Quantifying whole human hair scalp fibres of varying curl: A micro‐computed tomographic study

Abstract

Scalp hair is a key feature of humans and its variability has been the subject of a broad range of studies. A small subset of these studies has focused on geometric quantification of human scalp hair fibres, however the use of race‐ and ethnicity‐based classification systems makes it challenging to draw objective conclusions about fibre variability. Furthermore, sample preparation techniques for micro‐imaging studies often alter the original form of hair fibres. This study sought to determine which of the commonly reported descriptors could be resolved using micro‐computed tomography (micro‐CT) for fibres of varying curl. Images obtained from micro‐CT were used to reconstruct three‐dimensional images that were then analysed. The study also explored the capabilities and limitations of micro‐CT as an imaging modality by comparing and cross‐validating findings with those obtained from scanning electron microscopy (SEM) and laser micrometry. The former deals with surface imaging while the latter deals with cross‐sectional measurements. Micro‐CT was found to be highly effective at resolving cross‐sectional ellipsoidal parameters, but performed more poorly than SEM in reconstructing surface level details at a 2 $\mu \mathrm{m}$ resolution. The technique was, however, able to reveal the presence of the medulla in type VI (high curl) hair fibres. When compared with high curl fibres, greater intra‐fibre variability was observed for the low and medium curl fibres, highlighting the importance more objective classification systems.

1. INTRODUCTION

Scalp hair is one of the most distinguishing traits in humans which shows a wide range of phenotypes varying in colour, length, curliness, cross‐sectional shape and diameter. ¹ , ² , ³ A notable difference observed in human hair globally is the degree of curliness, which has led to terms such as straight, wavy, curly, frizzy, woolly, and kinky being used to describe the overall form Trotter. ⁴ Descriptors such as these are arbitrary as they are purely based on visual inspection and not any measurable quantity. Until recently, hair shape was classified according to race in scientific studies; for example, the overall form of scalp hair in Asian, Caucasian and African groups was described as straight, wavy and curly, respectively. ⁵ This way of grouping is not representative of the population as a whole, as different racial groups can share the same hair forms. ⁶

The majority of studies on hair form have used race and geographical location as a sampling criteria. Information regarding the hair donor and degree of curl is often omitted, with the hair described as straight, wavy or curly. Therefore, any quantitative measurements for single hair fibres is supposedly representative of an entire racial group. In order to improve the validity of comparative studies and reliably compare datasets from other studies, there needs to be a more objective classification system which is reported for any given hair samples. Several classification schemes have been put forward which aim to use quantitative features of hair shape. ¹ , ³ , ⁷ , ⁸

Hrdy (1973) quantitatively compared several population groups using different descriptors of hair form. Principle component analysis yielded a 3‐component model which related to the curvature and scale count, CS geometry, and regularity of the curl. The model grouped the populations into 4 clusters that for the most part split along racial groups. ⁸ Expanding on Hrdy's work, De La Mettrie (2007) and Loussouarn et al. (2007) focused on developing a scheme whereby hair could be assigned to a specific group based on measuring four hair descriptors (curve diameter, curl index, number of twist/kinks, and number of waves per hair sample). ¹ , ³ From the statistical analysis, they found that hair could be separated into 8‐curl groups. ¹ , ³ The classification scheme assigns specific ranges to the parameter descriptors which enables a more objective way of categorising hair curl. However, there is the issue as to whether it is applied consistently between individuals. A subsequent study by Mkentane et al. looked at the inter‐ and intra‐rater reliability of the 8‐group classification scheme. They found that two of the curling variables had more variability between observers. By combining groups V‐VIII into two groups, the 6‐curl group was put forward as a more reliable way to identify different hair types. ⁹

Hair form shows a wide range of permutations which can be described by their behaviour in 3‐D space. The overall conformation of hair is determined by the weight, elasticity and inherent curvature of the individual strands. ¹⁰ , ¹¹ Hair fibres change their orientation through either bending or twisting, which gives rise to different forms. ¹² , ¹³ Figure 1 shows the straight, wavy and curly hair forms that are produced when these two modes of deformation are applied. Straight hair fibres tend to have a more circular cross‐section and overall form that is cylindrically shaped with minimal curvature. ⁵ , ¹⁴ Wavy hair phenotypes result from the hair shaft bending in a clockwise and anticlockwise direction that resembles a planar sine wave. ⁴ , ¹³ The Undulations along the length of the fibre can vary in amplitude with the wave being either long and shallow, or short and deep. ⁴ Curly hair fibres can be described as a succession of spiral rings with a relatively small curve diameter and pitch. ⁴ Variation in the curve diameter is dependent on the length of time the bending occurs, which seems to be associated with the hair growth rate. A study by Mkentane looked at hair growth rates across 8 hair types, as well as racial groups (Asian, Caucasian, African and mixed). ¹⁵ The average hair growth rates were found to be highest in individuals of Asian descent, followed by mixed and Caucasian which had similar rates. The average growth rate in individuals of African descent was almost $50\%$ lower compared to the Asian group. Across the 8 hair groups, the growth rate was highest in groups I and II, while groups VI–VIII had the lowest. ¹⁵

FIGURE 1.

Schematic diagram showing the different forms a hair fibre can assume when the two modes are applied. A, A' indicates the regions where the hair shaft twists and changes direction. The ortho‐ (black) and paracortical cell (grey) distributions are indicated along the hair fibre.

Studies on wool and human hair observed an association with the distribution of cortical cells within the cortex and degree of curl. ¹⁶ , ¹⁷ In wool, there is a defined bilateral arrangement of the different cortical cell types, with the orthocortical cells distributed on the convex side of the curl and the paracortical cells on the concave side. ¹⁷ In human hair, a similar distribution pattern of the cortical cells has been observed, albeit not as well defined as observed in the wool cortex. ¹⁶ , ¹⁸ , ¹⁹ In curly hair phenotypes, the fibre will twist halfway along its longitudinal axis, causing an interruption in the curvature. As a result, the hair shaft will change direction at regular intervals along its length (Figure 1), where the twists occur in order to maintain the bilateral arrangement of the cortical cells. ⁸ , ¹² Similarly, in wavy hair a twist has to be introduced at the crest and trough, such that the orthocortex and paracortex regions are positioned on the convex and concave side, respectively. ¹²

Studies on hair fibre CS geometry and curvature have observed a wide variation across different population groups. ⁸ , ²⁰ , ²¹ Asian and African hair fibres are on average thicker compared to Caucasians hair, with the former having the largest fibre diameter. ²¹ Human hair fibres tend to have elliptically shaped cross‐sections which vary in the degree of ‘flatness’. ²² , ²³ The ellipticity ratio (major/minor axis) is useful for describing the degree to which an ellipse deviates from a circle. ²⁴ Asian hair has been observed to have more circular CS, whereas highly curled African hair has a more pronounced elliptical CS shape with higher ellipticity values being reported. The ellipticity for Caucasian hair fibre CS falls somewhere between the African and Asian groups. ² , ¹⁴ , ²³ Hair curvature was found to be significantly different between population groups; however the disparity among particular groups varied between studies. ⁸ , ²⁵ African and African diaspora groups showed significant differences in their curvature. ⁸ , ²⁵ Lasisi et al. (2021) applied the 8‐group classification on hair from ad‐mixed African and European origin, and compared with the quantitatively measured curvature. The high curled category was found to contain a disproportionate amount of variation. ²⁶ Studies focussed on the relationship between hair curvature and CS geometry found a stronger correlation between the two parameters across population groups compared to within individual groups. ⁸ , ²⁵ When accounting for the proportion of African heredity in these groups, the relationship between hair eccentricity and curvature was inconsequential. ²⁶

Hair cross‐sections have an effect on the physical properties of hair, such as the fracture behaviour, and the resistance to bending, twisting and extending. ²² , ²⁷ Due to the elliptical nature of the cross‐section, hair fibres will preferentially bend about the minor elliptical axis. Swift compared the relative bending stiffness, which was calculated from the measured cross‐sections of scalp hairs from 4 different racial groups. ²² A sharp decrease in the bending stiffness was observed in groups with larger ellipticity values. Therefore, the bending stiffness increases as the hair cross‐sections change from elliptical (African, European groups) to circularly shaped (Chinese, Asiatic Indian groups). ²² A study by Kamath et al. looked at the torsional effects in African hair. ²⁷ Due to the high frequency of twists present in African hair, the fibre will untwist when a load is applied. They found that the twists were not unidirectional and would change direction randomly along the length of the fibre.

