vmed þ 0:05 � ðd � 1000� 55Þ ð3Þ

where vmed is set at 4 m/s in our simulations (Nandedkar and Stål-berg, 1983a)

3.2. Extracellular potentials close to the fibre

The excitation wave can be considered as two stacks (on fordepolarization and the other for repolarization) of distributed cur-rent dipoles. Each stack contains identically oriented dipoleswhose strengths are proportional to the first spatial derivativesof the IAP. The orientation of the dipoles in one stack is oppositeto the orientation in the other one.

Far from the endplate and fibre ends, the whole depolarizationzone is formed. In this case, when the electrode is located in thevicinity of the fibre, the fibre-electrode distance is much shorterthan the length of the IAP spatial profile (a few millimetres atleast). As a result, the magnitude of the recorded SFAP is deter-mined mainly by the dipoles closest to the electrode, and the inter-action between opposite-directed dipole fields produced by the IAPde- and repolarization phases is weak. In such a case, the dipolefield produced by the IAP depolarization phase is considerablystronger, because the dipoles are distributed at a considerablyshorter fibre region. This means that the individual dipoles havea higher strength and their fields have a better spatial summation

870 J. Rodriguez et al. / Journal of Electromyography and Kinesiology 20 (2010) 868–878

than those corresponding to the longer spatial length of the IAPrepolarization phase.

Thus, just the IAP depolarization is the major determinant of theSFAP larger phases at short fibre–electrode distances typical forSFAP detection. The repolarization phase gives rise to the lower-amplitude, second positive phase component.

3.3. The modified D–D model. Excitation parameters and their defaultvalues

Dimitrov and Dimitrova proposed an IAP approximation thatprovides independent changes of different phases (Dimitrov andDimitrova, 1998). The time course of a typical IAP with a negativeafterpotential is divided into four portions: the rising phase, therapidly falling phase, the transition phase and the slowly fallingphase. The depolarization portion (rising phase) is characterizedby three parameters, namely A1, A2 and A3 (4).

RPðsÞ ¼ A1 � sA

2 � e�A

3s

0 6 s 6 smð4Þ

The duration of this phase sm can be calculated as the quotientA2/A3. The second, third and fourth IAP phases model the repolari-zation process occurring at the membrane of the cell after thedepolarization. The duration of this repolarization portion is con-trolled by parameter Tspl (Dimitrov and Dimitrova, 1998; Rodri-guez et al., 2007).

The main drawback of this description is that the IAP first deriv-ative was not sufficiently smooth. An alternative IAP approxima-tion that overcomes this problem has been proposed recently(Arabadzhiev et al., 2008). Nevertheless, since the target of thepresent study is to analyse the dependence of the SFAP PPR onthe IAP rising phase, the former IAP approach is preferable.

3.3.1. The new IAP description. Controlled variation of the PPRIn the modification of the IAP description proposed by Rodri-

guez et al. (2006a) a new parameter (A2b) was included so thatthe time course of the rising phase was divided into 2 portions;the first one (concave) controlled by parameters (A1, A2, A3) andthe second one (convex) controlled by parameters (A1, A2b, A3).Generally, we fix the values of parameters A1, A2 and A3 to thosesuggested by the D–D model (Dimitrov and Dimitrova, 1998) andvary the value of A2b. By doing this, the concave portion profile isfixed whereas the profile of the convex portion depends on therelationship between A2 and A2b [(Fig. 1)a].

The slope differences in the convex part of the IAP generateSFAPs with different shapes. In fact, when the IAPs with various

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

IAP profiles for differentA2 − A2b combinations

Time (ms)

(a)

a

bc

a : 5.0 4.5

b : 5.0 5.0

c : 5.0 5.5

A 2 A 2bNor

mal

ized

val

ues

Fig. 1. (a) Slope changes in the convex part of the IAP rising phase. (b) Generation of SFnormalized with respect to the maximum value for the second phase of SFAP a. Dedistance = 0.075 mm).

(A2, A2b) combinations (Fig. 1a) are convolved by the impulse re-sponse, SFAPs with different PPRs are obtained (Fig. 1b). As theparameter A2b increases (the slope of the convex part decreases),the SFAP PPR falls.

The magnitude of the new synthesized SFAP depends on the A2,A2b relative values. This could be predicted from Fig. 1a, where theIAP amplitude changed depending on the relation between A2 andA2b.

3.3.2. Default valuesWe shall refer to A2, A2b, A3 and Tspl as excitation parame-

ters. Their values will be set to those suggested by Dimitrovand Dimitrova (1998) and Rodriguez et al. (2006a) (A1 =125�21242, A2 = 5.0, A2b = 5.0, A2b = 5.0, A3 = 14 and Tspl = 2.5 ms),except when we vary one of them in the course of our study.These values will be called default values for the excitationparameters.

3.4. Impulse response parameters in the D–D model. Default values.Setting parameters

The impulse response of the D–D model (2) can be expressed asa function of four parameters, namely axial distance, z0, constant ofanisotrophy, Kan, fibre diameter, d, and radial distance, r,.

