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Mechanical parameters of human hair: possible application in the diagnosis and follow-up of hair disorders
This content has been downloaded from IOPscience. Please scroll down to see the full text. 1992 Clin. Phys. Physiol. Meas. 13 281 (http://iopscience.iop.org/0143-0815/13/3/008) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 137.30.242.61 This content was downloaded on 27/05/2014 at 15:06
Please note that terms and conditions apply.
Clin. Phys. Physiol. Meas., 1992, Vol. 13, No. 3,281-290. Pnntedin the UK
Mechanical parameters of human hair: possible application in the diagnosis and follow-up of hair disorders G Nikiforidist, C B a h t and D Tsambaos$ Departments of tMedical Physics and $Dermatology, University of Parras, 26 I 1 0 Parras, Greece Received 22 March 1991, in final form 4 November 1991 Abstract. Mechanical analysis of human hair may provide the dermatologists with several markers of considerable diagnostic importance. In the present paper, using a new computerised expenmental system, attemps were made firstly to interpret the curves of the elastic and viscous components of the mechanical behavior of human hair and secondly to determine characteristic paramerers which correlate well with its svucrural features. In order to overcome methoddo@cd problems due to the inhomogeneous structure of human hair, mechanical parameters were defined which either depend on the cortical microstructure or correlate well with the size of hair medulla.
1. Introduction
The quantitative determination of the mechanical parameters of human hair may provide the dermatologists with some useful markers for the diagnosis of hair disorders (Tronnier and Huske 1958, Swanbeck et al 1970) and for the evaluation of their response to therapeutic and cosmetic regimens. Such an approach would require an improved methodology which will reduce the dispersion of the values of the parameters, which should also correlate well with the structural features of the hair specimens. T h e reliable application of such methodology in the diagnosis of hair disorders necessitates the solution of problems connected with the following properties of human hair : (1) The viscoelastic behavior which, simultaneously, shows time and strain dependence in the course of the finite duration of the experimental determination of the stress-strain curve (Wainwright et a2 1976, Fung 1981). (2) The inhomogeneous structure which is characterised by three major compartments: the medulla, the cortex and the cuticle (Roth 1967). (3) The biphasic nature of hair cortex (Rudall 1964) during the extension of which a-keratin is transformed into P-keratin and the matrix undergoes a transition from a ‘gel’ to a ‘sol’ state (Danilatos and Feughelman 1980). The main purpose of the present paper is to interpret the time independent and time dependent components of the mechanical behaviour of human hair and to indentify characteristic parameters related to its structural features. In order to overcome problems due to the inhomogeneous structure of human hair, two types of mechanical parameters have been defined: those which are almost exclusively dependent on the cortical microstructure (Balas et a1 1989) and those which correlate well with the diameter of the hair specimens and therefore with the size of the medulla (Nikiforidis et al 1991). 0143-08151921030281 + 10 $02.50
0 1992 Institute of Physical Sciences in Medicine
281
G Nikiforidis et a1
282 2. M a t e r i a l s and methods
The mechanical parameters of the hair specimen are determined through the study of its stress- strain curve during longitudinal stretching. T h e stress generated in human hair during longitudinal stretching depends on the history of the applied strain (Jamison et a2 1968, Aklonis et a1 1972, Sanjeevi 1982). Thus, the stress response o(&,t)is a function of two variables, the strain E and the time t. The separate analysis of the time and strain dependence of a(&,t)requires a general formulation including the non-linear stress-strain characteristics. An alternative approach, t h e analytical basis of which is described in a recent publication (Nikiforidis et al 1992), may be provided by the sectional linearisation of the non-linear viscoelastic behaviour of hair. Experimentally the sectional linearisation can be performed by means of a continuous succession of steps (figure l), each of which O.* 0.7
t
V
io
20
Strain
30
40
Figure 1. Srepwjse stretching of hair for the experimcnral sectional linearisation of its viscoelastic behaviour.
consists of a phase characterised by an almost instantaneous strain (0.1 s ) with an increase of the initial length by 1% followed by a relatively long relaxation phase (5.0 s ) Characterised by a simple exponential function
Gi(t)=A,exp(-kit) where i corresponds to the order of the successive steps, because the material can be assumed to be linearly viscoelastic for such steps (Tao and Postle 1989 ). Since during the almost instantaneous strain practically no relaxation occurs, T(E) can be estimated (figure 2) ignoring the relaxation phases and connecting all phases of instantaneous strain. Schematically, thio procedure cnrresponds to the parallel shift ofphases of instantaneous strains and it compensates for the falls due to the relaxation of the respective steps. The time-dependent component K(&,t) can be obtained by connecting the successive relaxations that occur during the steps and represents the total relaxation of hair (figure 2). 2.1. Experimental procedure
Forty male human subjects divided in two age groups (3 -4Oy,
N = 30 and 60- 70y,
N = 10) were included in the study. The subjects had no history or evidence of any cutaneous or systemic disorders affecting the scalp. Hair specimens were obtained from the occipital region of each subject using forceps. Subsequent to a light microscopic examination of hair roots, only anagen hair specimens (N=5) from each
.r
Mechanical parameters of human hair
283
w,
&f)
cr a
0
20
30
40
Strain (%)
??
6
-1
-
K(s.9 Figure 2. Estimated curves ofthe stress response -2 O(E,C)and its elastic T(E) and viscous component K(w) during stepwise stretching of a hair specimen of finire duration.
subject were considered. This was done in order to avoid a possible influence of the hair cycle phases on the mechanical response of the hair specimens (Fisher and Hyatt 1984). The specimens (1.5cm in length) were cut 0.5cm above the scalp surface where the variability of the hair cross-sectional surface is negligible (Sims 1967). The estimation of the cross-section of the hair specimens was performed by means of an image analysis system (Ml, Imaging Research Incorporation). In order to perform the separate analysis of the T(E)and K(E,z) we designed a computerised experimental system which performs with high accuracy experiments on extension, creep, relaxation and the special step-wise procedure required for the sectional linearisation of I S ( E , ~ )The . main components of the apparatus are shown in figure 3 .
computer Figure 3. Computerised experimental system applied in rhe analysis and quantitative determination of the viscoelastic parameters of human hair.