Microscopy studies on the regions of the twist showed the cross‐sectional shape to be highly variable. The ellipticity values for the African hair fibres indicated a flattened elliptical shape. ²⁷ Seibert and Steggerda (1942) investigated the change in the dimension and shape of the cross‐section along the hair shaft. They sampled hair from two geographical regions, American Dutch Caucasian females and Maya females from Yucatan Mexico. Hair fibres (400–500 mm in length, $\sim$80–100 hairs) were sectioned at specified intervals from the cut end. For the majority of the samples, irrespective of race or age, there was an initial increase in the cross‐sectional area over the first 100 mm from the proximal end. Moving further along the hair shaft, the cross‐sectional area was more irregular. A similar trend was observed with the major axis but not the minor axis. ²⁸ This observation has been described in later studies. ²⁹ A similar study by Hutchinson and Thompson made observations based on cross‐sectional measurements of long hair. ³⁰ They hypothesised that during the initial anagen phase of the growth cycle, there is an abrupt increase and then decrease of the major diameter. The major axis continued to decrease towards the telogen bulb. A similar trend was observed for the cross‐sectional area and ellipticity, however there was relatively no change in the minor axis along the hair shaft. The study concluded that the cross‐section is not uniform along the hair shaft, but changes from being more elliptical on the distal end to more circular (and finer) towards the proximal end. The authors attributed the changes in the hair shaft cross‐section to variation in the follicular growth activity. ³⁰

Various modalities have been employed to accurately determine the cross‐sectional geometries of single hair fibres. ¹⁴ , ²⁵ , ²⁶ , ³¹ , ³² , ³³ , ³⁴ The standard method for measuring the cross‐sectional geometry of hair fibres usually involves embedding the fibres in resin, transverse sectioning, followed by light and electron microscopy. This technique requires the hair fibre to be chemically (fixation, dehydration and embedding) and mechanically (sectioned) processed. While this technique can provide a high throughput of hair cross‐sections to view, it is time consuming, and the cross‐sectional dimensions can be distorted if the hair is cut at an oblique angle. Other methods involve assessing the hair along its longitudinal axis, thereby providing information about the change in dimensions along the fibre length. One such method is the Optical fibre Diameter Analyser (OFDA), which is able to image a large number of fibre fragments ($\sim$2 mm in length), from which a mean diameter value is calculated. ³⁴ The measurements are relatively quick; however, the the diameter values are biased towards the long axis due to the preferential orientation of the hair fragments on a surface. Other types of longitudinal measurements involve placing a hair fibre between a light source and linear photodetector array. ¹⁴ , ³³ The region where the fibre and light interact results in a shadow being projected onto a photodetector array and recorded. One is able to observe the change in shape along the hair fibre. A downside to using this method, especially with curly hair, is that the fibres need to be kept taut in order for the light source to scan along the shaft. Lasisi et al. (2021) devised an automated image analysis software which could approximate the curvature and CS from the longitudinal and transverse images of the fibre. ²⁶ Techniques such as SEM, Optical Coherence Tomography (OCT) and photogrammetry have been used for 3‐D reconstruction of hair, albeit with limitations in the number of descriptors able to be measured. ²⁰ , ³⁵ , ³⁶ OCT is a non‐destructive imaging technique that is used to generate a 3‐D image of an object. ³⁶ , ³⁷ It is capable of obtaining high resolution cross‐sectional images of the internal structure of biological tissue at the micro‐level. This technique is based on the resultant interaction of a broadband light source with a biological material. ³² , ³⁶ The cross‐sectional OCT images can be combined to form a 3‐D image from which dimensional information can be obtained. A study by Velasco et al. showed OCT scans of African hair fibres were able to elucidate the cuticle, cortex and medulla. ³⁶ Micro‐Computed Tomography (micro‐CT) is a 3‐D imagining technique capable of producing high resolution 2‐D images of other biological tissues. This technique doesn't required invasive sample processing, thereby allowing the specimen to be imaged close to its natural form. The use of X‐rays allows for non‐invasive imaging over a larger field of view at high resolutions. ³⁸ The 3‐D models generated from the micro‐CT data have been used to extract dimensional information for other tissues, as well as elucidate the surface and internal features.

The aim of this study is to determine which of the commonly reported descriptors of hair form could be resolved with micro‐CT. The reconstructed 3‐D models of single hair fibres with varying degrees of curl were used to (1) observe the overall shape and surface topography, (2) elucidate any internal features, and (3) perform quantitative dimensional and volumetric analysis. The variability in the cross‐section profile within and between individual hair fibres was accessed. The results from the micro‐CT was compared with other techniques used to determine the hair form descriptors.

2. MATERIALS AND EXPERIMENTAL METHODS

2.1. Sample collection and processing

Permission to carry out the research project was obtained from the Human Research Ethics Committee of Faculty of Health Science, University of Cape Town (HREC REF: $431/2019$). The participants for this study were required to have a minimum of 6 cm of virgin hair, that is hair which has not been treated with hair dye and/or chemical relaxes or straighteners for over 7 months. Those participants that met the requirements and provided consent had a small portion of hair cut from two or more regions on the posterior vertex of the scalp. Hair sections were cut within 10 cm from the root end and the rest discarded. All hair samples were washed with a pH adjusted solution of 5% SDS (pH 5–6), followed by air‐drying at room temperature.

Hair from three participants which exhibited low, medium and high curled phenotypes (shown in Figure 2A) were selected and used throughout the study. The low and medium curled hair was from individuals of Caucasian descent while the high curled hair was from an individual of African descent. The participants ages ranged from 20 to 30 years. Approximately 21 hair strands from the selected hair samples were assessed according to the 8‐group hair classification scheme described by De La Mettrie et al. ¹ The high curled hair was further grouped according to the 6‐group classification outlined by Mkentane et al. ⁹

FIGURE 2.

Overview of the hair collection and processing. (A) The three hair samples selected for this study which displayed a low, medium and high curled phenotype. (B) The curve meter used to estimate the curve diameter ($CD$). (C) The curl index calculated from the ratio of the hair length in the stretched and relaxed state. Method for determining the (D) number of wave crests $\downarrow$ and (E) number of twists [] for the high curled hair.

The method for removing the hair samples and subsequent hair classification is shown in Figure 2. Each hair strand was cut into segments 6 cm in length, which were then used for the hair classification. The curve diameter (CD) was determined by placing the hair strands on the curl meter template shown in Figure 2B, and aligning the curvature of the hair with the nearest circle of known radius. The $CD$ value for the high curled hair was below 1.2 cm, indicating that the hair fell in the higher curl groups. The length of the hair was measured in the relaxed ($L_1$) and stretched ($L_2$) states (Figure 2C). The ratio of the two lengths gives the curl index, which is used to differentiate between curl group V and VI. The 5 cm segment of hair was placed between a length of 4 cm, resulting in a sigmoid shape. The number of peaks and/or valleys are counted, with the lowest value corresponding to the number of wave crests ($w$) (Figure 2D). The number of twists ($t$) were determined by extending the same hair strand to the full 6 cm length and counting the number of constrictions along the hair fibre (Figure 2D). A Zeiss Stemi 305 compact Greenough stereo microscope was used to identify the regions of the constrictions.