3.4.1. Default valuesWe shall refer to z0, Kan, d and r as IR parameters and except

when we vary one of them, their values will be set to z0 =20 mm, Kan = 5 (as suggested by Rosenfalck, 1969; Griep et al.,1978; Andreassen and Rosenfalck, 1981; Nandedkar and Stålberg,1983a) d = 0.055 mm (as suggested by Nandedkar and Stålberg,1983a,b; Nandedkar and Sanders, 1988) and r = 0.1 mm. These val-ues will be called default values for the IR parameters.

3.4.2. Setting parametersWe consider a 90 mm long fibre with a right semilength of

40 mm. We use a reference velocity of 4.5 mm/ms and a time step(sampling interval) of 4 ls (250 kHz). This means that the spacestep used for the simulations is 0.018 mm, which is suitable forthe radial distances of interest (0.01–0.25 mm).

3.5. Influence of IAP and IR parameters on SFAP PPR

In (Fig. 2) we show the dependence of SFAP PPR on excitationparameters (first row) and on IR parameters (second row). When

4.5 5 5.5-1.5

-1

-0.5

0

0.5

1

Time (ms)

SFAP profiles for differentA2 − A2 b combinations

(b)

a

bc

a : 1.25

b : 1.15

c : 0.93

P P R

APs with variable PPRs corresponding to the A2�A2b combinations of (a). SFAPs arefault values have been used for the excitation and IR parameters (except radial

A3A2 Tspl (ms)PP

R

v (m/s) rnaK (mm)

A2b

Z0 (mm)

Influence of IR parameters on SFAP PPR

Influence of excitation parameters on SFAP PPR

PPR

4 4.5 5 5.5

0.8

1

1.2

1.4

4 4.5 5 5.5

0.8

1

1.2

1.4

12 14 16

0.8

1

1.2

1.4

1 2 3 4

0.8

1

1.2

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0 20 40

0.8

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3 4 5 6 7

0.8

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1.4

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0.8

1

1.2

1.4

0.050.1 0.15 0.2 0.25

0.8

1

1.2

1.4

(a) (b) (c) (d)

(f)(e) (g) (h)

Fig. 2. PPR dependence on excitation (first row) and IR (second row) parameters. Default values have been used for excitation and IR parameters with the exception of theparameter under study in each case.

J. Rodriguez et al. / Journal of Electromyography and Kinesiology 20 (2010) 868–878 871

changing the value of each of them, we use the default values forthe non-arying parameters.

In (Fig. 2)a and b we see that the sensitivity of PPR with param-eters A2 and A2b is very high, whereas A3 has an almost negligibleeffect on PPR. Note also how PPR increases its value as Tspl getslower. This means that both the de- and repolarization portionsof the IAP have an influence on the SFAP PPR.

According to the curves in the first row of Fig. 2, we see that PPRis very sensitive to changes in the IAP rising phase. Thus, PPR re-flects how the ionic processes have taken place during the mem-brane depolarization. This result is not surprising: as weexplained in Section 3.2, at very short radial distances SFAP mainspike is essentially determined by the IAP depolarization portion.

The variation ranges for A3 and Tspl have been chosen as in pre-vious works (Rodriguez et al., 2006a, 2007). With regard to A2 andA2b, (Fig. 2)a and b show that PPR varies monotonically with theseparameters within the range 4.5–5.5 only. Thus, we will restricttheir variability to this range in the foregoing work.

The axial coordinate of the electrode, z0, does not affect the SFAPPPR except when the electrode is close to the neuromuscular or fi-bre-tendon junctions (Fig. 2)e. In these cases, the SFAP tends to bebiphasic and, therefore, the PPR changes dramatically. Similarly,the constant of anisotropy Kan has almost no influence on thePPR (Fig. 2)f. In contrast, fibre diameter and radial distance havea slight effect on PPR, this effect being more pronounced in the caseof the latter parameter (Fig. 2)h.

The variation ranges for Kan and v have been selected on the ba-sis of the works of various authors (Nandedkar and Stålberg,1983a; Arabadzhiev et al., 2008) In the case of radial distance,we will focus our analysis on the 0.005–0.25 mm range, as this isessentially the recording area of a single fibre-electrode.

3.6. PPR variation in the modified D–D SFAP model

From the last section it is clear that not all the parameters thatappear in the D–D model affect the PPR in the same way. Specifi-cally, parameter A3 in the excitation and parameters z0, Kan, and vin the impulse response hardly alter SFAP PPR. In fact, by makingsome reasonable assumptions on the muscle fibres and recordingconditions we could neglect the effect of these parameters. Firstof all, we can assume that our SFAPs have been recorded far fromthe neuromuscular and fibre-tendon junctions and so axial dis-

tance has no influence on the PPR. Secondly, we can assume thatfibre diameters and constant of anisotrophy do not vary signifi-cantly within the same muscle. Thus, in the modified D–D model,SFAP PPR can only be altered through variations of A2, A2b, Tspl

and radial distance.By using combinations of A2, A2b, Tspl and r, we calculate the