G Nikiforidis et a1
284
The central processor unit is built on two microprocessors 2-80 which are responsible for the management of the whole system. T h e programming of the measurement is performed through a series of selections (settings) while the type and the parameters of the experiment are defmed by a sequence of questions and answers between system and user. The user can define the type of loading, the sampling rate, the force and force rate, the strain and strain rate etc. The experimental data can be visualised on the screen of the device or be sent to the host computer for further elaboration. The host computer is a portable IBM compatible PC and the hardware requirements are RAM 5 12 K.The software package needs only DOS.3.2 or higher, the program is wtitten in turbo C and is organised in four sub-directories. T h e following operations can be executed through a system user interactive mode by displaying the available menu and indroducing the input request by mouse or keyboard: (1) Data collection and transfer to the hard disc. (2) Curve graphics: stress - time, force - time, stress - strain, strain - time. (3) Determination of T(E) and K(&,t)and parametric analysis. (4) Zoom on specific regions of the curves with corresponding enhancement of the analysis Several technical limitations had to be overcome in order to achieve an accurate standardisation of the measurements. T h e crimp of the hair specimen, which could cause a falsely sigmoidal stress-strain curve (Skelton 1967) was partially avoided by an aurom.a.ric estimation of the initial hair len-gh. Furthermore. since the mechanical behaviour of human hair depends strongly on the temperature and humidity (Wainwright et a1 1976), the measurements wcre performed under standard temperature (22OC) and humidity (45%). 2.2. Interpretation of the elasric T(E) and viscous K(E, t) components - identification of diaguostiially sigizzzificanr paranzetcrs
The experimental results show that T(&) is not linear in the pre-yield region. This can be seen in figure 4 and is primarily due to the initial crimping of the specimen and therefore to the inaccurate evaluation ofits initial length (Bendit 1978). Thus, the first sigmoidal part of the experimental curve T(E), particularly in the case of small specimens, has to be corrected in order to become linear; the maximal slope of the uncorrected curve in the pre-yield region represents the v u e slope of the latter (figure 4). For corrected strains with E ranging between E, = 0 and E= the resistance of 0.7
1
Figure 4. Effects of crimping on the initial pan of T(E);the intersection of t h e corrected pre-yield region (- - -) with the strain axis determines the true initial length of the hair specimen.
Mechanical parameters of human hair
285
the hair specimens to the applied strain remains constant and is represented by the modulus of elasticity (E,). T h e following characteristic and diagnostically important parameters of specimens can be drawn from the pre-yield region: The modulus of elasticity (E,), representing the slope of the stress-strain curve in the region of linearity where the stresslstrain ratio remains constant. The limit oflinearity (TL),corresponding to the stress beyond which the behaviour of the specimen is not linear. The swain energy (SE), representing the energy stored during the extension of the specimen in the pre-yield region (Fung 1981). The yield region begins for strains higher than E= and in the plot of T(E)in figure 2, two mechanisms related to the transformation of the cortical a-keratin into pkeratin are depicted (Wainwright et al 1976, Danilatos and Feughelman 1985). Indeed, during the transformation of a n individual fibre of a-keratin into !.-keratin (pleated sheets) its resistance to extension rapidly decreases. After the completion of this transformation, which corresponds to a given degree ofextension, the individual fibre becomes harder and reveals a higher modulus of elasticity (eP) as compared to (e,). Both mechanisms are observed in the yield region of T(E)as evidenced by the initial fall and the subsequent rise of its slope. If all individual fibres could be simultaneously transformed in response to the same degree of extension the detailed analysis of T ( E )would have been easy. However, the transformation of different akeratin fibres occurs in response to different values of extension; therefore T(E) expresses the characteristic features of the individual fibres convoluted with a modulation function. This modulation function is associated with the rate of numerical increase of P-keratin and the decrease of a-keratin fibres in relation to the change of extension. It can be suggested t h a t for E S Ethe ~ numbers of a- and P-keratin fibres are Nu, and No,, respectively for,
N
a0
+ N -N Po
(2)
-
where N is the total number of cortical fibres of the hair specimen. In the yield region (&>E& the a-keratin fibres start to undergo transformation into 0-keratin. T h e postyield region of T ( E )begins beyond a given value of extension (E& in which N P ( ~ p ) > N a ( In ~ pthis ) . region the mechanical behaviour of hair is dominated by the properties of p-keratin. Given that e, and e represent the modulus of elasticity of the individual a- and !.-keratin fibre respective y, then for the slope in the pre-yield region (modulus of elasticity E,) it follows that
P
(3) + NPo eP At the highest part of the post-yield region, just before the fracture of the specimen, almost all fibres have been transformed into to !.-keratin fibres. For the slope EP,of T(E),in this region
E",
U,,ea
ED= ( N , + N o )eo
(4)
Combining the relations ( 3 ) and (4) we have N u eu . .
It is obvious that Ea/EP primarily depends on the proportion of P-keratin in the unstretched specimen.
