Diffuse optical spectroscopy of lactating and non-lactating human mammary physiology

Breastfeeding provides widely recognized advantages for infant and maternal health. Unfortunately, many women experience trouble with breastfeeding. Nevertheless, few suitable imaging modalities are available to study human lactation and determine the possible causes of breastfeeding problems. In this study, we apply broadband, quantitative diffuse optical spectroscopy (DOS) for this purpose. We present a study of fourteen lactating and eight similarly aged, premenopausal, non-lactating women to investigate the feasibility of DOS to study the optical and physiological differences between 1) lactating and non-lactating breasts, 2) the areolar and non-areolar region within the breast, and 3) lactating breasts before and after milk extraction. Our study shows that i) the median total hemoglobin concentration [tHb] of the lactating breast is 51% higher than for the non-lactating breast. ii) the median [tHb] of the lactating breast is 37% higher in the areolar region compared to the non-areolar region. iii) lactating breasts exhibit a positive median difference of 8% in [tHb] after milk extraction. Our findings are consistent with the expected physiological changes that occur during the lactation period. Importantly, we show that DOS provides unique insight into breast tissue composition and physiology, serving as a foundation for future application of the technique in lactation research.


Introduction
Breastfeeding plays an important role in the health of infants and mothers.Short-term benefits of breastfeeding for the infant include a reduced risk of several life-threatening diseases early in life, such as pneumonia and diarrheal infections [1,2].Long-term benefits for the infant include a reduced risk of obesity and diabetes later in life [2].For the mother, breastfeeding has been shown to decrease the risk of ovarian and breast cancer.The advice of the World Health Organization (WHO) is therefore to exclusively breastfeed in the first six months of life and to supplementally breastfeed until two years of age [3,4].However, worldwide from 2016-2022 only 48% of newborns were exclusively breastfed in the first six months, and 71% and 45% of babies were breastfed in their first and second year, respectively [2].The main factor contributing to low breastfeeding rates is a perceived suboptimal milk supply [5][6][7][8]: in fact, 40-50% of breastfeeding mothers stop breastfeeding due to a perception of insufficient milk supply [6].Yet, it is estimated that 10-15% of women actually have an insufficient milk supply [9].
At present, no diagnostic point-of-care method exists that can identify physiological problems in the breast that lead to low milk supply [10].Broadband diffuse optical spectroscopy (DOS) is a non-invasive and sensitive imaging technique that provides information about breast tissue composition using red to near-infrared light [11].DOS could potentially be used to identify anomalies in breast physiology that play a role in lactation problems.
Previous work has shown that DOS can be used to detect changes in breast tissue composition during post-lactational involution [12].However, no work has been performed on women during the lactation period itself.On a macroscopic level, the human breast consists of blood, blood vessels, lymphatic vessels, nerves, glandular tissue, fatty tissue, and connective tissue [13].The glandular tissue consists of milk lobules for milk production and milk ducts for milk transport.The ducts converge underneath the nipple, forming on average nine main milk ducts [14,15].During pregnancy, the glandular tissue proliferates, and the cells mature to produce milk [16].It is observed that in animals, the overall blood volume in the body increases during the lactation period [17].In addition, it has been shown that mammary blood flow specifically is elevated overall during the lactation period [18], and temporarily during milk extraction [19].However, total hemoglobin concentration in the breast slightly decreases at the start of milk extraction, fluctuates during milk extraction, and increases after the end of milk extraction [20,21].
In this study, we investigate optically measurable parameters that are expected to differ between the lactating and non-lactating breast: the tissue blood concentration and the ratio between glandular and adipose tissue content.DOS can be used to quantify breast tissue composition in terms of the concentrations of oxyhemoglobin [HbO 2 ], deoxyhemoglobin [HHb], total hemoglobin [tHb], water [H 2 O] and [lipid], as well as percent tissue oxygen saturation (StO 2 ).The measured [H 2 O] has been demonstrated to correlate with the amount of water-rich glandular tissue, whereas the measured [lipid] correlates with the amount of lipid-rich adipose tissue [12,22,23], and the [tHb] correlates with blood content [12].We encapsulate these three parameters, [tHb], [H 2 O] and [lipid] into the Lactation Optical Index (LOI) to highlight the differences in breast tissue composition between lactating and non-lactating breasts.
Based on the physiological differences between lactating and non-lactating breasts, we formulate three hypotheses: i.) Lactating breasts differ from non-lactating breasts in water-to-lipid ratio, hemoglobin content, and LOI.Due to the increase in glandular tissue volume in the lactating breast [16], breast composition is expected to have an increased water-to-lipid ratio, compared to the non-lactating breast.In addition, due to the increase in blood volume [17], the lactating breast is expected to have elevated concentrations of [HbO 2 ], [HHb] and [tHb] in comparison to the non-lactating breast.ii.)Given the dense concentration of glandular tissue near the nipple [14,15], we expect that the water-to-lipid ratio in the areolar region is higher compared to the non-areolar region.We also expect that this difference is more prominent in the lactating breast, compared to the non-lactating breast, due to the increase in glandular tissue content during lactation [16].iii.)Based on observations of other studies [21,24], we expect that the concentration of [tHb] will increase in the lactating breast after milk extraction.
We tested these hypotheses in an observational clinical study of fourteen healthy lactating, and eight similarly aged healthy, premenopausal, non-lactating women.In addition, we evaluated the differences in DOS probing depth between lactating and non-lactating breasts.