maximum range of PPRs that the modified D–D model can gener-ate. According to (Fig. 2)a and b, the smaller PPR values will be ob-tained when A2 is close to 4.5 and A2b is close to 5.5, whereas thehigher PPR values will be obtained when A2 is close to 5.5 andA2b is close to 4.5. Hence, in order to determine the lower andupper margins of PPR we study different combinations of r and Tspl

when A2 = 4.5, A2b = 5.5 (Fig. 3)a and when A2 = 5.5, A2b = 4.5(Fig. 3)b. We also examine PPR variations when A2 = 5, A2b = 5.5(Fig. 3)c and when A2 = 5, A2b = 4.5 (Fig. 3)d. In all cases, curves a,b, c, d and e correspond to Tspl values 1.0, 1.5, 2.0, 2.5 and 3.0,respectively.

3.6.1. SFAP PPR dependence on the IAP rising phaseSince the values of A2, A2b and Tspl essentially determine the

time course of the IAP, curves of Fig. 3 can be used to study thedependence of PPR on radial distance for different IAP waveforms.As can be seen, these curves present noticeable differences: not allof them increase monotonically with radial distance, as (Fig. 2)hsuggested. For instance, curves in Fig. 3a increase monotonicallyonly for r greater than 0.1 mm, whereas curves in Fig. 3c increasemonotonically when r is greater than 0.04 mm. However, curvesin Fig. 3d increase up to 0.05 mm and then they decrease for somevalues of r.

Note that, although a variation in Tspl changes the profile of thecurves in Fig. 3, the general trend of these curves is essentiallydetermined by the A2–A2b combination. This means that PPRdependence on radial distance is highly influenced by the IAP ris-ing phase. In Section 4.3 we will analyse PPR variation with radialdistance for various sets of SFAPs recorded using needlemovement.

3.6.2. Analysis of PPR variation using the modified D–D modelAs can be seen in Fig. 3, the variation range of PPR depends on

the A2�A2b combination considered. As an example, for A2 = 4.5and A2b = 5.5, PPR ranges from 0.8 to 1.4, whereas for A2 = 5 andA2b = 4.5, PPR varies within range 1.0–1.8. The largest variation

0.05 0.1 0.15 0.2 0.250.6

0.8

1

1.2

1.4

1.6

1.8

0.05 0.1 0.15 0.2 0.250.6

0.8

1

1.2

1.4

1.6

1.8

(A2=4.5, A2b=5.5)

r (mm)

PPR

r (mm)

(A2=5.5, A2b=4.5)

(a) (b)

0.05 0.1 0.15 0.2 0.250.6

0.8

1

1.2

1.4

1.6

1.8

0.05 0.1 0.15 0.2 0.250.6

0.8

1

1.2

1.4

1.6

1.8

)5.4=b2A,5=2A()5.5=b2A,5=2A(

(c) (d)

PPR

a

bc

ed

a

bc

de

a

bc

e d

a

bc d e

Fig. 3. PPR dependence on radial distance for different combinations of parameters Tspl, A2 and A2b. The values of A2 and A2b are shown in the title of each figure. In all cases,curves a, b, c, d and e correspond to Tspl values 1.0, 1.5, 2.0, 2.5 and 3.0, respectively. The non–varying excitation and IR parameters have been set to their default values.

872 J. Rodriguez et al. / Journal of Electromyography and Kinesiology 20 (2010) 868–878

range (0.7–2.0) is obtained when A2 = 5.5 and A2b = 4.5 for the ra-dial distances of interest.

Note that, in all the cases the greater PPR values are obtainedwhen Tspl is very low (curve a, Tspl = 1.0 ms). In fact, if we had setthe lower bound of Tspl to 1.5 ms (curve b), then PPR could onlyhave risen to 1.5, producing a very narrow PPR range. Only byallowing Tspl be very low (1.0 ms) we can enlarge the maximumPPR variation range up to 2.0. This means that in the modifiedD–D model high values of PPR can only be obtained when the repo-larization portion of the IAP is very short.

4. Results

In this section we first show the PPR variability observed inSFAPs recorded from different subjects. Then, we analyse the fluc-tuations in the PPR corresponding to SFAPs recorded from the samemuscle fibre. Finally, we show how PPR changes with radial dis-tance for various sets of SFAPs recorded using needle movement.

4.1. Observed PPR variability

We carry out an analysis of the PPR considering each subjectseparately. By doing this, similarities and differences could be ob-served and general conclusions extracted. PPR histograms of sub-jects 1, 2, 3 and 4 are shown in Fig. 4a–d respectively.

As can be seen, PPR histograms have some features in common:

– PPR values range approximately from 0.3 to 2.5 in all cases.– All PPR histograms contain a well-defined single peak, showing

that most PPR samples grouped around the most frequentPPR.

– The number of occurrences decreases as PPR approaches itsupper and lower boundaries.