G Nikiforidis et al
286
The stress of viscous origin which is generated in the hair specimen during longitudinal stretching, depends on the viscocity coefficient and the strain rate (Park 1980), e.g. K(&,t)= -n(&)d&/dt.It is therefore obvious that the standardisation of the strain rate (dddt) is necessary, but not sufficient, for the successful application of K(&,f)in the diagnosis of hair disorders. A parameter of diagnostic importance can be drawn from the relation of the integral of K(&,t)to the integral of T(&)for a given extension. This parameter, which can be standardised, is related to the microstructure of the hair specimens and is given by the ratio 30%
LK(&,t)d&-
_-
where
Jo3?(&)d&
du
ssmr
represents the energy stored in the specimen during its 30% extension; and
is the dissipated energy which was induced by the viscous flow during the 30% CxtexiGE of *.e hnir sprcimrc. The viscous phenomena of human hair and therefore the above mentioned parameter, are primarily associated with the keratin matrix. Indeed, according to dynamic measurements (Danilatos and Feughelman 1985), the main part of the viscous loss within a hair specimen, as expressed by the dynamic loss modulus, is associated with the matrix. This is a structural water penetrable component with relatively few disulphide cross-links and a greater proportion of hydrogen bonds (Sikorski and Woods 1960). During extension the hydrogen bonds break down and reformation proceeds continuously, characterising the viscous behaviour of the matrix. On the contrary, in the microfibrils there is a preponderance of intermolecular S-S linkages, which would restrain the viscous flow (Curiskis and Feugelman 1985).
2.3. Evaluation of the diagnostic importance of the mechanicalparemeters of human hair in relation to in inhomogeneous structure. The diagnostic value of the parameters identified through the proposed methodology is limited because of the lack of homogeneity of hair, since for diagnosis of hair disorders it is important to know whether the change of the mechanical parameters is due to variations of the medullary cross-sectional surface area or to alterations in the cortical microstructure. A proper selection and application of our parameters may in part offset the above limitation. Thus: (1) E,/Ep and SdiJSstor ratios are not affected by the inhomogeneous structure of human hair and are closely related to the structural features of the hair cortex being, therefore, of specific diagnostic importance. A marked deviation of EJEP values from the normal range may be associated with an abnormal transformation of a-keratin into P-keratin. (2) T h e modulus of elasticity (Ea), the strain energy (SE) in the pre-yield region and the slope of T(E)in the post-yield region depend o n both the microstructural
287
Mechanical parameters of human hair
features of hair cortex and the relative size of the medulla. Indeed, it is known from previous investigations (Nikiforidis et al 1991) that the relative size of the medulla increases with the increase of the cross sectional surface area of hair shaft. Therefore it appears reasonable that the parameters E,, EDand SE of the hair of a given subject must be analysed with reference to normal hair wlth the same outer cross-sectional surface area 3. Results
The comparative evaluation of the mean values of E,IEp and SdisiS,,,,ratios in 150 and 50 hair specimens derived from 30 young and 10 elderly subjects respectively (table 1) reveals a statistically significant decrease (PC0.05) of EJE ratio in the hair specimens of the aged group, as compared with the young. E a h D and SE were evaluated comparatively in 40 hair specimens from the young group matched for hair shaft diameter with 40 specimens from the elderly subjects. T h e results of this paired evaluation (table 2) reveal a statistically significant decrease of E, and E p in the specimens of the aged subjects, as compared with the young ones. The regression lines of E, against D and EDagainst D ( D = outer diameter of the hair specimen) for the paired samples are diagrammatically shown in figures 5 and 6. Table 1. Comparative evaluation ofEalEpand SdiJS3,0r in hair specimens derived fiom elderly and young subjects.
EdEp
sddsno?
Elderly
Young
Elderly
Young
Mea" Srd deviation
0.87
0.92
80.90x10~2
0.10
0.10
1. 1 3 X 1 0 ~ 2
Observations
50
150
50
150
-3.04
0.375
Hwotbesis
198
H, : B, = B2
0.71
Ha:B , # B,
Degrees of freedom
198
Hwotbesis H 0 : B , = B,
Significance (p)
0.02
H,:B,#B,
T-statistic
80.76X10-2 1.67X10~2
Table 2. Paired evaluation of E,, Epand strain energy in hair specimens derived from elderly and young subjects. ~~
EJGPa) Elderly Young
~~
Ep(GPa)
Elderly
Young
3.94
4.77
Mean Paired observations
3.43
T-statistic
-3.38
Hwothesis
-2.1 I
Hwathesis
0.27
39
H,:B, =Ez H, : B, # Bz
39
H,:B, =B, H a : B, # B,
39
Degrees of freedom
Significance (p)
4.46
0.002
713.00
40
40
0.043
~~
Susin energy (@a) Elderly Young 688.30 40
0.786
Hwothesis H,:B, =E2 H a : BI = B,
4. Discussion
Previous studies on the mechanical behaviour of human hair were mostly phenomenological. Usually only the c(&,t) curve was evaluated and the resulting parameters had no clear mechanical significance. Indeed, because of the compensation of two mechanisms with opposite curvatures (the first associated with the viscous phenomena and the second with the crimping) o(&,t) reveals an almost
. .
. .
f SI
2t
I 20
0
60 80 Diameter, D (pn)
Variable CoefficientSld error a
7.07 -0.04
b
100
40
t
p
1.06 6.64 0.000 0.02 -2.51 0.016
,
0
.
:
20
. 40
60
a b
100
80
Diameter, D (Wm) Variable Coefficient Sld error
p
t
0.83 6.46 o.Oo0 0.01 -2.37 0.023
5.34 -0.03
Figure 5. Regression lines E, = a + bD of modulus of elasticity (E,) plotted against the diameter (D)in hair specimens of young (a) and elderly (b) subjects.