DOS instrumentation and data processing
The custom-built handheld DOS system used in this study, shown in Fig. 1(A), combines frequency domain near-infrared spectroscopy (FD-NIRS) with broadband continuous-wave (CW) spectroscopy (650-1000 nm) to produce quantitative measurements of tissue absorption and scattering properties [11].The hybrid DOS technique is described in detail by Bevilacqua et al. [11].In short, the FD-NIRS module component of the DOS device included four fiber-coupled laser diode sources (660, 690, 785, and 830 nm) that were amplitude-modulated (50-500 MHz).A 1 mm diameter avalanche photodiode (APD) sensor housed in the probe sampled the reflected light.

Research Participants and Data Acquisition
Data was collected from fourteen lactating women and eight non-lactating control participants (Table 1).Four lactating and five non-lactating women participated at the University of Twente (Enschede, The Netherlands) in November 2019.Ten lactating and three non-lactating women participated at the University of Notre Dame (Notre Dame, IN USA) between January and March 2022.All women were healthy, without any known breast diseases, benign breast lesions, breast surgeries, breast tattoos or breast piercings.The lactating women did not report any problems with breastfeeding at the time of the measurement.Ethical approval was obtained from CMO Arnhem-Nijmegen (#2019-5610) and the University of Notre Dame Institutional Review Board (#20-02-5907).All participants were recruited from the local communities and provided written informed consent.For data collection, the subject was positioned in a supine position.The handheld DOS sensing probe was placed in gentle contact with the breast tissue.For each participant, measurements were taken in a rectangular six by six cm grid pattern with 10 mm spacing in the upper outer quadrant of the breast, within and outside of the nipple-areolar complex.This resulted in a total of 36 sequentially measured points per breast, which took 5 to 10 minutes to measure in total (Fig. 2).Only one breast was measured per participant, due to time constraints and subject burden.The side was chosen by the participant, being the breast that felt most full with milk.
Two DOS measurements were taken per research participant.The first measurement was taken either directly before milk extraction (lactating group) or before a waiting period (non-lactating group) and the second measurement was taken directly after this period.The participants from the lactating group extracted milk with their own breast pump until the breast was empty, the participants from the non-lactating group sat quietly for ten minutes.We will refer to the first measurement as "pre" and the second measurement as "post".The CW consisted of a fiber-coupled tungsten halogen light source and a visible/near-infrared spectrometer (650-1000 nm) to measure the reflectance.The system was calibrated for system response by acquiring FD-NIRS and CW data on phantoms with known optical properties.The phantoms were fabricated following the procedure described by A. E. Cerussi et al. [25].
The DOS system was connected through fibers to a handheld probe, which was placed in gentle contact with the skin during subject measurements, as shown in Fig. 1(B).The source-detector distance was 28 mm for both FD-NIRS and CW.While collecting data, both sources and detectors were placed directly in contact with the skin.For two lactating participants, the source-detector distance was decreased to 22 mm, due to a low signal-to-noise ratio at 28 mm.
DOS data acquisition was performed following previously described methods [11].Here, both FD and CW components are modeled as originating from an isotropic point source within a semi-infinite, homogeneous medium, where the solution for the reflectance is defined by the Green's function with the extrapolated boundary condition for the p1 approximation to the radiative transport equation.The absorption (µ a ) and reduced scattering (µ s ' ) coefficients were determined with FD-NIRS for the four probed wavelengths.These were used to calibrate the intensity of the CW measurements and correct the broadband reflectance for scattering.
The The reduced scattering coefficient spectrum was characterized by µ s '(λ) = a(λ/λ 0 ) −b , with a the scattering prefactor (µ s ' at λ = 500 nm, with units cm −1 ) and b the unitless scattering power, which denotes the wavelength dependence of the scattering.

