1. Introduction

From a medical, social, economic and environmental perspective, human milk is the optimal source of nutrition for infants in early life [1,2]. Millions of years of evolution have adapted human milk composition to optimally support infant survival, growth, health and cognitive development [3]. Abundant evidence demonstrates that breastfeeding protects infants against many types of infections, diarrhea and dental malocclusions, and increases intelligence [1]. Also mothers benefit from breastfeeding, since it reduces the risk for breast cancer and improves birth spacing [1]. As a consequence, the deaths of 823,000 children and 20,000 mothers can be averted annually if all mothers worldwide would breastfeed their infants [1].

But despite all of this evidence, worldwide breastfeeding rates do not comply with the advice of the World Health Organization for mothers to exclusively breastfeed their infants until the age of 6 months, followed by continued breastfeeding with complimentary foods until a minimum age of 2 years [4]. In many high-income countries, breastfeeding rates at the age of 1 year are less than 20%, with less than 1% in the United Kingdom. The most important reasons for mothers to abandon breastfeeding are the perception of insufficient milk supply (PIM) and pain due to breastfeeding problems [5]. Besides many political and cultural challenges, solving this issue also involves a crucial responsibility for scientific research. Compared to other fields of medical research, the scientific activity on human milk and lactation research is underrepresented [6]. Nevertheless, for those mothers who experience breastfeeding problems, lactation support will benefit from a better scientific understanding on lactation physiology and pathology, as well as human milk composition and function.

Photonics offers many promising opportunities for the development of objective methods for the investigation of human milk and lactation, which to date have remained largely unexplored. Technologies like near-infrared spectroscopy (NIRS) [7], laser Doppler perfusion monitoring (LDPM) [8,9], diffuse optical imaging (DOI) [10] and photoacoustic mammography (PAM) can potentially provide important new insights into the dynamics of mammary tissue composition and the hemodynamics of lactation. In turn, these factors can be related to milk synthesis, milk removal from the breast and the development of breastfeeding problems, such as mastitis. Regarding human milk analysis, chemically highly specific optical technologies such as Raman spectroscopy have only been marginally explored for this purpose [11–14]. Human milk macronutrient analysis with NIRS is commercially available, but the technology needs to be improved for its main purpose of personalized human milk fortification in premature infants [15]. Therefore, it leaves no doubt that the biophotonics research community has a valuable opportunity to explore this important new area of application.

Comparable to any other application field in biophotonics, the optical investigation of both human milk and the milk containing lactating breast starts with a thorough understanding of how light interacts with human milk itself, which requires knowledge on its currently unexplored optical properties. These optical properties are essential for the prediction, modelling and interpretation of light tissue interactions. From studies on bovine milk, we know that the predominant scattering particles in milk are the fat globules (up to around 11 µm in diameter), followed by the casein micelles (around 200 nm in diameter) [16,17]. It is expected that a large variation exists within the normal range of optical properties of human milk, since human milk varies considerably in fat content between mothers, within individual mothers over the course of lactation, between consecutive feedings, and even within a single breastfeed [18]. The latter is caused by the fact that the milk released at the onset of a breastfeed (foremilk) generally has a lower fat concentration than the milk released at the end of a breastfeed (hindmilk). As a consequence, fat concentrations in human milk have been reported to vary between approximately 5 and 100 g/kg [15,18].

The aim of this study is therefore to provide a full set of the optical properties of human milk. Using a novel combination of spectroscopic optical coherence tomography (sOCT) and spatially resolved diffuse reflectance spectroscopy (SR-DRS), we quantify the absorption coefficient µ_a, the scattering coefficient µ_s, backscattering coefficient µ_b,NA, reduced scattering coefficient µ_s’ and scattering anisotropy g in the visible wavelength range (450 – 650 nm) of the foremilk, bulk milk and hindmilk from 14 volunteers. Since fat globules are the predominant scattering particles in human milk, we explain the biological variation in optical properties between milk samples using Mie theory, the biochemically determined fat concentration, and the fat globule size distribution per sample.

2. Materials and methods

2.1 Participants

The study population included healthy, breastfeeding mothers of term infants across the Netherlands. Between April and August 2018, a total of 16 women between 2 and 9 months of lactation were included (Table 1). The study was approved by the Committee on Research Involving Human Subjects (CMO Arnhem-Nijmegen, The Netherlands), and all participants gave written consent prior to the study.