2.2. Micro‐computed tomography

Micro‐computed tomography (micro‐CT) is a nondestructive method capable of imaging the surface and internal three‐dimensional structure of a solid object. ³⁹ The spatial resolution that is achievable for a micro‐CT system is between 0.5 and 0.9 $\mu \mathrm{m}$. ³⁹ The main components of the micro‐CT system are the X‐ray source, a rotary table upon which the sample is mounted, an X‐ray detector and a central processing unit for computation, visualisation and data analysis of the measurement result. ⁴⁰ The X‐rays are generated through the interaction of a beam of accelerated electrons and a metal target (tungsten). ³⁹ The sample is placed between the detector and X‐ray source such that the X‐rays are directed through and around the sample as it rotates. This in turn creates a number of different angular projection images. ⁴⁰ X‐rays that pass through the object are either absorbed, scattered and/or transmitted. The proportion of X‐rays that are absorbed or scattered are called attenuated. The grey levels observed in a CT slice image directly correspond to the X‐ray attenuation which is primarily a function of the X‐ray energy and the density and atomic number of the material being imaged. ⁴¹ The detector will convert the attenuated radiation into 2‐D digital images which will then be used to reconstruct the volume. ⁴⁰

2.2.1. Experimental set‐up

Hair fibres from the low, medium and high curled hair samples were imaged using the micro‐CT. Three hair strands selected from each group were cut into 10‐ to 20‐mm long snippets and individually mounted between two plastic frames. This was done so as to prevent any movement of the hair during the scan. When mounting the sample on the frame, care was taken to ensure the hair fibre was in a relaxed state and retained its natural form.

The micro‐CT system used for this study was the General Electric Phoenix Nanotom S system (General Electric, Boston, USA), at the CT Scanner Facility, Central Analytical Facilities, Stellenbosch University. ³⁹ The Phoenix Nanotom S system is equipped with a high‐power nanofocus tube with a maximum acceleration voltage of 180 kV and a maximum tube power of 15W, which produces a cone‐shaped X‐ray beam that images the samples onto a fully digital detector. The CT system is capable of scanning objects with dimensions of up to 150 mm (H) $\times$ 120 mm (W), and voxel‐resolutions down to 0.5 $\mu \mathrm{m}$. ⁴²

Two different types of rotational modes (continuous and stepwise) were used when scanning the hair fibres, in order to assess which one would produced the higher quality images. The continuous scan involves using a continuous rotation and imaging of the sample without any steps, while a stepwise rotation has one or more images acquired at each step position and averaged. In this case the first image was discarded and the two subsequent images averaged. The maximum achievable resolution of the Nanotom S was not adequate to resolve microstructural features of the cortex. Therefore, an isotropic voxel size of 2 $\mu \mathrm{m}$ was chosen for all scans, to resolve the three main regions of the hair fibre (i.e. cuticle, cortex and medulla). The machine parameters used during the scans are shown in Table 1.

TABLE 1.

Micro‐CT input parameters used for scanning the hair fibres.

Input ranges
Voltage	50 kV
Current	190–200 $\mu \mathrm{A}$
Voxel size	2 $\mu \mathrm{m}$
Rotation (${360}^o$)	Continuous/stepwise
X‐ray exposure time	1250 ms
Scan time	1 h

2.2.2. Data analysis

Simpleware ScanIP (Synopsys, Exeter, UK) was used for image reconstruction and analysis of the CT data. The typical workflow for 3‐D reconstruction and analysis of the micro‐CT data is shown in Figure 3. The first step involves importing the set of 2‐D projections into the image processing software, and determining a suitable lower and upper threshold bounds. This is an important step for accurate image segmentation which influences the resulting reconstructed geometry of the scanned object. ⁴⁰ The threshold will convert a grey image into a binary one, that is, the background (black) and the object (red). For our specific study, the threshold determines the boundaries between the object and the air, so that a surface can be assigned to the scanned object. Once a suitable threshold has been applied, the 2‐D images are reconstructed into a 3‐D voxel model. The threshold does not always remove pixels/voxels that are not part of the object. As a result, segmentation tools (i.e. island removal) are employed to remove imaging artefacts in order to distinguish the edges of the object. The software was then used to perform dimensional and volumetric analysis (i.e. fibre length, surface area, volume and cross‐sectional area) on the hair fibre model.

FIGURE 3.

Procedure for segmentation and reconstruction of micro‐CT data. Adapted from Villarraga‐Gómez et al. ⁴³

In order to carry out the dimensional analysis, a centreline was fitted along the model hair fibre axis. The centreline was smoothed followed by pruning of unwanted segments in order to ensure that the line is centred and continuous along the fibre axis. ‘Exclusion rules’ were applied to the cross‐sections in order to ensure that ellipses that passed close to a boundary and/or if neighbouring ellipses crossed one another would be excluded from the analysis. The hair fibre cross‐section was modelled using an ellipse as shown in Figure 4. A series of ellipses were fitted perpendicularly along the centreline at an incremental spacing of 5 voxels. The geometric parameters were extracted from the fitted ellipse, that is, the major diameter, minor diameter and cross‐sectional area (CSA_Ellipse). In addition to measuring the CSA_Ellipse, the software measures the cross‐sectional area of the contour (CSA_Contour) of the hair fibre surface at the point of the fitted ellipse. Using the contour of the hair fibre to determine the cross‐sectional area gives a more accurate estimation as it takes into account the unevenness of the fibre surface. The ellipticity was calculated for each point along the hair fibre using Equation (1),

$$\text{Ellipticity}=\frac{\text{major diameter}}{\text{minor diameter}}=\frac{a}{b},$$ (1)

where a is the major radius and b is the minor radius. The ellipticity is the ratio of the major and minor axis of an ellipse. It indicates the degree to which a shape deviates from being circular. The smaller the value for the ellipticity, the more circular the shape, whereas a higher value indicates a ‘flatter’ elliptical shape.

FIGURE 4.

Elliptical modelling of a human hair fibre cross‐section. (A) Diagram showing the parameters of an ellipse. (B) Light microscope image of hair cross‐section showing the fitted ellipse (dashes). (C) Reconstructed micro‐CT image showing the centreline and fitted ellipses (shown in red) along the fibre axis.

2.3. Surface imaging of hair

2.3.1. Sample preparation and imaging

Hair strands were selected from the low, medium and high curled hair samples, and secured onto glass slides with carbon tape. The hair strands were viewed using a Nikon Ti‐E Inverted Microscope (Nikon Instruments Inc., NY 11747‐3064, USA) in bright‐field mode at 20$\times$ magnification, in order identify any medullary structures that may be present along the hair shaft. Under transmitted light, the medulla appears as a black or opaque structure when light is transmitted through the hair shaft. ⁴⁴ The samples were sputter coated with gold using a Leica EM ACE200 gold coater (Leica Mikrosysteme GmbH, Vienna). Surface imaging of the hair samples were performed with a Zeiss EVO 10 Scanning Electron Microscope (Carl Zeiss Microscopy GmbH, 07745 Jena, Germany), using secondary electron mode.

2.3.2. Image analysis

The number of cuticle scales ($S_n$) were determined from the SEM micrographs using Materials Image Processing and Automated Reconstruction (${\text{MIPAR}}^{\text{TM}}$) software (MIPAR, Columbus, Ohio, USA). Pixel resolution was determined from the scale bar on the bottom left of image. The contrast of the image was adjusted in order to highlight the edges of the scales (brighter lines on the hair fibre surface). A line was drawn parallel to the fibre longitudinal axis, and a graph generated showing the pixel values along the line (Figure 5). In this case, the larger pixel values (peaks) correspond to a particular scale that intersects the line. $S_n$ was determined over a distance of 100 $\mu \mathrm{m}$.

FIGURE 5.

Example illustrating the measurements performed on the SEM micrographs to determine the number of scales ($S_n$) over a distance of 100 $\mu \mathrm{m}$.

2.4. Hair fibre cross‐sectional analysis: laser micrometre

2.4.1. Experimental set‐up

Measurements were carried out on hair fibre cross‐sections using a Fibre Dimensional Analysis System (FDAS770, Dia‐stron Ltd, Hampshire). Approximately 15 single hair fibres (ca. 10 cm in length) were randomly selected from each donor. Two brass crimps were secured on either end of each hair fibre to enable machine handling. The hair samples were placed in an environmentally controlled chamber (Electro‐tech systems Inc, USA) for 24 h before taking the measurements. The measurements were carried out at $25\pm 5^{\circ }\mathrm{C}$ and a relative humidity of $55\pm 5$%. Hair fibres are highly susceptible to swelling with increasing RH. ²¹ For this reason a mid‐range RH value was chosen which closely approximated the environmental conditions during the micro‐CT scans. A single fibre is placed perpendicular to a laser beam, which will scan and take measurements at discrete slices along the hair shaft (total of 31 slices at increments of 0.15 cm). At each slice the hair is rotated from 0 to 360, and the diameter measured at incremental angles. The hair is kept taut throughout the measurements. The system is controlled by the UvWin software (Dia‐stron Ltd, United Kingdom) which records the measurements and generates the raw data from which the maximum and minimum diameters and cross‐sectional area for an ellipse can be extracted.