The mode PPR value is different in each subject. Specifically, themost frequent PPR of subjects from one to four are 1.45, 1.15, 0.75

and 0.95, respectively. This means that PPR histograms contained asingle peak around the PPR value 1.0, which is in agreement withPPR histograms of fibrillation potentials reported recently (Rodri-guez et al., 2006a).

Variations in the position of the main peak of PPR histogramsreflect important differences in the features of SFAPs recorded. Insubject 3 for example, 66% of potentials have PPR below 1.0, show-ing that SFAPs of this subject have the first phase generally largerthan the second. In subject 1, however, only 26% of potentials pres-ent a first phase larger than the second. A question arises whetherthe volume conductor parameters, especially radial distance, canexplain such differences in SFAP PPR. Since the uptaking area ofthe electrode was limited within the 290-lm radius and consider-ing the large number of potentials recorded, radial distance shouldbe similarly distributed in all subjects. Thus, fibre–electrode dis-tance could not explain the differences observed in PPR betweendifferent subjects.

Histograms of Fig. 4 show that the overall range of variation ofPPR within each subject is 0.3–2.5. This variability in PPR clearlyexceeds the change in PPR that can be produced in the D–D modelby radial distance (see Fig. 3). Thus, there must be other factorscontributing to the observed PPR range. The proximity of therecording needle to the neuromuscular junction could explainPPR values around 2.5. In fact, when the electrode is located overthe endplate in the D–D model, the magnitude and duration ofthe SFAP first phase becomes very small and the resulting PPRcan rise up to 4.0 or 5.0. Potentials with such high PPRs, althoughsometimes registered experimentally, were not considered in ourstudy as their shape is largely distorted by the neuromuscularjunction. In contrast, experimental SFAPs with PPRs around 0.3 or0.4 were included in our study as long as their rise-times had sen-sible values and their main spikes resembled those of regularSFAPs.

However, it is not clear that SFAPs with PPRs between 2.0 and2.5 are actually affected by the neuromuscular junction. In addi-tion, the fraction of SFAPs with PPRs less than 1.0 is so large that

0.5 1 1.5 2 2.50

50

100

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0.5 1 1.5 2 2.50

50

100

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200

250

(a)

RPPRPP

PPR Histograms for different subject samples

(b)

(d)(c)

Nº o

focc

urre

nces

Nº o

focc

urre

nces

2tcejbuS1tcejbuS

4tcejbuS3tcejbuS

Fig. 4. PPR histograms (a), (b), (c) and (d) correspond to subjects 1, 2, 3 and 4, respectively. PPR values range approximately from 0.3 to 2.5 in all cases. In each subject, datawas taken from 50 sets of SFAPs, each of them comprising a number of potentials ranging from 50 to 99.

J. Rodriguez et al. / Journal of Electromyography and Kinesiology 20 (2010) 868–878 873

it is very unlikely that all of them were recorded near tendon. Thus,we conclude that we need to admit certain variability in the IAPwaveforms within a muscle in order to fully explain the largePPR range observed. Specifically, the existence of different profilesof IAP rising phases could explain at least part of the different val-ues of PPR.

4.2. PPR variability in sets of experimental SFAPs recorded from thesame fibre

We assess the variability observed experimentally in the PPR ofconsecutive potentials corresponding to the same SFAP set. Ascommented in Section 2, potentials that belong to a certain SFAPset have little variability in the value of Vpp (the coefficient of var-iation, CV, of Vpp is less than 5%).

The number of SFAP sets studied in each subject is the same(30), as can be seen in any of the rows of Fig. 5. In this figure, SFAPseries of subjects from one to four are depicted in rows from one tofour, respectively. The height of the box that appears above eachSFAP set reflects the variability of PPR within all the potentials thatbelong to that SFAP set. The height of each box corresponds to twotimes the standard deviation SD of the sample, and the horizontalline inside the box indicates the average value of PPR in a SFAP set.

Looking to any of the rows in Fig. 5 we see that the box heightsare in general very large, showing that SFAP PPR suffers significantfluctuations even within consecutive potentials of similar Vpp thatbelong to the same SFAP. A question arises whether any of the IRparameters (Kan, v or r) may account for this high variability inthe PPR. However, it is rather improbable that either the constantof anysotrophy or the propagation velocity could have changed be-tween consecutive discharges of the same SFAP. In addition, nointentional needle movement occurred (the CV of Vpp is less than5% for all the SFAP sets) between discharges. In Section 5.3 of thediscussion we carry out a further investigation on the possible rea-sons that may explain the changes in PPR.

To estimate the average variability in the PPR of SFAP sets with-in a certain subject we use the sample standard deviation, com-puted as the mean value of the SDs of the SFAP sets belonging to

that subject. Specifically, the sample standard deviations of sub-jects from one to four are 0.13, 0.14, 0.15 and 0.14, respectively.Thus, the variability of PPR in the different subjects is very similar,showing that the sources of variation of PPR are statistically verysimilar for all the subjects under study.