Table 1. Participant information.

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2.2 Acquisition of human milk samples

All participants followed a step-wise protocol for milk extraction, during which they collected 2x 1 mL of foremilk, 2x 1 mL of bulk milk and 2x 1 mL of hindmilk. The 1 mL milk samples were stored in two separate containers: one for the optical property measurements and one for the biochemical determination of fat concentration. The participants used their own breast pump for single-side milk expression on the breast that had not been emptied for the longest period of time. Most participants collected the samples autonomously, but optional support was provided by a researcher upon request of the participant herself.

The protocol involved the following steps: 1) after expression of the first 5 mL, the participant interrupted the milk expression to collect 2x 1 mL of the foremilk, 2) milk expression was resumed until the breast had almost been emptied completely, after which milk expression was interrupted again, and 3) the last 5 mL were collected in a separate milk container, from which the participant collected 2x 1 mL of hindmilk. The 2x 1 mL of bulk milk was collected from the total expressed milk volume. After cooled transport, the collected samples were stored at −18 °C for a maximum period of 10 months, until the measurements were performed. The milk samples from two participants (#2 and #3) were excluded from this study, due to a deviation from the sample collection procedure. Therefore, this study included milk samples from 14 participants, leading to a total of 42 milk samples for optical property determinations.

2.3 Sample preparation for optical property measurements

After thawing the milk samples in a water bath at 20°C, the samples were homogenized by inverting them by hand, followed by pipetting the entire sample volume up and down several times. Automated homogenization methods such as sonification or vortexing were not used, as these may change the size of the fat globules, which can affect the optical properties [15,19].

High fat concentrations can hinder successful determination of the optical properties, either due to the contribution of multiple scattering to the sOCT signal [20,21], or due to high signal losses in the diffuse reflectance setup. Therefore, strongly scattering milk samples were diluted with phosphate buffered saline (PBS) until µ_s < 6 mm⁻¹ or µ_s’ < 1 mm⁻¹ at 550 nm – i.e. values for which the measured optical properties scaled linear with the dilution factor. Assuming concentration independence for single scattering events, the optical properties of the original sample were retrieved by rescaling the measured optical properties with the dilution factor. All optical property measurements were performed in triplo.

2.4 Determination of fat concentration

A modified Mojonnier ether extraction method for human milk sample volumes of around 1 mL was used to determine the fat concentration of all samples [22]. In short, the total mass of the milk sample was registered, followed by dissolving the milk fat globules in ether. After centrifuging, a fat containing ether layer was formed. Isolation of this layer, followed by evaporation of the ether allowed for measurements of the mass of the remaining fat. As a result, the fat concentration was expressed in grams of fat per kilogram milk. The coefficient of variation for this procedure was determined by the in triplo measurement on an extra bulk milk sample (>3 mL) that was additionally donated by one of the participants.

2.5 Spatially resolved diffuse reflectance spectroscopy (SR-DRS)

SR-DRS is an effective method for the determination of the reduced scattering coefficient µ_s’ and absorption coefficient µ_a [23]. We used a home-built fiber-based SR-DRS system (Fig. 1(a)), in which a 400 µm core diameter multimode fiber (FT400EMT, Thorlabs, Newton, NJ, USA) guided light from a halogen light source (AvaLight-Hal, Avantes, Apeldoorn, The Netherlands) to the sample. A second 400 µm core diameter multimode fiber (FT400UMT, Thorlabs, Newton, NJ, USA) guided the diffusely reflected light from the sample to a spectrometer (AvaSpec-2048, Avantes, Apeldoorn, The Netherlands). The tips of both fibers were immersed directly under the sample surface. The source-detector distance r was varied by translation of the detection fiber by a motorized stage (T-LS28M, Zaber Technologies, Vancouver, Canada) from r₀ = 2.2 mm to r_end = 4.7 mm in steps of 50 µm. The integration time was set such that the diffuse reflectance at r₀ filled approximately 80% of the dynamic range of the spectrometer. The dark noise was measured by obtaining a spectrum without sample illumination.