2.4.2. Data analysis

The UvWin software (Dia‐stron Ltd, United Kingdom) determines the maximum and minimum diameter values for each slice. These values were used to calculate the ellipticity, cross‐sectional area (CSA) and focus ($F$) for an ellipse (Equations 1 and 2). All data processing was performed using MATLAB^® 2022a (The MathWorks, Inc., United States).

$$\text{CSA}=\pi \text{ab.}$$ (2)

2.5. Statistical analysis of dimensional data

A Pearson's correlation was performed to investigate the relationship between the two methods for modelling the CSA. The Bland–Altman method for statistical comparison was carried out to assess the level of agreement between the the two methods used for measuring the CSA of the fibre Giavarina. ⁴⁵ The Bland–Altman analysis was performed in Matlab using the ‘Bland–Altman and Correlation Plot’ code. ⁴⁶ In this analysis, the average (x‐axis) and difference (y‐axis) between the two measurements are presented in a scatterplot. In addition to this, the average of the differences (known as mean bias) and limits of agreement mean ($\pm$1.96 s) are displayed on the plot. ⁴⁵ The distribution of the difference data was tested for normality using the Kolmogorov–Smirnov test.

3. RESULTS

3.1. Shape and surface morphology of human hair fibres

Hair fibres from 3 participants with a low, medium and high curled phenotypes were characterised using the 6‐group classification method. ⁹ The low curled hair can be described as having long curved wavy fibres. The medium curled hair had a shorter curve with some hairs forming ringlets, while others showed a change in the direction of the curve. The high curled hair fibres spiralled forming ringlets with small diameters, however, varied in pitch both along and between strands. The results from the individual hair strand assessment is shown in Table 2. Each column shows the proportion of sampled hair strands that lie within a specific CD range for the 3 hair phenotypes. The low curled hair fibres were found to be distributed within hair types I to IV, with $66.7\%$ of the samples being classified as type II. Similarly, the medium curled hair was found to lie within hair types II to VI, with $65\%$ of the hair fibres being classified as type IV. All hair fibres with the high curled phenotype were classified as type VI. The average number of twists and number of waves for the high curled hair was determined to be 12.33 $\pm$ 0.59 and 6.81 $\pm$ 0.25 (over a 5 cm segment of hair), respectively. The distance between twists going from peak to peak was measured to be between 0.3 and 0.5 cm.

TABLE 2.

Distribution of the characterised hair strands from each donor using the 6‐group classification method Mkentane et al. ⁹ The curve diameter range for each hair type is shown in brackets (values for the curve diameter (cm) taken from Loussouarn et al., 2007).

		Type I (%)	Type II (%)	Type III (%)	Type IV (%)	Type V–VI (%)
Hair sample	N	[$10.8<$]	[$5.7<.<10.8$]	[$3.1<.<5.7$]	[$1.2<.<3.1$]	[$<1.2$]
Low curl	21	14.3	66.7	9.5	9.5	0
Medium curl	20	0	5.0	5.0	65.0	25.0
High curl	21	0	0	0	0	100

Three hair strands from each hair group were selected for 3‐D‐imaging using micro‐CT. Figure 6 shows examples of the individual hair strands secured onto plastic frames before being scanned. The 3‐D models of the type II, IV, and VI hair fibres generated from the micro‐CT images are shown in Figure 7. The model statistics determined for the each 3‐D reconstructed segment of hair scanned using the micro‐CT is shown in Table 3. Included in the table is the values for the CD, the number of waves and number of twists for each hair strand imaged using the micro‐CT. The type II hair fibres (Figure 7A–C) had planar (2‐D) shape with CD values ranging between 6 and 9 cm. Similarly, the type IV hair strands (Figure 7D–F) had a planar form with a more pronounced curvature and CD values between 2 and 3 cm. It should be noted that the micro‐CT is unable to capture the full length of the fibre curvature for the low and medium curled hair due to a portion of the fibre lying outside of the selected field of view (FOV). A larger FOV with dimensions similar to the CD values of the low and medium curled hairs would be required to fully image the curvature. The type VI hair strands (Figure 7G–I) have a nonplanar (3‐D) helical configuration with CD values of $\le 0.2$ cm. The CD values were consistent across all type VI hair samples that were analysed; however, the pitch of the helical geometry varied, which could be due to external stresses from handling the hair. The type VI hair strands had longer segments that were scanned compared to the other two hair types (Table 3). This is due to the CD values for each turn of the spiral lying within the FOV. Therefore, a larger segment of hair with a higher number of turns could be scanned. The helical form of the high curled hair fibre indicates the presence of twists along the hair shaft. It is not evident from Figure 7G–I, where the twists are positioned along the hair shaft.

FIGURE 6.

Images showing the (A) low curled (type II), (B) medium curled (type IV) and (C) high curled (type VI) hair fibres mounted in plastic frames ($\sim$10−20 mm $\times$ 5 mm).

FIGURE 7.

3‐D models of the (A–C) low curled (type II), (D–F) medium curled (type IV), and (G–I) high curled (type VI) hair fibres obtained from the micro‐CT scan and generated with Simpleware ScanIP.

TABLE 3.

Model statistics for the segments of hair scanned using the micro‐CT.

	Low curl (type II)			Medium curl (type IV)			High curl (type VI)
	Strand 1	Strand 2	Strand 3	Strand 1	Strand 2	Strand 3	Strand 1	Strand 2	Strand 3
Total length (mm)	4.628	3.248	3.122	4.64	3.64	3.716	12.958	22.308	13.122
Surface area (${\text{mm}}^2$)	1.05	0.7509	0.6322	1.032	0.7132	0.7909	3.878	6.917	2.598
Volume (${\text{mm}}^3$)	0.01602	0.01199	0.00858	0.01545	0.009434	0.01205	0.07442	0.1431	0.03184
Curve diameter (cm)	8–9	8–9	6–7	3	2–3	2	0.2		0.2
Number of waves $w$	−	−	−	−	−	−	5		4
Number of twists $t$	−	−	−	−	−	−	9		7

Note: The classification procedure outlined in Figure 2B–E was used to determine the $\mathrm{CD}$, $w$ and $t$ values of each hair segment scanned with the micro‐CT.

The ability of the micro‐CT to resolve the surface topology of the real hair fibres was compared with surface images taken with the SEM. Figure 8 shows the enhanced surface images of the 3‐D model (left) and those taken with the SEM (right), for the three hair types. Using the SEM images, the average spacing between neighbouring cuticle scales (scale interval) and the number of scales was measured over a distance of 120 $\mu \mathrm{m}$ at three different locations along the hair fibre. On average the type II hair fibres were found to have fewer cuticle scales with 12 scales/120 $\mu \mathrm{m}$, compared to the type IV and VI hair fibres which both had 15 scales/120 $\mu \mathrm{m}$. The type IV hair fibres had the smallest surface scale interval with a value of $7.61\pm 0.45$ $\mu \mathrm{m}$, followed by the type VI and II hair fibres with values of $8.24\pm 1.16$ $\mu \mathrm{m}$ and $9.85\pm 1.10$ $\mu \mathrm{m}$, respectively.

FIGURE 8.

Enhanced images showing the surface topography (left) and SEM image (right) of the (A) low curled (type II), (B) medium curled (type IV), and (C) high curled (type VI) hair fibres.