Research participants and data acquisition
Data was collected from fourteen lactating women and eight non-lactating control participants (Table 1).Four lactating and five non-lactating women participated at the University of Twente (Enschede, The Netherlands) in November 2019.Ten lactating and three non-lactating women participated at the University of Notre Dame (Notre Dame, IN USA) between January and March 2022.All women were healthy, without any known breast diseases, benign breast lesions, breast surgeries, breast tattoos or breast piercings.The lactating women did not report any problems with breastfeeding at the time of the measurement.Ethical approval was obtained from CMO Arnhem-Nijmegen (#2019-5610) and the University of Notre Dame Institutional Review Board (#20-02-5907).All participants were recruited from the local communities and provided written informed consent.

Table 1. Overview of the lactating and non-lactating group
participated at the University of Notre Dame (Notre Dame, IN USA) between January and March 2022.All women were healthy, without any known breast diseases, benign breast lesions, breast surgeries, breast tattoos or breast piercings.The lactating women did not report any problems with breastfeeding at the time of the measurement.Ethical approval was obtained from CMO Arnhem-Nijmegen (#2019-5610) and the University of Notre Dame Institutional Review Board (#20-02-5907).All participants were recruited from the local communities and provided written informed consent.For data collection, the subject was positioned in a supine position.The handheld DOS sensing probe was placed in gentle contact with the breast tissue.For each participant, measurements were taken in a rectangular six by six cm grid pattern with 10 mm spacing in the upper outer quadrant of the breast, within and outside of the nipple-areolar complex.This resulted in a total of 36 sequentially measured points per breast, which took 5 to 10 minutes to measure in total (Fig. 2).Only one breast was measured per participant, due to time constraints and subject burden.The side was chosen by the participant, being the breast that felt most full with milk.
Two DOS measurements were taken per research participant.The first measurement was taken either directly before milk extraction (lactating group) or before a waiting period (non-lactating group) and the second measurement was taken directly after this period.The participants from the lactating group extracted milk with their own breast pump until the breast was empty, the participants from the non-lactating group sat quietly for ten minutes.We will refer to the first measurement as "pre" and the second measurement as "post".
For data collection, the subject was positioned in a supine position.The handheld DOS sensing probe was placed in gentle contact with the breast tissue.For each participant, measurements were taken in a rectangular six by six cm grid pattern with 10 mm spacing in the upper outer quadrant of the breast, within and outside of the nipple-areolar complex.This resulted in a total of 36 sequentially measured points per breast, which took 5 to 10 minutes to measure in total (Fig. 2).Only one breast was measured per participant, due to time constraints and subject burden.The side was chosen by the participant, being the breast that felt most full with milk.
Each grid point was designated as either within ('areola') or outside ('non-areola') the areolar region, by visual inspection of the breast skin pigmentation.The optical and chromophore properties were analyzed separately for the two regions.
We introduced the Lactation Optical Index (LOI) to better define the expected differences between the lactating and non-lactating breast.As detailed in the hypotheses, we expect an increase in [HbO 2 ], [HHb], [tHb] and the water-to-lipid ratio between lactating and non-lactating breasts.We expect enhanced contrast due to the physiological differences between lactating and non-lactating breasts by defining the LOI as The mean difference between the chromophore concentrations in the areolar and nonareolar region of the breast per research participant was defined as: with []  the chromophore concentration difference per participant, [  ] the mean Two DOS measurements were taken per research participant.The first measurement was taken either directly before milk extraction (lactating group) or before a waiting period (non-lactating group) and the second measurement was taken directly after this period.The participants from the lactating group extracted milk with their own breast pump until the breast was empty, the participants from the non-lactating group sat quietly for ten minutes.We will refer to the first measurement as "pre" and the second measurement as "post".