 

Fig. 1 Schematic overview of the optical methods used to determine the full set of optical properties. a) Illustration of the SR-DRS setup. Light from the illumination fiber diffuses through the sample, which can be detected as a function of inter-fiber distance r by translation of the detection fiber. b) Schematic overview of the sOCT setup. c) Flowchart of the experimental and numerical methods in this study, with the optical properties they provide. MMF: multi mode fiber, r: source-detector distance, MS: motorized stage, NDF: neutral density filters, L#: lens #, BS: beam splitter, DCG: dispersion compensation glass, PDM: piezo driven mirror, C: cuvette with sample, SMF: single mode fiber.

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2.5.1 Reduced scattering coefficient (µ_s’) and absorption coefficient (µ_a)

The reduced scattering, and absorption coefficient were estimated by following the method of Farrell et al. [23] This diffusion theory based model describes the diffuse reflection R_theory as a function of r and the optical properties µ_a and µ_s’:

First, by assuming negligible optical absorption between 530 – 650 nm for human milk, µ_s’ was retrieved in this wavelength range by fitting Eq. (2) to the dark noise corrected R_meas(r):

In case the model validity limit (r > 1/[µ_s’ + µ_a]) was not met, r₀ was increased until the condition is satisfied. r_end was kept constant throughout this work.

2.6 Spectroscopic optical coherence tomography (sOCT)

sOCT is an effective method for the spectrally resolved determination of the scattering coefficient µ_s and backscattering coefficient µ_b,NA, as we have demonstrated for a wide range of scattering samples (µ_s = 0.15–34 mm⁻¹, µ_b,NA = 2.10⁻⁶–2.10⁻³ mm⁻¹) in our previous work [20,25]. We used a broadband Michelson interferometer-based sOCT system, which measured the low-coherent interference between the backscattered light from the sample and a reference beam (Fig. 1(b)). Short time Fourier transformation with a spectral resolution of 5 nm resulted in a spatially and spectrally confined data set of the backscattered intensity from the sample S(λ,d) with a spatial resolution ranging from 15 µm (at λ = 450 nm) to 31 µm (at λ = 650 nm). The lateral resolution of the system was 2.5 µm in air. Our system combined focus tracking with zero-delay acquisition, which ensures that the measured attenuation of S(λ,d) as a function of sample depth d is only affected by the optical attenuation of the sample itself. A detailed description of our sOCT system is given in Veenstra, et al. [26]. In short, focus tracking was achieved by translation of the sample lens with respect to the sample. Zero-delay acquisition at all investigated depths within the sample was achieved by filtering out the DC component and mirror image from the Doppler shifted signal, by an oscillating reference mirror.

2.6.1 Scattering coefficient (µ_s)

Under the assumption of single scattering, the sample’s attenuation spectrum (µ_t = µ_s + µ_a) can be quantified by fitting Beer’s law to S(λ,d) [20]:

2.6.2 Backscattering coefficient (µ_b,NA)

The backscattering coefficient of the sample within the NA = 0.08 of the sOCT system can be obtained from α(λ) in Eq. (4). Hereto, it is assumed that α(λ) consists of two factors [20]:

2.6.3 Anisotropy (g)

The anisotropy factor g was obtained indirectly by combining the results from µ_s and µ_s’ (Fig. 1(c)), following:

2.7 Mie theory

Besides the experimentally derived optical properties, we used Mie-theory calculations in MatScat [27,28] to investigate the influence of the fat globule size distribution, as well as the less dominant scattering contribution by casein on the optical scattering properties of human milk. Hereto, milk was modeled as a suspension of scattering casein micelles and fat globules in whey with refractive index n_whey = 1.345 [29]. The concentration of casein micelles N_cas and their scattering cross section σ_cas were approached by modelling casein micelles as monodisperse homogeneous spheres with the average properties of bovine casein micelles [16,17,30]: diameter d_casein = 200 nm and n_casein = 1.5, as literature values for human milk casein micelles were unavailable. The concentration of casein micelles was fixed to the average concentration for human milk (1.68 mL/L [31]), since casein concentrations do not vary significantly between foremilk, bulk milk and hindmilk [18]. To account for the high amount of variation in fat globule scattering between milk samples, we used the sample dependent fat globule size distribution as an input for our Mie calculations. All Mie calculations were performed at 550 nm.