10
I
:
io
U
40
60
Variable Coefficient Std omor
a' b
io0
60
Diameter. D (pm) 8.98 -0.06
f
p
L , , : ,/ 20
0
:
:
,
40 $3 Diameter, D ()"
,
Variable Coefficient Std error
1.32
6.79 0.000
a'
0.02
-3.02 0.004
b
6.40 -0.04
0.82 0.01
:
eo t
:1 : p
7.85 0.000 -3.18 0.003
Figure 6. Regression lines Ep = a' + b'D of the slope of T(E)in the post-yield region plotted against the diameter (Dl in hair specimens ofyoung (a) and elderly (6) subjects.
linear region with a slope that has been falsely regarded as the modulus of elasticity (Bendit 1978). In the present paper attempts were made firstly to provide specific diagnostic data by evaluating the mechanical parameters of hair specimens through a stepwise isolation of different factors implicated in their mechanical response; and secondly to improve the diagnostic specificity of the methodological approach through a combination of information given separately by all mechanical parameters studied. The methodology described here is applied in the study of the effects of the aging processes on the mechanical parameters of human hair. Their comparative evaluation in hair specimens derived from young and elderly subjects revealed statistically significant differences betwen these groups with regard to E,, Ep and E,/Ep, The values of E, and E,, are significantly higher in the individual specimens of the young group, as compared with the aged subjects. Comparing the slopes of the regression lines of E, against D and Ep against D it can be suggested that the differences found between the two groups with regard to E, and Ep,may be due to the fact that in the young subjects the size of medulla increases with the increase of the hair shaft diameter more rapidly than that of the elderly group. This is substantiated by image analysis of the cross-section of the specimens (paper in preparation). On the other hand, the unpaired evaluation of the mechanical parameters of hair in these groups reveals a statistically significant difference with regard to E,/E,,, Since
Mechanical parameters of human hair
289
EaEP does not depend on the size of medulla, it seems likely that hair aging is associated with an impaired transition process of a-keratin into P-keratin during stretching. This alteration may be primarily related to the reduced proportion of pkeratin in hair specimens of the elderly subjects in the pre-yield region. No statistically significant differences could be found between the two groups with regard to the strain energy, because the aged hair specimens reveal a smaller resistance to strain but a greater limit of linearity, as compared with the young ones. Furthermore, since no statistically significant difference was detected between the two groups with regard to SdiJS,,,, it may be concluded that the viscosity of the matrix remains practically unaffected by the aging processes. In conclusion, the method applied in this study enables us to detect the influence of a hair disorder on the mechanical parameters of hair and may implicitly provide indication for the occurrence of alterations in the structure of hair matrix, on the transformation process of a-keratin into P-keratin and on the orientation of the microfibrils with regard to the longitudinal axis of the hair (Krenchel 1964).
References Aklonis J J, Macknight W J and She“ M 1972 Innoducrlon t u Polymer Viscoelartt2iW (New York Wiley Interscience) Balas C, Nikifotidis G and Tsambaos D 1989 Determination of the mechanical pammeten of hair cortex Roc. V Mediteranenn Conference ott Medical and Bioloe’colErzgineminp, Pamar pp 72-3 Bendit E G 1978 Properties of the matrix in keratins. Pan I 1 The “Hookem” region in the stress-strain cume of keratins Text. Res. 3. 48 712- 22 Curiskis J I and Feughelman M 1985 A micromechanics analysis of the mechanical behavior of the akeratin composite a t low strains. Part I: Theoretical formulation Text. Res. J. 5 5 425- 44 relationships in the mechanical properties of Danilatos G and Feughelman M 1980 The microfibril-“% the matrix during the extension of or-keratin fiber Text. Res. 3, 50 568- 74 Fisher K H and Hyatt A L 1984 The anatomy of the skrn and phySiohgy of hair growth The Cause and Managemenr of Hirsutism eds R B Grecnblatt, V B Mahesh and R Don Gambrel1R (Lancaster and New Jersey: Parthenon Publishing Group) pp 175-97 Fung Y C 1981 Bio-viscoelastic solids Biomechanics - Mechanicalhpenies ofLiving Tissues ed Y C Fung (Berlin: Springer-verlag) pp 186-260 Jamison C E, Marangoni R D and Glaser A A I968 Viscoelastic properties of soft tissmes by discrete model charactetization?. Biomsch. I 33-46 Krenchel H 1964 Fiber Reinforcement (Stockholm: Akademisk Vorlag) pp 151-2 Nikiforidis G, Balas C, Tsambaos D, 1992 Viscoelastic response of human hair conex Med. Bid. Eng. Compur. (in press). Nikifondis G, Tsambaos D, Balas C, Bezerianos A and Sampalis F 1991 Mechanical properties of human hair in relation to its gross morphological and microstructural features Demotology in Europe ed E Panconesi (Oxford Blackwell) pp 832-6 Park J B 1980 Biomatmals. A n Introduction (New York: Plenum Press) Rath S 1967 Hair and nail Ulnosrmcture o f N o m a l ond Abno-ol Skin ed A S Zelickson (Philadel~hia:Lea and Fehiger) R u d d K 1964 The biomolecular structure of hair keratin Roaresr in the Biolorical Sciences in Relotion CO Dermatology Vo1.2 eds A Rook and R H Champion (Landon: Cambridge University Press) p 355 S a n j c e ~R 1982 A viscoelastic model for the mechanical properties of biological materialsJ. Biomech. 15 107-9 Sikorski J and Woods H J 1960 X-ray and electron microscope studies of the staining of keratin by silver 3. Texr. Inrt. SI 506-22 Sims RT 1967 “Beaus” lines in hair. Reduction of hair shaft diameter associated with illness Br. 3. Demotol. 79 43-9 Skelton J 1967 The effects of planar crimp in the measurement of the mechanical properties of fiben, flaments and yams3. T~xI. Inst. 58 533-66
290
G Nikiforidis et a1
Swanbeck G, Nyren J and Juhlin L 1970 Mechanical properties of hair from patients with different types of hair diseases3. Invest. Dematol. 54 248-51 Tao X and Postle R 1989 A viscoelastic analysis of the keratin composite. Pan I: Longirudinal and trsnwerse mechanics! properties Text.Res. 3, 59 123-38 Tronnier H and Huske G 1958 Methodische Untersuchungen zur registrierbaren Schnellpnrfung keratolydscher und keratinfestigender Stoffe Pa&m. Kormet. 39 507-10 Wainwright S A, Bigges W D, Currey J D and Gosllne J M 1976 Fracture of viscoelastic materials MechanicnlDesign in Organisms ed H Wainwright a al (London: Edward Amold) pp 39-41
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My IOPscience
Mechanical parameters of human hair: possible application in the diagnosis and follow-up of hair disorders
This content has been downloaded from IOPscience. Please scroll down to see the full text. 1992 Clin. Phys. Physiol. Meas. 13 281 (http://iopscience.iop.org/0143-0815/13/3/008) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 137.30.242.61 This content was downloaded on 27/05/2014 at 15:06
Please note that terms and conditions apply.