4.3. PPR changes with needle movement

In this experiment we study various sets of SFAPs recorded withintentional needle movement from the same muscle fibre. Whenthe needle is moved during the recording process, the values ofthe IAP parameters are not supposed to vary, whereas among theIR parameters theoretically only the value of the radial distanceis changed. Thus, studying SFAP sets recorded with needle move-ment allows us to analyse how PPR varies with radial distance.However, information about the recording distances at which aSFAP is recorded has not proved feasible yet (Van Veen et al.,1993). Since Vpp depends on this distance, then PPR will be studiedas a function of Vpp.

We recorded 23 different sets of SFAPs with intentional needlemovement. For the sake of clarity, however, in Fig. 6 we show thevariation of PPR with Vpp for only 12 sets of SFAPs. When recordingeach SFAP series, the electromyographist moved the needle so thatthe maximum variation of Vpp was obtained. As a result, the varia-tion range of Vpp is different in each SFAP set (see Fig. 6). A largenumber of SFAPs is desirable in each collection. In our case, thesmallest set contained 57 SFAPs, whereas the largest contained 97.

In order to study the dependence of PPR on radial distance, thenormalized coefficients of correlation (q) between PPR and Vpp

were calculated for each set. We divided SFAP sets in three groupsdepending on the magnitude and sign of q: the first group containsSFAP series with strong-negative correlations (q < �0.5), the sec-ond group contains SFAP sets with strong-positive correlations(q > 0.5) and the third group comprises sets with low correlations(|q| 6 0.5). From our 23 SFAP sets, five present q < �0.5 (four ofthem are shown in the first row of Fig. 6), six have q > 0.5 (fourare shown in the second row of Fig. 6), and twelve sets presentlow correlations (four are shown in the third row of Fig. 6). Note

PPR

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

1.0

2.0

0.0

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

1.0

2.0

0.0

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

1.0

2.0

0.0

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

1.0

2.0

0.0

PPR

PPR

PPR

(a)

(b)

(c)

(d)

Subject 1

Subject 2

Subject 3

Subject 4

Series of SFAPs

Fig. 5. Variability in PPR for different sets of SFAPs. Rows from one to four contain SFAP sets corresponding to subjects from one to four, respectively. Thirty SFAP series arestudied for each subject. Each SFAP set comprises consecutive discharges recorded with little variability in Vpp (the coefficient of variation of Vpp for SFAPs within a certain setis less than 5%). The height of the box that appears above each SFAP set measures the variability of PPR between the potentials that belong to that SFAP. The height of each boxcorresponds to two times the standard deviation SD, and the horizontal line inside shows the average value of PPR within each SFAP set.

874 J. Rodriguez et al. / Journal of Electromyography and Kinesiology 20 (2010) 868–878

that in Fig. 6 the correlation value of each SFAP set is shown insidethe PPR–Vpp diagram corresponding to that set.

4.3.1. Significant relationship between PPR and radial distanceAs can be seen, approximately half of the series shows a strong

correlation between PPR and Vpp (|q| P 0.5). This means that PPRand radial distance present a significant relationship only for halfof the SFAP collections. Using the values of q together with thePPR–r curves of Fig. 3 we can obtain information about the IAP pro-files that may have generated some SFAP sets.

In those SFAP sets with a negative q (Fig. 6a–d), PPR has in-creased with radial distance. According to the simulations carriedout in Fig. 2, PPR increases monotonically with radial distance onlywhen A2 = 5.5 and A2b = 4.5 (Fig. 3)b. This means that SFAPs in thefirst row of Fig. 6 are likely to be generated by an IAP with A2b = 4.5,i.e., an IAP with a steep slope in the rising phase [see (Fig. 1)b]. Thehigh PPR values of the SFAPs in Fig. 6a and c support this hypoth-esis as PPR values around 2.0 can only be generated using an IAPwith A2b = 4.5.

For those SFAP sets with a positive q (Fig. 6e–g) we can say thatPPR has decreased with radial distance. According to the simula-tions carried out in Fig. 2, PPR decreases with radial distance forthe combination A2 = 4.5, A2b = 5.5 and only for short radial dis-tances (up to 0.1 mm) [Fig. 3a]. Note the high Vpp values of SFAPsin Fig. 6f and h could only have been generated at very short radialdistances. This means that SFAPs in the second row of Fig. 6 arelikely to be generated by an IAP with A2b = 5.5, i.e., an IAP with aslow slope in the rising phase [see (Fig. 1)b]. The low PPR values

of the SFAPs in Fig. 6e–h support this conclusion as PPR values be-low 1.0 can only be generated using an IAP with A2b = 5.5.

4.3.2. Low correlation between PPR and radial distanceMore than half of the SFAP sets present low correlations be-

tween PPR and Vpp (Fig. 6e,f,j–l). For these series no conclusioncan be obtained about the relationship between PPR and radialdistance. One of the reasons that may explain this lack of correla-tion is the high variability of PPR even within SFAPs of similaramplitudes, as described in the previous section. In fact, lookingto any of the PPR–Vpp diagrams of Fig. 6, we can see that for asmall range of Vpp values in the x-axis a large range of PPR isobtained.

5. Discussion

Several issues arising from the study of the variability of SFAPPPR deserve comment.