Each grid point was designated as either within ('areola') or outside ('non-areola') the areolar region, by visual inspection of the breast skin pigmentation.The optical and chromophore properties were analyzed separately for the two regions.
We introduced the Lactation Optical Index (LOI) to better define the expected differences between the lactating and non-lactating breast.As detailed in the hypotheses, we expect an increase in [HbO 2 ], [HHb], [tHb] and the water-to-lipid ratio between lactating and non-lactating breasts.We expect enhanced contrast due to the physiological differences between lactating and non-lactating breasts by defining the LOI as The mean difference between the chromophore concentrations in the areolar and non-areolar region of the breast per research participant was defined as: with ∆[c] j the chromophore concentration difference per participant, [c a ] the mean chromophore concentration in the areolar region and [c na ] the mean chromophore concentration in the non-areolar region.
We assessed the change in tissue composition following milk extraction by the percentage change (δ%) in the chromophore concentrations between the "pre" ([c] pre ) and "post" ([c] post ) measurements.The mean percent change δ% [c],j per research participant, per chromophore is defined as: with where δ% [c],j,k is the percent change of the chromophore concentration between the "pre" and "post" measurement, per participant per measurement point, and K is the total number of measurement points.

Statistical analysis
Due to the small sample size and the non-normal distribution of the data, we performed a Mann-Whitney U test [26] to evaluate whether there was a significant difference in optical properties, chromophores and DOS probing depth between both the lactating and non-lactating group.This was done both for the areolar and non-areolar region of the breast.We also performed a Mann-Whitney U test to evaluate whether there was a statistically significant difference in chromophore δ% following milk extraction between the lactating and the non-lactating group.Statistically significant differences between the lactating and non-lactating group were defined for a significance level smaller than 0.05 (p < 0.05).

Probing depth simulations
The probing depth for DOS in the lactating and non-lactating breast was determined in order to to compare the penetration depth and probed physiological structures between subjects.The probing depth was calculated through Monte Carlo simulations using MC MATLAB [27].The tissue was modeled as a homogeneous, semi-infinite medium, with the mean measured optical properties of the breast for each research participant as input values for µ a (λ) and µ s ' (λ).The anisotropy (g) was set to a value of 0.97 for breast tissue (λ = 650-1000 nm), according to Peters et al. [28].The source was modeled as an isotropic point source.Each simulation described the trajectory path of 1 × 10 7 photons in a grid of 335 × 335 × 800 voxels, with a voxel size of 300 × 300 × 250 µm.The absorption sensitivity was calculated based on the coupled forward-adjoint radiance distribution method as described by Gardner et al. [29].In this method, a Monte Carlo simulation is performed by launching photons from both the source and detector location, the two resulting distributions are then multiplied, which results in a 3D spatially resolved sensitivity distribution (σ µ a ).An example of the resulting projection of σ µ a is shown in Fig. 3(A).The σ µ a is integrated in both lateral x and y directions to obtain the depth-dependent cumulative absorption sensitivity Σµ a (z).An example of Σµ a (z) is shown in Fig. 3(B).We defined the probing depth as the depth at which Σµ a (z) is equal to two standard deviations (96%) of Σµ a (max), i.e. 96% of the area under the curve (AUC).