3.2. Dimensional analysis of the hair fibre cross‐section

3.2.1. Hair fibre cross‐sectional analysis: micro‐CT

Figure 9A–C shows plots of the CS diameter along the length of the fibre for the type II, IV and VI hairs. To account for differences in fibre lengths, the distance along the fibre shaft ($z$‐axis) was normalised for all plots. The type II and IV hair strands (Figure 9A and B) showed slight smooth variation in the major and minor diameters along the length of the fibre. These changes can be visually seen in Figures 10 and 11 which shows the 3‐D view of the centrelines and best fit ellipse to the individual cross‐sections coloured by maximum and minimum radius length, respectively. The changes in the major and minor diameters along the hair shaft showed a similar profile for the type II and IV hair. In both cases the diameter values oscillate close to the mean for the hair strand (Table 4). Within each curl group, the individual strands showed varied separation between the major and minor diameters, with a slightly larger difference observed in the type IV hair. It was also observed that the range of the major diameters for the type II (67.43–93.96 $\mu \mathrm{m}$) and IV (66.48–95.93 $\mu \mathrm{m}$) hairs overlapped. Similarly, there is an overlap between the minor diameter values for the type II (38.29–66.83 $\mu \mathrm{m}$) and type IV (46.12–66.44 $\mu \mathrm{m}$) hair fibres. The type VI hair strands showed a more abrupt variation in the major (73.50–154.92 $\mu \mathrm{m}$) and minor (38.26–86.68 $\mu \mathrm{m}$) diameters along the length of the fibre (Figure 9C). Figures 10 and 11 appear to show regions of high and low values for the CS diameters that repeat at varying length intervals along the hair fibre. Overall, strand 2 had the largest mean values for the major and minor diameters (Table 4), followed by strand 1 and 3 which was significantly smaller. For all three hair strands, the differences in the major and minor diameters along the fibre length were larger compared to the type II and IV hairs. The plots for all three hair types also showed that when the diameter increases along the transverse direction (e.g. $x$‐axis), there is a corresponding decrease or ‘flattening’ along the perpendicular direction (e.g. $y$‐axis).

FIGURE 9.

Plots showing the (A–C) CS diameter, (D–F) CSA and (G) ellipticity profile along the 3‐D hair models.

FIGURE 10.

3‐D views of the centrelines showing individual cross‐sections coloured by maximum radius length.

FIGURE 11.

3‐D views of the centrelines showing individual cross‐sections coloured by minimum radius length.

TABLE 4.

Summary of the ellipsoidal parameters describing the cross‐section of the 3‐D hair models.

	Low curl (type II)			Medium curl (type IV)			High curl (type VI)
	Strand 1	Strand 2	Strand 3	Strand 1	Strand 2	Strand 3	Strand 1	Strand 2	Strand 3
	($N=463$)	($N=324$)	($N=313$)	($N=463$)	($N=364$)	($N=371$)	($N=1296$)	($N=2231$)	($N=1312$)
Major diameter ($\mu \mathrm{m}$)	78.9 (0.1)	86.7 (0.2)	73.6 (0.1)	85.5 (0.1)	74.7 (0.2)	74.0 (0.1)	118.7 (0.1)	126.5 (0.1)	81.2 (0.1)
Minor diameter ($\mu \mathrm{m}$)	62.5 (0.1)	61.5 (0.2)	53.8 (0.1)	56.1 (0.1)	49.1 (0.1)	61.3 (0.1)	68.9 (0.1)	74.7 (0.1)	44.0 (0.1)
Ellipticity	1.3 (0.0)	1.4 (0.0)	1.4 (0.0)	1.5 (0.0)	1.5 (0.0)	1.2 (0.0)	1.7 (0.0)	1.7 (0.0)	1.9 (0.0)
${\text{CSA}}_{\text{Ellipse}}$ ($\times {10}^2$ $\mu \mathrm{m}$ )	38.7 (0.1)	41.8 (0.1)	31.1 (0.1)	37.7 (0.1)	28.8 (0.1)	35.6 (0.1)	64.2 (0.1)	74.2 (0.1)	28.0 (0.1)
${\text{CSA}}_{\text{Nearest}}$ ($\times {10}^2$ $\mu \mathrm{m}$ )	34.5 (0.0)	36.6 (0.0)	26.8 (0.1)	33.5 (0.1)	25.6 (0.0)	32.0 (0.0)	57.1 (0.1)	64.4 (0.1)	24.1 (0.1)

Note: The values represent the average ($\overline{x}$) of all the points measured along the hair fibre length. Uncertainty estimated using the standard deviation of the mean:

$${\sigma }_{\overline{x}}=\frac{\sigma }{\sqrt{n}},\left(\text{sample size}=n;\text{standard deviation}:\sigma =\sqrt{\frac{{\sum }_{i=1}^n{(x_i-\overline{x})}^2}{n-1}}\right).$$ (3)

The inter‐ and intra‐fibre variability of the cross‐sectional diameter for the low, medium and high curled hair is shown with boxplots in Figure 12A. The type II and IV hair had similar median values for both the major and minor diameters, but were smaller than the type VI hair. The only exception was strand 3 of the type VI hair, which had comparable values to the other two hair types. The interquartile range (IQR) had slight variation in size both between and within hair groups. Overall, the type II and IV hair had similar distributions in their diameter values, with the exception of the type II hair strand 2 which was comparable to the type VI hair. The type VI hair fibres had the largest distribution of the major and minor diameters, with strand 2 having a wider range compared to all other strands. For all three hair types, the distribution of the cross‐sectional diameter data was slightly skewed, with the type VI hair (strand 2) having a definite right skewness. The most number of outliers were observed in the type VI hair (strand 1 and 2).

FIGURE 12.

Boxplots showing the (A) CS diameters, (B) CSA and (C) ellipticity for the 3‐D hair models, measured using a fitted ellipse. $\square$ Interquartile range (IQR), $\boxminus$ median, $+$ outliers.

Plots of the ${\text{CSA}}_{\text{Ellipse}}$ and ${\text{CSA}}_{\text{contour}}$ along the length of the fibre for the type II, IV and VI hair strands are shown in Figure 9D–F. The type II and IV hair strands (Figure 9D and E) showed a small degree of variability in the ${\text{CSA}}_{\text{Ellipse}}$ and ${\text{CSA}}_{\text{contour}}$ along the length of the fibre. These changes can be visually seen in Figure 13, which shows the 3‐D view of the centrelines and best fit ellipse to the individual cross‐sections coloured by ${\text{CSA}}_{\text{Ellipse}}$. The ${\text{CSA}}_{\text{Ellipse}}$ values for the type II (2027.85–4504.38 $\mu \mathrm{m}$ ) and type IV (2539.29–4238.26 $\mu \mathrm{m}$ ) hairs was observed to overlap. The CSA values determined from the fitted contour were found to be lower than the ${\text{CSA}}_{\text{Ellipse}}$ values, for all curl groups. Similarly, there was an overlap between the type II and IV hair ${\text{CSA}}_{\text{contour}}$ values, with the ranges being smaller compared to those determined form the fitted ellipse. As is the case for the diameter changes, the type VI hair strands also showed abrupt changes in the CSA for both the fitted ellipse and contour values, along the length of the fibre (Figure 9F). This can be seen in Figure 13 which shows regions with significantly higher and lower values for the CSA that vary at irregular intervals along the hair fibre. Strand 3 of the type VI hair showed similar variability along the hair fibre as seen in the other two hair strands; however, the values were significantly smaller compared to strands 1 and 2.

FIGURE 13.

3‐D view of the centrelines showing individual cross‐sections coloured by ${\text{CSA}}_{\text{Ellipse}}$.

A summary of the results for the CSA measurements for the three hair types are shown with boxplots in Figure 12B. The median values for the ${\text{CSA}}_{\text{Ellipse}}$ and ${\text{CSA}}_{\text{contour}}$ showed a distinct separation between the type II/IV and type VI hair, with the latter having the overall higher values. The only exception was strand 3 of the type VI hair, which had comparable CSA values to the low and medium curled hair. The IQR was largest in the type VI hair, while the type II and IV hair strands had similar distributions for the CSA. The dispersion in the CSA values were significantly smaller in the type II and IV hair strands compared to the type VI hair. This distribution is slightly larger in the ${\text{CSA}}_{\text{Ellipse}}$. The CSA data was for the most part normally distributed with a few strands showing a slight skewness. Overall, the CSA data for the type VI hair showed significantly more outliers in for strands 1 and 2.