5.1. Range of variation of PPR in experimental SFAPs

The IAP description proposed by Rodriguez et al. (2006a) pro-vides an expansion of the PPR range in comparison with the D–Dclassical IAP (Dimitrov and Dimitrova, 1998). Specifically, for radialdistances within the 250 lm radius, the D–D classical model pre-sents a PPR range between 1.0 and 2.0 whereas the range for theD–D model that uses the new IAP description fluctuates between0.7 and 2.0 (Fig. 2).

Vpp (mV)

PPR

PP

RV p p

Vpp (mV) Vpp (mV) Vpp (mV)

PPR

2 2.5 3

1

1.5

2

1 1.5 2 2.5 3 3.5

1.5

2

2.5

0.5 1 1.5 2

0.8

1

1.2

1.4

1.6

0.6 0.8 1 1.2

0.4

0.6

0.8

1

1 1.5 2

0.4

0.6

0.8

1

2 3 4

0.8

0.9

1

1.1

2 3 4 50.5

1

1.5

1 1.5 2

0.8

1

1.2

1.4

1.6

1.8

1 2 3

1

1.5

2

1 1.5 20.6

0.8

1

1.2

1.5 2 2.5 3 3.51.5

2

2.5

3

3.5

1.5 2 2.5 3 3.50.6

0.8

1

(d)(c)(b)(a)

(h)(g)(f)(e)

(l)(k)(j) (i)

ρ = - 0.92 ρ = - 0.76ρ = - 0.77 ρ = - 0.67

ρ = 0.80 ρ = 0.62 ρ = 0.52ρ = 0.58

ρ = - 0.05

ρ = 0.33

ρ = - 0.33

ρ = - 0.17

PPR variation with

Fig. 6. PPR–Vpp diagrams of 12 different sets of SFAPs. PPR–Vpp diagrams in the first row present strong–negative correlations (q < �0.5), PPR–Vpp diagrams in the second rowhave strong–positive correlations (q > 0.5) and diagrams in the third row present low correlations (|q| 6 0.5). The correlation value of each SFAP set is shown inside the PPR–Vpp diagram corresponding to that set. Note that the variation range of Vpp is different in each PPR–Vpp diagram.

J. Rodriguez et al. / Journal of Electromyography and Kinesiology 20 (2010) 868–878 875

5.1.1. Lower bound of PPRNote that, although the overall increment in the PPR range is

not significant (less than 25%), the IAP proposed by Rodriguezet al. (2006a) is able to synthesize SFAPs with V1 larger than V2.This is very important since the fraction of SFAPs with PPRs lessthan 1.0 is considerable (26%, 37%, 66% and 45% in subjects fromone to four, respectively). Thus, PPRs within the range 0.3–2.5should be considered normal since it is very unlikely that all ofthem were recorded near the tendon (even in a muscle with a pen-nate architecture such as the tibialis anterior). With regard topotentials with PPR equal to or less than 0.3, they were rarely re-corded. In addition, they generally have strange features (morethan three phases, very short rise-times, etc.), as shown inFig. 7a. These potentials may have been registered close to the fi-bre-tendon junction [see (Fig. 2)e], although we have no evidenceto prove this.

5.1.2. Upper bound of PPRThe new IAP model does not enlarge the upper bound of the PPR

range (2.0) with respect to the D–D IAP. However, most of theexperimental PPR histograms presented in Fig. 4 clearly exceed thisupper limit. In fact, all histograms contained SFAPs with PPRs with-in 2.0–2.5, showing that these PPR values are not unusual in exper-imental SFAPs. Potentials with very high PPR values (4.0, 5.0 orgreater) were sometimes recorded (Fig. 7b). Due to the smallamplitude and short duration of their first phase, these potentialsare hypothesized to be recorded close to the endplate [see(Fig. 2e)].

5.1.3. Limitations of the modelAs commented in Section 3.6, both the modified and the classi-

cal D–D model can only generate high values of PPR using low val-

ues of Tspl in the IAP. This means that they could not synthesizeSFAPs with high PPRs using IAPs with long repolarizations.

From the studies of Rodriguez et al. (2007) we know that an IAPwill have a long repolarization phase if the distance between thetwo positive phases of its corresponding SFAP is large. In (Fig. 7)cwe show SFAPs with large distances between their positive phasesand with PPRs greater than 2.0. Similarly, we could find moreexamples of experimental SFAPs with high PPR values that mightcorrespond to IAPs with long repolarizations. This suggests thatwe should revise again the modified IAP description proposed inRodriguez et al. (2006a) in order to synthesize high PPR valuesusing IAPs with long repolarizations.

5.2. Variability in experimental IAPs

In Section 4.1, we have seen that all subjects under study con-tain SFAPs with PPRs ranging from 0.3 to 2.5. This variability inPPR clearly exceeds the change in PPR that can be introduced by ra-dial distance (see Fig. 3).