Clin. Phys. Physiol. Meas., 1992, Vol. 13, No. 3,281-290. Pnntedin the UK
Mechanical parameters of human hair: possible application in the diagnosis and follow-up of hair disorders G Nikiforidist, C B a h t and D Tsambaos$ Departments of tMedical Physics and $Dermatology, University of Parras, 26 I 1 0 Parras, Greece Received 22 March 1991, in final form 4 November 1991 Abstract. Mechanical analysis of human hair may provide the dermatologists with several markers of considerable diagnostic importance. In the present paper, using a new computerised expenmental system, attemps were made firstly to interpret the curves of the elastic and viscous components of the mechanical behavior of human hair and secondly to determine characteristic paramerers which correlate well with its svucrural features. In order to overcome methoddo@cd problems due to the inhomogeneous structure of human hair, mechanical parameters were defined which either depend on the cortical microstructure or correlate well with the size of hair medulla.
1. Introduction
The quantitative determination of the mechanical parameters of human hair may provide the dermatologists with some useful markers for the diagnosis of hair disorders (Tronnier and Huske 1958, Swanbeck et al 1970) and for the evaluation of their response to therapeutic and cosmetic regimens. Such an approach would require an improved methodology which will reduce the dispersion of the values of the parameters, which should also correlate well with the structural features of the hair specimens. T h e reliable application of such methodology in the diagnosis of hair disorders necessitates the solution of problems connected with the following properties of human hair : (1) The viscoelastic behavior which, simultaneously, shows time and strain dependence in the course of the finite duration of the experimental determination of the stress-strain curve (Wainwright et a2 1976, Fung 1981). (2) The inhomogeneous structure which is characterised by three major compartments: the medulla, the cortex and the cuticle (Roth 1967). (3) The biphasic nature of hair cortex (Rudall 1964) during the extension of which a-keratin is transformed into P-keratin and the matrix undergoes a transition from a ‘gel’ to a ‘sol’ state (Danilatos and Feughelman 1980). The main purpose of the present paper is to interpret the time independent and time dependent components of the mechanical behaviour of human hair and to indentify characteristic parameters related to its structural features. In order to overcome problems due to the inhomogeneous structure of human hair, two types of mechanical parameters have been defined: those which are almost exclusively dependent on the cortical microstructure (Balas et a1 1989) and those which correlate well with the diameter of the hair specimens and therefore with the size of the medulla (Nikiforidis et al 1991). 0143-08151921030281 + 10 $02.50
0 1992 Institute of Physical Sciences in Medicine
281
G Nikiforidis et a1
282 2. M a t e r i a l s and methods
The mechanical parameters of the hair specimen are determined through the study of its stress- strain curve during longitudinal stretching. T h e stress generated in human hair during longitudinal stretching depends on the history of the applied strain (Jamison et a2 1968, Aklonis et a1 1972, Sanjeevi 1982). Thus, the stress response o(&,t)is a function of two variables, the strain E and the time t. The separate analysis of the time and strain dependence of a(&,t)requires a general formulation including the non-linear stress-strain characteristics. An alternative approach, t h e analytical basis of which is described in a recent publication (Nikiforidis et al 1992), may be provided by the sectional linearisation of the non-linear viscoelastic behaviour of hair. Experimentally the sectional linearisation can be performed by means of a continuous succession of steps (figure l), each of which O.* 0.7
t
V
io
20
Strain
30
40
Figure 1. Srepwjse stretching of hair for the experimcnral sectional linearisation of its viscoelastic behaviour.
consists of a phase characterised by an almost instantaneous strain (0.1 s ) with an increase of the initial length by 1% followed by a relatively long relaxation phase (5.0 s ) Characterised by a simple exponential function
Gi(t)=A,exp(-kit) where i corresponds to the order of the successive steps, because the material can be assumed to be linearly viscoelastic for such steps (Tao and Postle 1989 ). Since during the almost instantaneous strain practically no relaxation occurs, T(E) can be estimated (figure 2) ignoring the relaxation phases and connecting all phases of instantaneous strain. Schematically, thio procedure cnrresponds to the parallel shift ofphases of instantaneous strains and it compensates for the falls due to the relaxation of the respective steps. The time-dependent component K(&,t) can be obtained by connecting the successive relaxations that occur during the steps and represents the total relaxation of hair (figure 2). 2.1. Experimental procedure
Forty male human subjects divided in two age groups (3 -4Oy,
N = 30 and 60- 70y,
N = 10) were included in the study. The subjects had no history or evidence of any cutaneous or systemic disorders affecting the scalp. Hair specimens were obtained from the occipital region of each subject using forceps. Subsequent to a light microscopic examination of hair roots, only anagen hair specimens (N=5) from each
.r
Mechanical parameters of human hair
283
w,
&f)
cr a
0
20
30
40
Strain (%)
??
6
-1
-
K(s.9 Figure 2. Estimated curves ofthe stress response -2 O(E,C)and its elastic T(E) and viscous component K(w) during stepwise stretching of a hair specimen of finire duration.
subject were considered. This was done in order to avoid a possible influence of the hair cycle phases on the mechanical response of the hair specimens (Fisher and Hyatt 1984). The specimens (1.5cm in length) were cut 0.5cm above the scalp surface where the variability of the hair cross-sectional surface is negligible (Sims 1967). The estimation of the cross-section of the hair specimens was performed by means of an image analysis system (Ml, Imaging Research Incorporation). In order to perform the separate analysis of the T(E)and K(E,z) we designed a computerised experimental system which performs with high accuracy experiments on extension, creep, relaxation and the special step-wise procedure required for the sectional linearisation of I S ( E , ~ )The . main components of the apparatus are shown in figure 3 .
computer Figure 3. Computerised experimental system applied in rhe analysis and quantitative determination of the viscoelastic parameters of human hair.