From the above plots it can be seen that the CSA measured using the ellipse model is always larger than the nearest contour, for all 3 hair types. Figures S1–S3 show the regression line between the CSA measured using the nearest contour and ellipse methods. The Pearson's correlation coefficients (Table S2) for the type II, IV and VI hairs strands showed a strong positive correlation between the nearest contour and fitted ellipse methods used to measure the cross‐sectional area of the hair fibre, which were statistically significant. The one exception was strand 2 of the type II, which had a weaker relationship between the two methods; however, it was statistically significant. One drawback with the correlation analysis is that it only provides information about the strength of the linear relationship between two variables, and not how they are related. ⁴⁷ , ⁴⁸ The difference data for the type II and IV hair was normally distributed, whereas the type VI data was skewed to the left. Therefore, the parametric Bland–Altman analysis was carried out on the type II and IV, while the nonparametric analysis was applied to the type VI data. Figures S1–S3 shows the Bland–Altman plots for the 3 hair types, which displays every difference between the two methods for determining the CSA of the fibre against the average of the measurement methods. The mean bias and limits of agreement are indicated by the solid and dotted lines, respectively. The results for the mean bias and limits of agreement are shown in Table S2. In all cases, the plots showed a negative mean bias, with an overall negative trend along the plots. The two methods cannot be used interchangeably as the limits vary by more than 200 $\mu \mathrm{m}$ for the type II and IV hair, and by more than 400 $\mu \mathrm{m}$ for the type VI. The line of equality ($x$=0) was found to lie outside the limits of agreement for all hair strands. This indicates that the bias is significant, and the measurement using the fitted ellipse overestimates compared to the method using the nearest contour.

Figure 9G shows the ellipticity profile along the length of the fibre for the type II, IV and VI hairs. The type II and IV hairs showed a more gradual change in the cross‐sectional shape along the fibre length, while the type VI hairs were more erratic. The largest ellipticity values were found in the type VI hair strands, followed by type IV and type II hair (Table 4). The one exception was strand 3 of the type IV hair, which had the smallest ellipticity values out of all the hair strands. Strand 3 of the type VI hair had a similar ellipticity profile and range to strand 1 and 2, even though the cross‐sectional diameter values were significantly smaller. The higher ellipticity values in the type VI hair are expected due to the bigger differences in the major and minor diameter.

The inter‐ and intra‐fibre variability of the ellipticity for the three hair types is shown with boxplots in Figure 12C. The medians for each hair type were well separated, with the type VI hair having the highest ellipticity followed by type IV and type II. One exception was found in strand 3 of the type IV hair, which had the lowest median value for the ellipticity. The IQR for the type II and IV hair showed significant variation between hair strands and groups. However, the type VI hair had a more consistent distribution in the ellipticity between strands. Type II (1.16–1.76) and type IV (1.06–1.79) had similar ranges for the ellipticity, while the type VI range (1.4–2.24) was on the higher side. The distribution in the ellipticity for all three hair types showed a slight skewness, with the type IV and VI having a high number of outliers.

3.2.2. Hair fibre cross‐sectional analysis: laser micrometre

The previous section focused on quantifying the hair cross‐section at a higher resolution using 3‐D models of short hair segments. In this section the inter‐ and intra‐fibre variability is investigated for the different cross‐sectional parameters over a longer piece of hair.

Boxplots in Figure 14A–C show the distribution of the cross‐sectional diameters for the type II, IV and VI hair ($\pm 15$ strands). The variation of the major and minor diameters along individual hair strands was relatively small in the type II hair; however, this increased with increasing curliness. The diameter median values are more consistent in the type II hair. For the type IV and VI hair, the median diameter values showed increased variability between hair strands. This variability is more pronounced in the major diameter compared to the minor diameter. Table 5 shows the cross‐sectional parameters calculated by combining all hair strands for each hair type.

FIGURE 14.

Boxplots showing the (A–C) CS diameters, (D–F) CSA and (G–I) ellipticity for the different hair types, measured with the FDAS. $\square$ IQR, $\boxminus$ median, $+$ outliers.

TABLE 5.

Cross‐sectional dimensions for the 3 hair types measured with the FDAS.

	Type II	Type IV	Type VI
	($N=496$)	($N=465$)	($N=589$)
Major diameter ($\mu \mathrm{m}$)	68.2 (0.3)	79.3 (0.6)	100.7 (0.6)
Minor diameter ($\mu \mathrm{m}$)	53.6 (0.2)	49.2 (0.2)	58.2 (0.4)
Ellipticity	1.28 (0.0)	1.6 (0.0)	1.7 (0.0)
${\text{CSA}}_{\text{Ellipse}}$ ($\times {10}^2$ $\mu \mathrm{m}$ )	28.7 (0.2)	30.7 (0.3)	46.8 (0.5)

Values represent the average of the concatenated values consisting of 30 points measured along a hair shaft, repeated on 15–18 hair fibres. Uncertainty estimated using the standard deviation of the mean (see Equation 3).

Boxplots showing the distribution of the CSA along the hair strands for the type II, IV and VI hair are given in Figure 14D–F. The type II and IV curl groups showed similar distributions in the CSA between individual hair strands. However, the type VI hair had greater variability in the CSA distribution between hair strands. The variation in the median CSA values between strands increased significantly when moving from the low to high curled hair types. The average CSA (Table 5) for the type II and IV hairs were relatively close, with the latter having a slightly larger value. The largest CSA values was observed in the high curled hair, which also had the most variation between individual strands.

The boxplots in Figure 14G–I show the distribution of the ellipticity in the three hair types. The spread of the ellipticity values in individual hair strands was larger in the type IV and VI hairs. The type IV hair had the most variability in the median ellipticity values between strands.

3.3. Influence of the medulla

The 3‐D model of strand 2 type VI hair revealed an internal cavity that runs intermittently along the centre of the hair fibre (Figure 15A). This cavity may be the medulla due to its location along the hair fibre axis and the relative size compared to the fibre as a whole. The volume of the cavity was measured to be 1.243 $\times$ ${10}^6$ $\mu \mathrm{m}$ , which made up approximately 1% of the total volume of the hair. No internal cavity was observed in the other hair fibres scanned using the micro‐CT.

FIGURE 15.

(A) 3‐D image of the type VI hair fibre (strand 2) showing the medulla (dark purple region) along the length of the fibre (top). Zoomed in image of inset (bottom). (B–D) Light micrographs of three hair types taken from the proximal end, at 20$\times$ magnification.

Light micrographs in Figure 15B–D show the different medullary forms present in the type II, IV and VI hair fibres. For all three hair types, the medulla was observed to be present in some of the hair strands while completely absent in others. For those strands that had a medulla, the overall form varied both along and between strands of the same hair group. The type II and type IV hair had fragmented medulla that were spindle shaped, with variable sized gaps in‐between. The diameter of the medulla changed more frequently moving along the fibre axis. The type VI hair had a fragmented medulla; however, the length of the intact regions was longer and more consistent in diameter along the hair shaft.

A comparison of the hair fibre cross‐section parameters and position of the medulla along the fibre axis is shown in Figure 16. The medulla was observed in strand 2 of the type VI hair which had the largest dimensions out of all the hair strands. The segment of hair scanned using the micro‐CT had a medulla running along the majority of its axis. There were distinct regions where the medulla was highly connected, fragmented or completely absent. From first glance, it would appear that the regions with the larger major diameters (yellow regions in Figure 16B) correspond to fragmented or absent medulla. However, this is not consistent throughout, as there are medullated regions with larger diameters. The minor radius and cross‐sectional area (Figure 16C and D) showed less variation along the hair fibre, with no discernible association with the presence or absence of the medulla and dimension.

FIGURE 16.

3‐D views of the (A) type VI hair fibre (strand 2) showing the medulla, and the corresponding (B) major radius, (C) minor radius and (D) cross‐sectional area along the length of the fibre axis.