It does not seem likely that the proximity of the recordingelectrode to the neuromuscular and/or fibre-tendon junctionscan be responsible for the entire range of observed PPR values.Therefore, another source of variability (probably in the excitationsource) should exist in order to explain the large fluctuations ob-served in the SFAP PPR. Thus, we should admit certain variabilityin the profile of the IAPs within a muscle in order to fully explainthe large PPR range observed. Specifically, a variety of profiles inthe IAP rising phase could generate the different values of PPRobserved.

More studies (Trayanova and Dimitrov, 1982; Van Veen et al.,1993; Rodriguez et al., 2006a, 2007) have shown the necessity ofconsidering the excitation source as a variable function in order

0.34 0.35 0.36 0.37 0.38-4-202468

x 1 0 - 4

(a)

0.62 0.63 0.64 0.65 0.66 0.67

0

1

2

3x 1 0 - 30.29 0.3 0.31 0.32 0.33

-8-6-4-202

Volta

ge (m

v)Vo

ltage

(mv)

Volta

ge (m

v)

x 0.1

x 0.1

PPR = 0.3

PPR = 4.0

PPR = 2.2

(a)

(b)

(c)

Time (sec.)

Consecutive SFAPs from the same fibre

Fig. 7. Three sets of four consecutive SFAPs recorded from the same muscle fibre. SFAPs in (a), (b) and (c) were extracted from different muscle fibres.

876 J. Rodriguez et al. / Journal of Electromyography and Kinesiology 20 (2010) 868–878

to explain the variations observed in some features of the SFAP.From the experimental recordings of Wallinga et al., 1985 we knowthat IAPs of the same muscle can present important differences. InWallinga et al., 1985, IAPs from two different muscles of a rat wereexamined: the extensor digitorum longus and the right m. soleus.Then, various parameters in the IAP profile were defined and thevariability observed in those parameters was assessed. From thiswork we know that the repolarization behaviour of the fibres with-in a muscle is rather variable. Similarly, the rate of depolarizationwas found to be rather variable too.

5.3. Sources of variation of SFAP PPR

In the experiment presented in Section 4.2 we analysed the var-iability of PPR within several consecutive SFAPs recorded from thesame muscle fibre. Although the amplitudes of these SFAPs werevery similar (the CV of their Vpp was less than 5%) we saw that theirPPRs presented significant variability.

What physiological phenomena could account for thisvariability in the PPR?. It is rather improbable that any of the vol-ume conductor parameters (z0, Kan, v, and r) could have changedsignificantly between consecutive discharges of the same SFAP.First, potentials were recorded within a short period (less than1.5 s.), second, no intentional needle movement occurred (in factVpp changed very little). Besides, according to our simulations,the sensitivity of PPR with Kan and/or v is very small (Fig. 2f andg). Thus, even if we admit certain small fluctuations in the valuesof Kan, v and r they could not have produced such large variabilityin SFAP PPRs. However, the proximity of the recording site to theneuromuscular or fibre-tendon junctions may be a critical factorfor PPR variations. If the electrode is close to the endplate, forexample, slight changes in its axial distance z0 will have a pro-nounced effect on V1 and, therefore, on PPR [see (Fig. 2e)]. Never-theless, the effect of axial distance could only have affected to asmall number of the SFAP sets studied in the present work.

We can think of a number of variables involved in the recordingprocess that may have introduced variation in the PPR: changes in

electrode orientation, changes in tissue conductivity, errors due tothe finite sampling rate of the EMG recording system, baseline fluc-tuation, random noise, etc. The sample frequency used (50 kHz)may be a bit low for the purpose of our study. Indeed, SFAP PPRis very sensitive to changes in the value of V1 and V2 and a largetime step (sampling interval) may introduce variability in theseamplitudes. The fluctuation of the baseline should be also consid-ered. If the SFAP is upshifted, for example, then V1 would decreasewhereas V2 would increase, and this would surely produce anoticeable increment in SFAP PPR (the opposite would occurredif the SFAP is downshifted). After applying the baseline cancella-tion algorithm of Rodriguez et al. (2006b) to our sets of SFAPs weassessed that the sample standard deviations of PPR of subjectsfrom one to four were 0.07, 0.09, 0.10 and 0.08, respectively. Thismeans that the baseline drift can explain in some cases almost50% of the observed PPR variability.

5.4. PPR dependence on the IAP spatial profile

From the studies of some authors (Håkansson, 1957; Nanded-kar and Stålberg, 1983a; Dimitrova and Dimitrov, 2006; Arabadz-hiev et al., 2008) we know that at very short radial distances theIAP spatial profile essentially determines the features of the SFAPmain spike. In fact, SFAP rise-time has found to be relatively inde-pendent of the fibre–electrode distance at distances very close tothe fibre.