G Nikiforidis et a1
284
The central processor unit is built on two microprocessors 2-80 which are responsible for the management of the whole system. T h e programming of the measurement is performed through a series of selections (settings) while the type and the parameters of the experiment are defmed by a sequence of questions and answers between system and user. The user can define the type of loading, the sampling rate, the force and force rate, the strain and strain rate etc. The experimental data can be visualised on the screen of the device or be sent to the host computer for further elaboration. The host computer is a portable IBM compatible PC and the hardware requirements are RAM 5 12 K.The software package needs only DOS.3.2 or higher, the program is wtitten in turbo C and is organised in four sub-directories. T h e following operations can be executed through a system user interactive mode by displaying the available menu and indroducing the input request by mouse or keyboard: (1) Data collection and transfer to the hard disc. (2) Curve graphics: stress - time, force - time, stress - strain, strain - time. (3) Determination of T(E) and K(&,t)and parametric analysis. (4) Zoom on specific regions of the curves with corresponding enhancement of the analysis Several technical limitations had to be overcome in order to achieve an accurate standardisation of the measurements. T h e crimp of the hair specimen, which could cause a falsely sigmoidal stress-strain curve (Skelton 1967) was partially avoided by an aurom.a.ric estimation of the initial hair len-gh. Furthermore. since the mechanical behaviour of human hair depends strongly on the temperature and humidity (Wainwright et a1 1976), the measurements wcre performed under standard temperature (22OC) and humidity (45%). 2.2. Interpretation of the elasric T(E) and viscous K(E, t) components - identification of diaguostiially sigizzzificanr paranzetcrs
The experimental results show that T(&) is not linear in the pre-yield region. This can be seen in figure 4 and is primarily due to the initial crimping of the specimen and therefore to the inaccurate evaluation ofits initial length (Bendit 1978). Thus, the first sigmoidal part of the experimental curve T(E), particularly in the case of small specimens, has to be corrected in order to become linear; the maximal slope of the uncorrected curve in the pre-yield region represents the v u e slope of the latter (figure 4). For corrected strains with E ranging between E, = 0 and E= the resistance of 0.7
1
Figure 4. Effects of crimping on the initial pan of T(E);the intersection of t h e corrected pre-yield region (- - -) with the strain axis determines the true initial length of the hair specimen.
Mechanical parameters of human hair
285
the hair specimens to the applied strain remains constant and is represented by the modulus of elasticity (E,). T h e following characteristic and diagnostically important parameters of specimens can be drawn from the pre-yield region: The modulus of elasticity (E,), representing the slope of the stress-strain curve in the region of linearity where the stresslstrain ratio remains constant. The limit oflinearity (TL),corresponding to the stress beyond which the behaviour of the specimen is not linear. The swain energy (SE), representing the energy stored during the extension of the specimen in the pre-yield region (Fung 1981). The yield region begins for strains higher than E= and in the plot of T(E)in figure 2, two mechanisms related to the transformation of the cortical a-keratin into pkeratin are depicted (Wainwright et al 1976, Danilatos and Feughelman 1985). Indeed, during the transformation of a n individual fibre of a-keratin into !.-keratin (pleated sheets) its resistance to extension rapidly decreases. After the completion of this transformation, which corresponds to a given degree ofextension, the individual fibre becomes harder and reveals a higher modulus of elasticity (eP) as compared to (e,). Both mechanisms are observed in the yield region of T(E)as evidenced by the initial fall and the subsequent rise of its slope. If all individual fibres could be simultaneously transformed in response to the same degree of extension the detailed analysis of T ( E )would have been easy. However, the transformation of different akeratin fibres occurs in response to different values of extension; therefore T(E) expresses the characteristic features of the individual fibres convoluted with a modulation function. This modulation function is associated with the rate of numerical increase of P-keratin and the decrease of a-keratin fibres in relation to the change of extension. It can be suggested t h a t for E S Ethe ~ numbers of a- and P-keratin fibres are Nu, and No,, respectively for,
N
a0
+ N -N Po
(2)
-
where N is the total number of cortical fibres of the hair specimen. In the yield region (&>E& the a-keratin fibres start to undergo transformation into 0-keratin. T h e postyield region of T ( E )begins beyond a given value of extension (E& in which N P ( ~ p ) > N a ( In ~ pthis ) . region the mechanical behaviour of hair is dominated by the properties of p-keratin. Given that e, and e represent the modulus of elasticity of the individual a- and !.-keratin fibre respective y, then for the slope in the pre-yield region (modulus of elasticity E,) it follows that
P
(3) + NPo eP At the highest part of the post-yield region, just before the fracture of the specimen, almost all fibres have been transformed into to !.-keratin fibres. For the slope EP,of T(E),in this region
E",
U,,ea
ED= ( N , + N o )eo
(4)
Combining the relations ( 3 ) and (4) we have N u eu . .
It is obvious that Ea/EP primarily depends on the proportion of P-keratin in the unstretched specimen.