4. DISCUSSION

Various studies have used different methodologies and metrics to determine the cross‐sectional parameters of hair fibres. The inconsistencies in the way hair is categorised (race, objective), selective sampling, as well as the environmental conditions the experiments were performed under, make cross‐comparisons with values reported in literature challenging. Very few studies on the quantification of hair fibre geometry have reported according to hair curl type classification schemes. ¹⁵ , ⁴⁹ , ⁵⁰ In the cases where the curl type is not explicitly defined in the literature, and a race‐based classification is applied, we use Asian, Caucasian and African hair as a proxy for very straight (or low curl), wavy (or medium curl) and curly (or high curl) hair, respectively. In this way we can then broadly compare the cross‐sectional parameters determined for the racial‐ and curl‐groups (see Tables 6, 7, 8).

TABLE 6.

Summary of the cross‐sectional diameter ($\mu \mathrm{m}$) values for human hair.

	Asian	Caucasian	Mexican	African
Seta et al. 29	94.28 $\pm$ 3.05	81.94 $\pm$ 2.47		98.23 $\pm$ 2.45
Seta et al. 29 , *	76.79 $\pm$ 2.13	56.74 $\pm$ 1.33		58.52 $\pm$ 1.87
Franbourg et al. 14	86 $\pm$ 1	60 $\pm$ 1		98 $\pm$ 2
Franbourg et al. 14 , *	70 $\pm$ 1	80 $\pm$ 1		55 $\pm$ 2
Wolfram 23	$69-86$	$67-78$		$54-85$
Aslan et al. 49	85.5	68.6	79.5	82.3

	Type II	Type IV		Type VI
Mkentane 15	67	74		74.5

^* All values in table are for the major diameter unless indicated with an asterisk.

TABLE 7.

Summary of the cross‐sectional area ($\mu \mathrm{m}$) values for human hair.

	Asian	Caucasian	African
Franbourg et al. 14	4804 $\pm$ 159	3857 $\pm$ 132	4274 $\pm$ 215
Seta et al. 29	5817 $\pm$ 407	3787 $\pm$ 186	4649 $\pm$ 256
Lasisi et al. 25	7352 (2034)	4266 (980)	4690 (1119)

	Type II	Type IV	Type VI
Mkentane 15	2302–6054	1629–7144	2324–5471
Porter et al. 50		5200	3400–4000

TABLE 8.

Summary of the ellipticity values for human hair.

	Asian	Caucasian	Mexican	African
Franbourg et al. 14	82 $\pm$ 4	76 $\pm$ 4		57 $\pm$ 3
Wolfram 23	1.21–1.36	1.43–1.56		1.67–2.01
Seta et al. 29	82.64 $\pm$ 1.l7	71.16 $\pm$ 1.41		59.96 $\pm$ 1.07
Lasisi et al. 25	1.354 (0.12)	1.402 (0.13)		1.569 (0.14)
Koch et al. 2	$1.17\lambda 1.48$	$1.28\lambda 1.59$		$1.73\lambda 2.11$
Aslan et al. 49	1.27	1.40	1.34	1.62

	Type II	Type IV		Type VI
Porter et al. 50		1.58		1.72–1.74

4.1. Shape and surface morphology of human hair fibres

The results from the curl classification showed a greater intra‐fibre variability in the low and medium curled hair phenotypes compared to the high curled hair. Furthermore, the high curled hair showed more uniformity between hair strands compared to the low and medium curled phenotypes, of which $65\%$ and $66.7\%$ fell within type II and type IV, respectively.

The type II and IV hair fibres had very similar cuticle morphologies, with the scales having relatively smooth edges and being more regularly spaced along the longitudinal axis. The cuticle scales for the type VI hair was more irregular in shape, with the edges having a more jagged appearance. The type IV and VI hair had slightly higher $S_n$ values compared to the type II hair. A similar trend was observed by Hrdy (1973), where Caucasian and Asian hair had similar number of scales/per unit length, compared to African hair which had the highest. ⁸ The scale interval was larger in the type II hair fibres, while the type IV had the lowest values. Studies on the surface structure of blond Caucasian hair, measured using a profilometer, were found to be smaller with values ranging from 5 to 7 $\mu \mathrm{m}$. ⁵¹ The 3‐D models showed perturbations on the surface which were more pronounced in the type II and IV hair models. The surface of the type II and IV models had a ‘smeared’ appearance which did not resemble the cuticle layers observed in the SEM images. This may be due to slight movements of the fibre during the scan. The surface of the type VI model showed smaller perturbations which more closely resembled the overlapping scales seen on the hair cuticle. In all cases, the models could not be used to quantify $S_n$ or scale interval due to the scales being poorly resolved.

4.2. Dimensional analysis of the hair fibre cross‐section

4.2.1. Hair fibre cross‐sectional analysis: micro‐CT

The most significant variation in both the major and minor diameters was found in the type VI hair. Strand 3 of the type VI hair showed the same variability trend along the hair fibre as seen in the other two hair strands. However, the values for the major diameter were comparable to those found in the other two hair types, while the minor diameter values were smaller. The type VI hair strands had noticeable changes in the major and minor axis which is related to the regions where the hair fibre forms twists. ¹⁴ This is consistent with the findings of Kamath et al. (1984), who found that the cross‐sectional shape of the hair shaft changes significantly in the regions of the twists. ²⁷ In these regions, the hair will flatten and change direction. ⁸ , ²⁷ On visual inspection of the hair fibres, the twists were found to repeat every 3–5 mm. However, Figure 9C does not show maxima and minima values for the diameter repeating at specific intervals along the hair fibre. For all hair types, the variation in the minor diameter was less pronounced compared to the major axis.

A similar trend was observed by Mkentane, where the mean diameters for hair type II was found to be significantly lower than groups I, V and VI, and comparable to type IV. ¹⁵ However, the type IV hair mean diameter was similar to the type VI. The difference between the average major and minor diameters increased by a factor of 2 in the high curled hair. Other studies have shown a similar increase in the size difference between the major and minor diameters in African and Caucasian hair. ¹⁴ , ²⁹ , ³⁰ The mean diameter values (shown in Table 4) were larger than those reported for Caucasian and African hair types. ²³ , ⁴⁹ However, both the major and minor diameters for the type II hair had very similar values to those measured on Caucasian hair by Hutchinson et al. and Franbourg et al. ¹⁴ , ³⁰

The CSA values for the type II and IV hair had a more uniform distribution; however, there were slight differences in the mean values between strands (Table 4). The most significant variation in both the ${\text{CSA}}_{\text{Ellipse}}$ and ${\text{CSA}}_{\text{contour}}$ was observed in the type VI hair. The CSA values for the type VI hair showed maxima and minima at irregular intervals along the hair fibre, with the largest changes occurring along strand 2. In all three hair types, the ${\text{CSA}}_{\text{Ellipse}}$ was always slightly larger than the ${\text{CSA}}_{\text{contour}}$ which indicates that the fitted ellipse model may be overestimating the geometrical parameters for the fibre CS. In addition to this, the ${\text{CSA}}_{\text{contour}}$ had less variation along the fibre length compared to the ${\text{CSA}}_{\text{Ellipse}}$ values.