2.7.1 Fat globule size distribution

Fat globule size distributions with 0.5 µm bins were obtained from 3 bright field microscopic images per sample (EVOS FL Cell Imaging System, Thermo Fisher, MA, USA). Images were processed by Matlab (2015b, Mathworks, MA, USA) using the built-in function ‘imfindcircles’ to retrieve particle diameters. To investigate the variation in fat globule size distributions between participants and milk samples, the centroid of the size distribution was calculated for every sample. The average size distributions for foremilk, bulk milk and hindmilk were used as an input for the Mie-calculations. To evaluate the variation in optical properties due to variations in size distribution, Mie-calculations were also performed for the size distributions of the individual samples.

Furthermore, we investigated the relation between fat globule size and the scattering properties of human milk. Hereto, we first normalized the scattering properties of all individual samples with their fat concentration, ruling out the influence of fat concentration on the scattering properties. Subsequently, we calculated the correlation between the normalized scattering properties with the centroid diameter.

2.7.2 Mie calculations of optical properties

Fat globules were modeled as homogeneous spheres [32,33] with n_fat = 1.46 and Mie calculations were performed independently for every fat globule diameter i in both the individual, and the average fat globule size distribution per milk type, resulting in scattering cross section σ_s,fat,i and phase function P(ϴ)_fat,i. The amount of fat globules with diameter i per volume N_fat,i was calculated using densities of 0.92 g/ml [34] and 1.03 g/ml [35] for fat and milk, respectively. The scattering coefficient of each milk sample was calculated by a summation of the individual contributions of all scattering particles:

3. Results

3.1 Experimentally derived optical property spectra

The median spectra and their range of variation for all experimentally derived optical properties are shown in Fig. 2 for foremilk, bulk milk and hindmilk. The absorption coefficient shows a peak around 460 nm, which can be ascribed to absorption by riboflavin or beta-carotene. Values of µ_a at 460 nm (µ_a,460nm) range between 1.1 x 10⁻² to 8.3 x 10⁻² mm⁻¹. The absorption shows an increasing trend with milk type: from foremilk, to bulk milk and hindmilk, the median µ_a,460nm increases from 1.7 x 10⁻² mm⁻¹, to 2.6 x 10⁻² mm⁻¹ and 4.7 x 10⁻² mm⁻¹.

 

Fig. 2 Experimentally derived optical property spectra for foremilk, bulk milk and hindmilk. Thick, solid lines represent the median values for all participants, dashed lines represent the 25th and 75th percentiles, and dash-dot lines represent the minimum and maximum values (0th and 100th percentile).

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Also the measured scattering properties µ_s, µ’_s and µ_b,NA vary considerably between samples, with a total range at 550 nm in µ_s,550nm = 2.6 – 21.0 mm⁻¹, µ’_s,550nm = 0.24 – 2.48 mm⁻¹, and µ_b,NA,550nm = 1.1 x 10⁻⁴ – 1.6 x 10⁻³ mm⁻¹. Overall, the value of scattering properties µ_s, µ’_s and µ_b,NA increase with milk type: from foremilk, to bulk milk and hindmilk, the median µ_s,550nm increases from 4.9 mm⁻¹, to 9.7 mm⁻¹ and 15.7 mm⁻¹, the median µ’_s,550nm increases from 0.44 mm⁻¹, to 0.79 mm⁻¹ and 1.58 mm⁻¹, and the µ_b,NA,550nm varies from 4.1 x 10⁻⁴ mm⁻¹, to 4.0 x 10⁻⁴ mm⁻¹ and 4.5 x 10⁻⁴ mm⁻¹. Large variations can be observed within milk types (foremilk, bulk milk and hindmilk), with differences between the lowest and highest bulk milk values amounting up to a factor 4.5, 6 and 6 for µ_s,550nm, µ_s’_,550nm, and µ_b,NA,550nm, respectively. The measured µ_s spectra have a curved shape with an increase in µ_s beyond 600 nm.

The scattering anisotropy g_550nm ranges from 0.82 to 0.96. Results are similar for the three milk types with median g_550nm values of 0.91, 0.92 and 0.90 for respectively foremilk, bulk milk and hindmilk. Foremilk shows less variation in anisotropy between participants, compared to bulk milk, and hindmilk.