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286
The stress of viscous origin which is generated in the hair specimen during longitudinal stretching, depends on the viscocity coefficient and the strain rate (Park 1980), e.g. K(&,t)= -n(&)d&/dt.It is therefore obvious that the standardisation of the strain rate (dddt) is necessary, but not sufficient, for the successful application of K(&,f)in the diagnosis of hair disorders. A parameter of diagnostic importance can be drawn from the relation of the integral of K(&,t)to the integral of T(&)for a given extension. This parameter, which can be standardised, is related to the microstructure of the hair specimens and is given by the ratio 30%
LK(&,t)d&-
_-
where
Jo3?(&)d&
du
ssmr
represents the energy stored in the specimen during its 30% extension; and
is the dissipated energy which was induced by the viscous flow during the 30% CxtexiGE of *.e hnir sprcimrc. The viscous phenomena of human hair and therefore the above mentioned parameter, are primarily associated with the keratin matrix. Indeed, according to dynamic measurements (Danilatos and Feughelman 1985), the main part of the viscous loss within a hair specimen, as expressed by the dynamic loss modulus, is associated with the matrix. This is a structural water penetrable component with relatively few disulphide cross-links and a greater proportion of hydrogen bonds (Sikorski and Woods 1960). During extension the hydrogen bonds break down and reformation proceeds continuously, characterising the viscous behaviour of the matrix. On the contrary, in the microfibrils there is a preponderance of intermolecular S-S linkages, which would restrain the viscous flow (Curiskis and Feugelman 1985).
2.3. Evaluation of the diagnostic importance of the mechanicalparemeters of human hair in relation to in inhomogeneous structure. The diagnostic value of the parameters identified through the proposed methodology is limited because of the lack of homogeneity of hair, since for diagnosis of hair disorders it is important to know whether the change of the mechanical parameters is due to variations of the medullary cross-sectional surface area or to alterations in the cortical microstructure. A proper selection and application of our parameters may in part offset the above limitation. Thus: (1) E,/Ep and SdiJSstor ratios are not affected by the inhomogeneous structure of human hair and are closely related to the structural features of the hair cortex being, therefore, of specific diagnostic importance. A marked deviation of EJEP values from the normal range may be associated with an abnormal transformation of a-keratin into P-keratin. (2) T h e modulus of elasticity (Ea), the strain energy (SE) in the pre-yield region and the slope of T(E)in the post-yield region depend o n both the microstructural
287
Mechanical parameters of human hair
features of hair cortex and the relative size of the medulla. Indeed, it is known from previous investigations (Nikiforidis et al 1991) that the relative size of the medulla increases with the increase of the cross sectional surface area of hair shaft. Therefore it appears reasonable that the parameters E,, EDand SE of the hair of a given subject must be analysed with reference to normal hair wlth the same outer cross-sectional surface area 3. Results
The comparative evaluation of the mean values of E,IEp and SdisiS,,,,ratios in 150 and 50 hair specimens derived from 30 young and 10 elderly subjects respectively (table 1) reveals a statistically significant decrease (PC0.05) of EJE ratio in the hair specimens of the aged group, as compared with the young. E a h D and SE were evaluated comparatively in 40 hair specimens from the young group matched for hair shaft diameter with 40 specimens from the elderly subjects. T h e results of this paired evaluation (table 2) reveal a statistically significant decrease of E, and E p in the specimens of the aged subjects, as compared with the young ones. The regression lines of E, against D and EDagainst D ( D = outer diameter of the hair specimen) for the paired samples are diagrammatically shown in figures 5 and 6. Table 1. Comparative evaluation ofEalEpand SdiJS3,0r in hair specimens derived fiom elderly and young subjects.
EdEp
sddsno?
Elderly
Young
Elderly
Young
Mea" Srd deviation
0.87
0.92
80.90x10~2
0.10
0.10
1. 1 3 X 1 0 ~ 2
Observations
50
150
50
150
-3.04
0.375
Hwotbesis
198
H, : B, = B2
0.71
Ha:B , # B,
Degrees of freedom
198
Hwotbesis H 0 : B , = B,
Significance (p)
0.02
H,:B,#B,
T-statistic
80.76X10-2 1.67X10~2
Table 2. Paired evaluation of E,, Epand strain energy in hair specimens derived from elderly and young subjects. ~~
EJGPa) Elderly Young
~~
Ep(GPa)
Elderly
Young
3.94
4.77
Mean Paired observations
3.43
T-statistic
-3.38
Hwothesis
-2.1 I
Hwathesis
0.27
39
H,:B, =Ez H, : B, # Bz
39
H,:B, =B, H a : B, # B,
39
Degrees of freedom
Significance (p)
4.46
0.002
713.00
40
40
0.043
~~
Susin energy (@a) Elderly Young 688.30 40
0.786
Hwothesis H,:B, =E2 H a : BI = B,
4. Discussion
Previous studies on the mechanical behaviour of human hair were mostly phenomenological. Usually only the c(&,t) curve was evaluated and the resulting parameters had no clear mechanical significance. Indeed, because of the compensation of two mechanisms with opposite curvatures (the first associated with the viscous phenomena and the second with the crimping) o(&,t) reveals an almost
. .
. .
f SI
2t
I 20
0
60 80 Diameter, D (pn)
Variable CoefficientSld error a
7.07 -0.04
b
100
40
t
p
1.06 6.64 0.000 0.02 -2.51 0.016
,
0
.
:
20
. 40
60
a b
100
80
Diameter, D (Wm) Variable Coefficient Sld error
p
t
0.83 6.46 o.Oo0 0.01 -2.37 0.023
5.34 -0.03
Figure 5. Regression lines E, = a + bD of modulus of elasticity (E,) plotted against the diameter (D)in hair specimens of young (a) and elderly (b) subjects.