Porter et al. (2009) found an inverse linear relationship between the CSA and the curlier hair groups (type IV–VIII). ⁵⁰ The CSA values were lower for the curlier hair types, with a smaller range reported. This differs from the study by Mkentane (2016), who observed a considerable overlap in the CSA values between all curl groups. ¹⁵ Statistical analysis revealed the type II hair to be significantly different from the type I and V. ¹⁵ The one exception was the CSA values for hair strand 1 and 2 of the type VI hair, which fell outside the ranges reported by Mkentane (2016). The mean CSA values reported for African hair tended to be lower than those found for the type VI hair (Table 4). ¹⁴ , ²⁵ , ²⁹ , ⁵⁰ However, the type II CSA values are in better agreement with those same studies. Based on the Bland–Altman analysis, the ellipse model is shown to not be an accurate approximation for the hair fibre CS. Therefore, using the nearest contour to estimate the dimensional parameters may be more accurate given that the fibre cross‐section can vary between circular and elliptical depending on the hair type. Previous studies have observed the cross‐sectional shape to be highly variable along the a single hair fibre. ²⁷ , ²⁹ The ellipticity range showed considerable overlap between the curl groups. The ranges for the type II and VI were larger than those reported by Wolfram and Koch, for Caucasian and African hair. ² , ²³

4.2.2. Hair fibre cross‐sectional analysis: laser micrometre

The difference in the average major and minor diameter is observed to increase with increasing curvature. The increase in the difference between the major and minor diameter has been observed between Caucasian and African hair. ¹⁴ , ²⁹ The fibre diameter for African and Caucasian hair was previously shown to have considerable overlap in their distributions. ⁴⁹ The minor diameter values for the three hair types were relatively similar. On the other hand, the mean major diameter increased moving from the low to high curled hair. This trend is consistent with what was observed by Mkentane (2016); however, the values for the type VI hair measured in this study were larger. In the same study, there was no significant difference between the type VI and type IV hair. ¹⁵ The diameter values for the type IV and VI hair were in good agreement with those determined from the 3‐D models; however, the type II hair had a slightly smaller value. The range values for the major and minor diameters were comparable with those reported for Caucasian and African hair. ⁸ , ¹⁴ , ²⁹ , ⁵² Previous studies on the hair fibre diameter from a single head of hair have shown the inter‐fibre variability. ⁵² , ⁵³ Yin et al. found that hair strands from a Caucasian individual could be separated into 3 groups based on a specified diameter range. ⁵² The distribution in the average diameter between hair strands from the same individual head could be linked to the stage of the hair cycle the hair was sampled. ²⁸ , ²⁹ , ³⁰

All three hair types showed considerable overlap in their CSA ranges. Another study, which used the FDAS to measure the fibre dimensions, also found sizeable overlap in the CSA distributions between different curl types. ¹⁵ The CSA values determined from the 3‐D models were similar for the type IV hair, but smaller in the type II and type VI hair. The CSA values were in agreement with those reported in other studies. ¹⁴ , ¹⁵ , ²⁵ The decrease in the CSA with increasing curl type (IV–VIII), as reported by Porter et al. (2009), was not observed. ⁵⁰

It can be seen that as the curvature increases, the variation in cross‐sectional shape along individual hair strands increases. The overall distribution of the ellipticity values from each head hair type showed considerable overlap. The type VI group skewed towards the higher elliptical values, whereas the type II towards the lower values. Interestingly, the type IV hair had ellipticity values spread over both the type II and VI ranges. Previous studies did not show this overlap in Caucasian and African hair; however, the ranges were in agreement with those found in this study. ² , ¹⁴ The study by Aslan et al. (2019) showed an overlap in the distribution for Caucasian, Asian, Mexican and African hair, with the latter being heavily skewed to the the higher elliptical values. ⁴⁹ The mean ellipticity data for the type II hair strands shows the cross‐section to be more circular to oval in shape, whereas the type VI hair has a more ‘flattened’ CS. The type IV hair showed the most variation in the CS shape, with individual strands varying between more circular to ‘flattened’ ellipse. The average ellipticity values for the three curl types were in good agreement with those determined from the 3‐D models.

It can be seen in Table 2, the type II and IV head hairs can be classified into more than one curl group, with the latter falling within the highest number of groups (II–VI). The differences in the shape of individual hairs from the same head may explain the variation observed in the cross‐sectional parameters. The type VI hair also shows a great deal of variation in the cross‐section both between and within hair strands from the same head. The hair classification showed a more homogeneous form for the type VI hair, even though there is considerable variation between hair strands. This may be due to using the 6‐group instead of a 8‐group classification, which may not fully resolve the differences in the hair form between strands. The variation observed within individual strands is related to the change in the hair diameter due to the twists. In addition to this, the stage of the hair cycle the hair was in when it was sampled should be noted, as this may also influence the variability observed along the hair fibre.

4.3. Influence of the medulla

An internal cavity running intermittently along the centre of the type VI hair model was speculated to be the medulla. The models of the type II and IV hair did not show a medulla. This could be due to the medulla being absent at the specific location scanned along the fibre, or from the fibre as a whole. Scalp hair medulla are highly variable structures which can be completely absent, fragmented or continuous along the hair shaft. ⁴⁴ Wagner et al. (2006) proposed that two types of medulla could be identified based on the thickness, which was determined by electron microscopy observations. ⁵⁴ The variability in the medulla profile has been observed both within and between population groups, as well as along individual fibres. ⁸ , ⁵⁵ , ⁵⁶ , ⁵⁷

The relationship between medullary types and hair form (straight, smooth, flat wavy, broad wavy, narrow wavy, frizzly) in different tribes in India was investigated by Banerjee (1965). ⁵⁵ All three medullary types were observed at different frequencies within each group. The fragmented medulla had the highest proportion, while the continuous medulla was observed the least amongst the different groups.

The inconsistency in the presence of the medulla could be due to the particular stage of the hair growth. A study by Hutchinson and Thompson looked at the cross‐sectional profile of the medulla over the anagen and telogen stage of the hair growth cycle. ⁵⁷ They found that the medulla form was continuous in the early stages of anagen, thereafter, becoming progressively more fragmented moving towards the proximal end. The medulla was largely absent or highly fragmented close to the telogen bulb. The authors concluded that the medulla was largely influenced by the hair cycle. The medullary form over the entire hair shaft could not be ascertained for this study, as only hair closest to the root end was kept for analysis. Therefore, the hair that was collected would have been at different stages of the hair cycle.

There does not appear to be a correlation between the medullary forms and dimensions of the fibre cross‐section. One drawback was the dimensions of the medulla cross‐section could not be measured. This would have helped in determining the extent of the size relationship between the medulla and fibre cross‐section. This result is contrary to other studies which have looked at the relationship between the fibre diameter and medullary type. ⁸ , ⁵⁶ , ⁵⁷ Hrdy (1973) observed a positive correlation between hair diameter and medullation in individuals from different populations and hair curl type. The frequency of medullation followed with an increase in the hair cross‐sectional diameter, which was highest in the Asian groups followed by the African and European groups. A similar study done on various Indian tribes found the same correlation. ⁵⁶ Another study by Hutchinson and Thompson (1999) was able to generate a profile of the medullary form along a whole hair fibre. They found the medulla cross‐section increased in size moving from the telogen bulb to the anagen tip. Similarly, the shape (ellipticity) of the medulla changed from elliptical to circular moving from the proximal to distal end. A positive correlation between the size of the medulla and size of the whole hair shaft was observed. ⁵⁷

5. CONCLUSION

Micro‐CT is an highly efficient technique in that a number of hair form descriptors are able to be extracted from a single data set. Unlike other methods which involve 2‐D image analysis, micro‐CT was able to produce high resolution 3‐D images of hair fibres in their natural form. The CS geometry along the hair model was approximated by fitting an ellipse. The hair fibre CS shape showed large variation along the hair fibre, especially for the higher curled hair. The ability to virtually section the hair models allows for more control over selecting as close to the true CS. Using the ellipse model may not fully account for the changes in the CS that deviate beyond the circular/elliptical shapes.

Overall, the sensitivity at a 2 $\mu \mathrm{m}$ resolution was not able to resolve the overlapping scales on the surface of the hair fibre, however it was able to elucidate the medulla within the curly hair fibre. The medulla was found to be highly variable along the hair fibre, however further studies are needed to determine any correlation between hair diameter and the medulla.

The sample size for this study was limited which made it difficult to statistically compare the hair descriptors for different curl groups. Future work would be to expand the curl range and increase the sample size in order to discern the relationship between hair descriptors within and between curl groups. Other factors such as the age, sex and stage of the hair growth should also be taken into account when sampling hair.

Supporting information

Supporting Information

Berg, C. v. d. , Khumalo, N. P. , & Ngoepe, M. N. (2025). Quantifying whole human hair scalp fibres of varying curl: A micro‐computed tomographic study. Journal of Microscopy, 297, 227–251. 10.1111/jmi.13365