3.2 Fat globule size distributions

Figure 3(a) shows the average fat globule size distributions per milk type, normalized to the sum of fat globules per milk type. The average size distributions of foremilk, bulk milk and hindmilk all have a maximum around a particle diameter of 5 µm and smaller, local maxima around particle diameters of 1.75 µm and 10.5 µm. Figure 3(b) shows the centroid diameter for every sample per participant. For ten out of fourteen participants, foremilk has the smallest centroid diameter and hindmilk has the largest centroid diameter. The average centroid diameters are 5.2 µm, 5.6 µm and 6.2 µm for foremilk, bulk milk and hindmilk respectively.

 

Fig. 3 Fat globule size distributions and concentration. A: Average fat globule size distribution for foremilk, bulk milk and hindmilk, normalized with the total amount of particles. B: Centroid diameter of the fat globule size distribution for every sample within this study (error bars represent standard deviations). C: biochemically determined fat concentration per participant and sample (error bars represent the coefficient of variation in the fat determination). Participant 2 and 3 were excluded from the analysis, due to deviation from the sample collection procedure.

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After normalizing the optical properties of all individual samples with their fat concentration, the centroid diameter of the fat globule size distribution showed weak, but significant correlation with scattering coefficient µ_s (R_s = −0.43, p < 0.01), anisotropy g (R_s = −0.62, p < 0.01) and backscattering coefficient µ_b,NA (R_s = −0.44, p < 0.01). No significant correlation was found between centroid diameter and µ_s’ (R_s = −0.20, p = 0.20).

3.3 Optical properties versus fat concentration

Similar to our findings on the optical properties, fat concentrations vary considerably between milk types and participants, with a range of 3.6 – 20.6 g/kg (median 14.0 g/kg), 8.6 – 64.2 g/kg (median 24.4 g/kg) and 13.4 – 95.6 g/kg (median 52.5 g/kg), for foremilk, bulk milk and hindmilk, respectively. For individual participants, foremilk consistently has the lowest, and hindmilk had the highest fat concentration (Fig. 3(c)). Figure 4 shows the measured optical properties for all samples as a function of fat concentration. The precision of our methods is indicated by the error bars, representing the standard deviation of the triplo measurements per sample. To reduce the influence of measurement noise, µ_a was averaged between 450 – 470 nm, and all other optical properties were averaged between 530 – 570 nm. The coefficient of variation for the fat determination procedure was 8%, as indicated by the horizontal error bars in Fig. 4.

 

Fig. 4 Optical properties versus fat concentration – experimental data and Mie calculations. The experimentally derived absorption coefficient was averaged between λ = 450 – 470 nm, and all other experimentally derived optical properties were averaged between λ = 530 – 570 nm. Vertical error bars represent standard deviations. Mie calculations were performed at λ = 550 nm using the average size distributions of all foremilk, bulk milk and hindmilk samples. The Mie theory upper and lower limit are based on the size distributions of individual samples. Horizontal error bars represent the coefficient of variation in the biochemical fat determination.

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The scattering properties µ_s and µ_s’ increase significantly with fat concentration (Spearman correlation coefficient R_s = 0.77, p < 0.01 and R_s = 0.80, p < 0.01, respectively). For µ_a and µ_b,NA the correlation with fat concentration is less pronounced, but still significant (R_s = 0.38 and R_s = 0.44, p ≤ 0.01, respectively). As expected, the scattering anisotropy g does not correlate with fat concentration (R_s = −0.02, p = 0.88).

The age of the mother, lactation period and time since last breastfeed showed no significant correlation with fat concentration (all p > 0.05).

3.4 Mie-calculations of optical scattering properties

The Mie-calculated optical properties based on the average fat globule size distributions of foremilk, bulk milk and hindmilk are indicated by the dashed lines in Fig. 4. Due to the modeled scattering contribution of casein, Mie theory predicts µ_s = 0.57 mm⁻¹ and µ_s^’ = 0.34 mm⁻¹ for a fat concentration of 0 g/kg. The upper and lower limits of the Mie-calculated values for the size distributions of individual samples are indicated by the dotted lines in Fig. 4. Overall, the experimental results and Mie calculations are in the same order of magnitude and are showing similar variation between samples for both µ_s and µ_s’.

Mie theory predicts that the anisotropy of casein micelles is g_cas = 0.41. For high fat concentrations, the Mie-calculated g approaches an asymptotic value given by the anisotropy of fat globules alone. Measured g values and Mie calculations agree well for fat concentrations lower than 50 g/kg. For higher fat concentrations, Mie calculations tend to overestimate the measured g.