10
I
:
io
U
40
60
Variable Coefficient Std omor
a' b
io0
60
Diameter. D (pm) 8.98 -0.06
f
p
L , , : ,/ 20
0
:
:
,
40 $3 Diameter, D ()"
,
Variable Coefficient Std error
1.32
6.79 0.000
a'
0.02
-3.02 0.004
b
6.40 -0.04
0.82 0.01
:
eo t
:1 : p
7.85 0.000 -3.18 0.003
Figure 6. Regression lines Ep = a' + b'D of the slope of T(E)in the post-yield region plotted against the diameter (Dl in hair specimens ofyoung (a) and elderly (6) subjects.
linear region with a slope that has been falsely regarded as the modulus of elasticity (Bendit 1978). In the present paper attempts were made firstly to provide specific diagnostic data by evaluating the mechanical parameters of hair specimens through a stepwise isolation of different factors implicated in their mechanical response; and secondly to improve the diagnostic specificity of the methodological approach through a combination of information given separately by all mechanical parameters studied. The methodology described here is applied in the study of the effects of the aging processes on the mechanical parameters of human hair. Their comparative evaluation in hair specimens derived from young and elderly subjects revealed statistically significant differences betwen these groups with regard to E,, Ep and E,/Ep, The values of E, and E,, are significantly higher in the individual specimens of the young group, as compared with the aged subjects. Comparing the slopes of the regression lines of E, against D and Ep against D it can be suggested that the differences found between the two groups with regard to E, and Ep,may be due to the fact that in the young subjects the size of medulla increases with the increase of the hair shaft diameter more rapidly than that of the elderly group. This is substantiated by image analysis of the cross-section of the specimens (paper in preparation). On the other hand, the unpaired evaluation of the mechanical parameters of hair in these groups reveals a statistically significant difference with regard to E,/E,,, Since
Mechanical parameters of human hair
289
EaEP does not depend on the size of medulla, it seems likely that hair aging is associated with an impaired transition process of a-keratin into P-keratin during stretching. This alteration may be primarily related to the reduced proportion of pkeratin in hair specimens of the elderly subjects in the pre-yield region. No statistically significant differences could be found between the two groups with regard to the strain energy, because the aged hair specimens reveal a smaller resistance to strain but a greater limit of linearity, as compared with the young ones. Furthermore, since no statistically significant difference was detected between the two groups with regard to SdiJS,,,, it may be concluded that the viscosity of the matrix remains practically unaffected by the aging processes. In conclusion, the method applied in this study enables us to detect the influence of a hair disorder on the mechanical parameters of hair and may implicitly provide indication for the occurrence of alterations in the structure of hair matrix, on the transformation process of a-keratin into P-keratin and on the orientation of the microfibrils with regard to the longitudinal axis of the hair (Krenchel 1964).
References Aklonis J J, Macknight W J and She“ M 1972 Innoducrlon t u Polymer Viscoelartt2iW (New York Wiley Interscience) Balas C, Nikifotidis G and Tsambaos D 1989 Determination of the mechanical pammeten of hair cortex Roc. V Mediteranenn Conference ott Medical and Bioloe’colErzgineminp, Pamar pp 72-3 Bendit E G 1978 Properties of the matrix in keratins. Pan I 1 The “Hookem” region in the stress-strain cume of keratins Text. Res. 3. 48 712- 22 Curiskis J I and Feughelman M 1985 A micromechanics analysis of the mechanical behavior of the akeratin composite a t low strains. Part I: Theoretical formulation Text. Res. J. 5 5 425- 44 relationships in the mechanical properties of Danilatos G and Feughelman M 1980 The microfibril-“% the matrix during the extension of or-keratin fiber Text. Res. 3, 50 568- 74 Fisher K H and Hyatt A L 1984 The anatomy of the skrn and phySiohgy of hair growth The Cause and Managemenr of Hirsutism eds R B Grecnblatt, V B Mahesh and R Don Gambrel1R (Lancaster and New Jersey: Parthenon Publishing Group) pp 175-97 Fung Y C 1981 Bio-viscoelastic solids Biomechanics - Mechanicalhpenies ofLiving Tissues ed Y C Fung (Berlin: Springer-verlag) pp 186-260 Jamison C E, Marangoni R D and Glaser A A I968 Viscoelastic properties of soft tissmes by discrete model charactetization?. Biomsch. I 33-46 Krenchel H 1964 Fiber Reinforcement (Stockholm: Akademisk Vorlag) pp 151-2 Nikiforidis G, Balas C, Tsambaos D, 1992 Viscoelastic response of human hair conex Med. Bid. Eng. Compur. (in press). Nikifondis G, Tsambaos D, Balas C, Bezerianos A and Sampalis F 1991 Mechanical properties of human hair in relation to its gross morphological and microstructural features Demotology in Europe ed E Panconesi (Oxford Blackwell) pp 832-6 Park J B 1980 Biomatmals. A n Introduction (New York: Plenum Press) Rath S 1967 Hair and nail Ulnosrmcture o f N o m a l ond Abno-ol Skin ed A S Zelickson (Philadel~hia:Lea and Fehiger) R u d d K 1964 The biomolecular structure of hair keratin Roaresr in the Biolorical Sciences in Relotion CO Dermatology Vo1.2 eds A Rook and R H Champion (Landon: Cambridge University Press) p 355 S a n j c e ~R 1982 A viscoelastic model for the mechanical properties of biological materialsJ. Biomech. 15 107-9 Sikorski J and Woods H J 1960 X-ray and electron microscope studies of the staining of keratin by silver 3. Texr. Inrt. SI 506-22 Sims RT 1967 “Beaus” lines in hair. Reduction of hair shaft diameter associated with illness Br. 3. Demotol. 79 43-9 Skelton J 1967 The effects of planar crimp in the measurement of the mechanical properties of fiben, flaments and yams3. T~xI. Inst. 58 533-66
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Swanbeck G, Nyren J and Juhlin L 1970 Mechanical properties of hair from patients with different types of hair diseases3. Invest. Dematol. 54 248-51 Tao X and Postle R 1989 A viscoelastic analysis of the keratin composite. Pan I: Longirudinal and trsnwerse mechanics! properties Text.Res. 3, 59 123-38 Tronnier H and Huske G 1958 Methodische Untersuchungen zur registrierbaren Schnellpnrfung keratolydscher und keratinfestigender Stoffe Pa&m. Kormet. 39 507-10 Wainwright S A, Bigges W D, Currey J D and Gosllne J M 1976 Fracture of viscoelastic materials MechanicnlDesign in Organisms ed H Wainwright a al (London: Edward Amold) pp 39-41