On the basis of the simulations studies reported here, it can beconcluded that both the SFAP PPR and its variation with radial dis-tance are highly dependent on the IAP rising phase. The relation-ship between PPR and radial distance observed experimentallygives contradictory results: in some SFAP sets there is a strong-po-sitive correlation between PPR and r, in other SFAP sets the corre-lation PPR–r is strong but negative, and in the rest the correlation isnot significant. However, since the tibialis anterior muscle has apennate architecture with an extensive central aponeurosis andwidely distributed endplates (Aquilonius et al., 1984; Wolf andKim, 1997), some of the needle movements recorded for the pres-

J. Rodriguez et al. / Journal of Electromyography and Kinesiology 20 (2010) 868–878 877

ent study may be affected by the proximity to the neuromuscularand/or fibre-tendon junctions. As a result, we should be very cau-tions when using the PPR–Vpp diagrams of Fig. 6 to obtain informa-tion about the IAP rising phase.

Neuromuscular diseases affect intracellular and extracellularpotentials. Some studies have shown that abnormal calcium accu-mulation in muscle fibres, typical in mitochondrial myopathy andmuscular dystrophy (Bertorini et al., 1982, 1991), could lead tochanges in propagation velocity and IAP shape (Ishiko and Sato,1957; Howell and Snowdowne, 1981). Ludin, 1973 found thatthe duration of the IAP rising phase was increased to 0.38 ms indystrophic human muscle fibres compared to 0.26 ms in normalones. It has to be examined to what extent these changes in theduration of the IAP rising phase are followed by changes in thePPR of the corresponding SFAP. The PPR statistics of non–diseasedmuscles reported in the present work could be used as a refer-ence to compare measurements of PPR from dystrophic musclefibres.

6. Conclusions

1. According to our experimental data, SFAP PPR ranges from 0.3to 2.5 in healthy subjects. PPR histograms contain a well-defined single peak around the PPR value 1.0.

2. In order to fully explain the large PPR observed in experimentalSFAPs we should admit larger variability in the IAP waveformswithin a muscle.

3. SFAP PPR presents a high variability even within consecutivepotentials of similar Vpp recorded from the same muscle fibre.A reduction in the baseline fluctuation and increment of thesample frequency should decrease this variability considerably.

4. According to our simulations, the SFAP peak-to-peak ratio (PPR)is a parameter very sensitive to changes in rising (depolariza-tion) phase of the IAP.

5. The modified D–D model generates PPRs that covers only therange 0.7–2.0. Besides, in the modified D–D model high valuesof PPR can be generated only by using IAPs with shortrepolarizations.

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Javier Rodríguez Falces was born in Pamplona in 1979.He graduated in 2003, and obtained the PhD in 2007 inTelecommunication Engineering from the PublicUniversity of Navarra, Pamplona, Spain. He is currentlyAssistant Professor of the Electrical and ElectronicsEngineering Department of this University. His researchfocuses on signal processing applied to biomedicalsignals, modeling of biological systems and electro-myography.

Armando Malanda Trigueros was born in Madrid,

Spain, in 1967. In 1992 he graduated in Telecommuni-cation Engineering at the Madrid Polytechnic Univer-sity. In 1999 he received his Ph.D. degree from theCarlos III University, Madrid. In 1992 he joined theSchool of Telecommunication and Industrial Engineer-ing of the Public University of Navarra. In 2003 hebecame Associate Professor in the Electrical and Elec-tronics Engineering Department of this University.During all this period he has been teaching severalsubjects related to digital signal processing, imageprocessing and biomedical engineering. His areas ofinterest comprise the analysis, modeling and simulationof bioelectrical signals, particularly EEG and EMG.

grap

Luis Gila Useros received his MD degree from theComplutense University, Madrid, Spain in 1983. In 1988

he completed his specialization in Neurology at the‘‘Ramón y Cajal” Hospital, Madrid. Between 1989 and1998 he worked as a neurologist at the ‘‘San Millán”Hospital, Logroño, Spain. From 1998 to 2001 he carriedout his specialization training in Clinical Neurophysi-ology at the ‘‘Virgen del Camino” Hospital, Pamplona,Spain, where at the present time he is a staff member atthe Department of Clinical Neurophysiology. Hisresearch interests include quantitative electromyogra-phy and the automatic analysis of electromyographicsignals.

878 J. Rodriguez et al. / Journal of Electromyo

Ignacio Rodriguez Carreño was born in Madrid in1976. In 2000 he obtained his degree in Telecommuni-cation Engineering from the Public University of Nava-rre, Pamplona, Spain. In 2001 he worked as an engineerin the development of software and hardware forcommunications systems. In 2002 he joined the PublicUniversity of Navarre as Assistant Professor of theDepartment of Electrical and Electronics Engineeringand he started his doctoral courses. Since 2003 he hasbeen granted a research fellowship by the NavarraGovernment to complete his Ph.D. His area of researchis the development of software and algorithmic meth-ods for the processing of EMG signals.

Javier Navallas Irujo was born in Pamplona in 1976. Hegraduated in 2002, and he obtained the PhD in 2008 in

Telecommunication Engineering from the Public Uni-versity of Navarra, Pamplona, Spain. He has also workedas a software engineer. He is presently Assistant Pro-fessor of the Electrical and Electronics EngineeringDepartment of this University. His research interests aremodeling of biological systems and neurosciences.

hy and Kinesiology 20 (2010) 868–878