According to Mie theory, the casein contribution to the total backscattering coefficient is µ_b,NA,cas = 2.3 x 10⁻⁴ mm⁻¹. On average, our Mie calculations tend to overestimate the experimentally obtained µ_b,NA.

4. Discussion

In this study, we measured the optical property spectra (µ_a, µ_s, µ_s’, g, µ_b,NA) of human milk by combining SR-DRS and sOCT, and investigated the dependency of the optical properties on fat concentration. We compared our experimental results to Mie calculations, using the fat globule size distributions of the investigated samples. The combination of SR-DRS and sOCT allowed for measurements of a full set of optical property spectra, whereas SR-DRS and sOCT individually can only provide single sets of µ_a and µ_s’, or µ_t and µ_b,NA, respectively. Knowledge of the full set of these optical properties will facilitate future studies that aim to investigate light tissue interactions with human milk, or the milk containing lactating breast.

Fat concentrations varied considerably between milk samples (3.6 to 95.6 g/kg). Our results are consistent with literature, where human milk fat concentrations of approximately 5 – 100 g/kg have been reported [15]. Furthermore, the observed differences in fat concentrations between foremilk, and hindmilk (median values of 14.0 to 52.5 g/kg) are also similar to the variations reported in literature [18].

The fat globule size distributions that we obtained by bright field microscopy have a maximum at 5 µm and show a smaller local maximum at 10.5 µm, which is in good agreement with the bulk milk size distributions that have been measured using dynamic light scattering [36,37]. To our knowledge, the differences in fat globule size distributions between foremilk, bulk milk and hindmilk have not yet been described in literature. Limited by the settings of our microscopic measurements, we were unable to identify particles smaller than 1.5 µm, which may explain the local maximum at 1.75 µm in our fat globule size distributions. Although this neglects a considerable amount of fat globules, these smallest fat globules only account for a few percent of the milk’s volume [36]. As a consequence, our Mie calculations predict that these smallest fat globules have a negligible effect (<2%) on the scattering properties of human milk.

From the composition of human milk [31] it is expected that riboflavin and beta-carotene are the main contributors to the absorption between 450 – 530 nm [38,39]. Although fat is also a chromophore in this spectral region, it contributes for only ~1% to the measured absorption in the present concentrations [40]. Nevertheless, a significant correlation between the absorption coefficient and fat concentration was found, which can be explained by the high solubility of beta-carotene in fat [31].

Whereas the measured absorption coefficient of human milk is similar to that of bovine milk, the measured scattering properties (both µ_s and µ_s’) are lower than those of bovine milk [16]. We explain this difference by higher concentrations of fat in bovine milk [41] compared to our fat estimations in human milk, as well as lower casein concentrations in human milk [31] compared to bovine milk [41]. Similar to bovine milk, scattering by human milk increases from foremilk towards hindmilk and shows a lot of variation between individuals [16].

As demonstrated in our previous work, the accuracy of sOCT in the determination of µ_t and µ_b,NA is approximately 10% [20], and the accuracy of SR-DRS in the determination of µ_a and µ_s’ is approximately 15% and 10% respectively [24]. Since µ_s and g were estimated by combining the results from both SR-DRS and sOCT, inaccuracies in either of these methods will propagate in the results for µ_s ( = µ_t - µ_a) and g ( = 1 - µ_s / µ_s’). However, as µ_a is approximately two orders of magnitude smaller than the measured µ_t by sOCT, any errors in the estimation of µ_a will be negligible in the determination of µ_s through µ_s = µ_t - µ_a. As g depends on the ratio between µ_s and µ_s’, the propagating error in g is more substantial than for the other optical properties, amounting to an accuracy of approximately 14% with a precision of approximately 7% (error bars, Fig. 4). Considering the spread in optical properties in both the experimental (Fig. 2) and numerical results (Fig. 4), the accuracy of our experimental methods was sufficient to map the full range of optical properties. The curved shape of the measured µ_s spectra (Fig. 2) with an increase in µ_s beyond 600 nm can be explained by the fat globule size distributions of the milk samples, as Mie theory also predicts an increase in µ_s with wavelength beyond 600 nm. Our assumption on the power law dependency of µ_s’ on wavelength remains valid, as Mie-theory does not predict this increase with wavelength for µ_s’.

To avoid the influence of multiple scattering, strongly scattering milk samples were diluted prior to the measurements. Retrieving the optical properties of the original samples by rescaling with the dilution factor can introduce an overestimation of the actual scattering properties if concentration dependent scattering occurs [21]. However, the effects of concentration dependent scattering are lower than the precision of our measurements, given the volume fraction and diameter of the major scatterers in the milk samples (fat globules of around 5 µm) [21].

Overall, our experimental results are described well by our Mie calculations (Fig. 4). However, some experimental data points fall outside of the upper and lower limits of our Mie calculations. This may be caused by: I) The fixed concentration and particle size of casein for all Mie calculations. In reality, both concentration and particle size are likely to vary across samples, resulting in different outcomes for the casein contribution to the optical properties across samples. II) The assumption of scattering by homogeneous spheres in Mie theory. This is a simplification of fat globule and casein micelle structure, as fat globules consist of a lipid core surrounded by a phospholipid membrane [42] and casein micelles are composed of a complex of proteins and calcium phosphate [43]. III) For some of the input parameters in our Mie-calculations (casein diameter d_casein, casein refractive index n_casein, fat refractive index n_fat), we used values for bovine milk, since no literature values for human milk are available. These parameters may be different for human milk. IV) The refractive index of whey is assumed constant, while variations in whey composition may result in variations of the whey’s refractive index. The refractive index for skimmed bovine milk [44] has been reported to vary between 1.345 and 1.348. Mie calculations show that this variation in refractive index may alter µ_b,NA up to 15%, while the effect is negligible for the other scattering properties (< 1%). In general, µ_b,NA estimations are very sensitive to small deviations from any of the assumptions mentioned in this paragraph, due to the fact that only 2.5% of all possible scattering angles was investigated to retrieve µ_b,NA (NA = 0.08). This leads to a larger variation in experimental results than can be explained by the variation in size distributions using Mie-theory.

This study gives a thorough overview of the optical properties of mature milk, which is produced by the mammary gland after approximately 2 weeks postpartum [31]. Up to 3-4 days postpartum, the mammary gland produces colostrum, followed by a period with transitional milk until mature milk is produced. The scattering properties of colostrum and transitional milk are expected to be different from mature milk, as fat globules in colostrum are smaller [36] (diameter of around 2 µm) and fat concentrations are lower [45]. Furthermore, the bright yellow appearance of colostrum implies that absorption also plays a more prominent role for wavelengths lower than 500 nm, which is likely to be caused by higher beta-carotene concentrations [31,46]. Further research is required to map the optical properties of colostrum and transitional milk.

This study explored the interaction of light with human milk. We hope that our findings will form a starting point for further biophotonic studies on human milk and lactation, with potential applications ranging from human milk analysis, to studies on lactation physiology, and objective methods to support mothers who experience breastfeeding problems. As our findings indicate a significant correlation between fat concentration of human milk and its optical properties (µ_a, µ_s, µ_s’ and µ_b,NA) within the visible wavelength region, this can potentially lead to a cost-effective alternative for (near)-infrared analysis of human milk fat concentration.

5. Conclusion

In this study, we used a novel combination of spatially resolved diffuse reflectance spectroscopy and spectroscopic optical coherence tomography to quantify the optical properties of human foremilk, bulk milk and hindmilk between 450 – 650 nm. The observed range of variation between subjects in the optical properties was µ_a,460nm = 1.1 x 10⁻² – 8.3 x 10⁻² mm⁻¹, µ_s,550nm = 2.6 – 21.0 mm⁻¹, µ_s^’_,550nm = 0.24 – 2.48 mm⁻¹, g = 0.82 – 0.96, and µ_b,NA,550nm = 1.1 x 10⁻⁴ – 1.6 x 10⁻³ mm⁻¹. Significant correlations with fat concentration were found for µ_a, µ_s, µ_s’ and µ_b,NA (R_s = 0.38, R_s = 0.77, R_s = 0.80, and R_s = 0.44, respectively). Mie calculations on the measured fat globule size distribution of human milk were in good agreement with the experimentally derived optical properties. In conclusion, the variation in the optical properties of human milk between and within mothers can be deduced largely to biological variations in fat concentration and fat globule size distribution.