Optical properties
Figure 4 presents the differences in the median optical absorption and scattering spectra of the lactating and non-lactating group over the measured wavelength range, for the pre-measurements before milk extraction (lactating participants) or waiting period (non-lactating participants).Lactating breasts showed a significantly higher µ a than non-lactating breasts for both the areolar and non-areolar region (p < 0.05 for λ = 650-1000 nm).For the lactating breast, µ a was significantly higher for the areolar region compared to the non-areolar region (p < 0.05, for λ < 680 nm and λ > 940 nm).Although the areolar region of the non-lactating breast shows a higher µ a compared to the non-areola for λ = 950-1000 nm, no statistical significant differences were found between the areolar and non-areolar region in the non-lactating group (p > 0.05).No significant differences were found for µ s ' between groups and breast regions (p > 0.05).For µ a the respective minimum and maximum ranges are; 0.03-0.10cm −1 for lactating non-areola, 0.06-0.18cm −1 for lactating areola, 0.03-0.06cm −1 for non-lactating non-areola, 0.02-0.06cm −1 for non-lactating areola.For µ s ' this is 1.0-1.5 cm −1 for lactating non-areola, 1.3-3.3cm −1 for lactating areola, 0.83-1.3cm −1 for non-lactating non-areola, 1.1-1.8cm −1 for non-lactating areola.Figure 5 presents the scattering prefactor (a) and the scattering power (b) for lactating and nonlactating breasts (pre-measurements), for both the areolar and non-areolar region.No significant differences were found in the scattering prefactor between the lactating and non-lactating breast, and the areolar and non-areolar region (p > 0.05).The scattering power was significantly higher for the areolar region compared to the non-areolar region for both the lactating (p = 0.037) and non-lactating breast (p = 0.0499).
No correlation is found (p > 0.05) between the BMI and [lipid], and BMI and LOI of both the lactating and non-lactating group.Fig. 6.Breast tissue chromophore concentrations, StO 2 and LOI of lactating and nonlactating breasts in the non-areolar region (pre-measurements: before milk extraction/waiting period).Significant differences (p < 0.05) between groups are indicated by an asterisk (*).

Areolar versus non-areolar region
Figure 7 shows the mean difference in tissue composition between the areolar and non-areolar regions for the lactating and non-lactating breast (pre-measurements), as calculated by Eq. ( 2).Non-lactating breasts showed little differences between the areolar and non-areolar regions for most chromophores, except for [H 2 O] and [lipid].Lactating breasts showed differences in most DOS parameters between both breast regions.The [HbO 2 ], [tHb], [H 2 O] and LOI were higher for the areolar than for the non-areolar region, whereas the lipid concentration was lower.When comparing the areolar region to the non-areolar region, the distinction between the lactating and non-lactating breasts was significant for [HbO 2 ] (p = 0.013) and [tHb] (p = 0.0086).Though not significant (p > 0.05), LOI trends are higher for the lactating breast than for the non-lactating breast, and shows a larger variability.

Before versus after milk extraction
Figure 8 shows the δ% in tissue composition after milk extraction (lactating group) or after a waiting period (non-lactating group) for the non-areolar region of the breast.Significant differences were found between lactating and non-lactating breasts for the [tHb] concentration (p = 0.0024) and LOI (p = 0.027).For the areolar region (not included in the graph), the same trend was observed: significant differences were found for the δ% in tissue composition for [HbO 2 ] (p = 0.019) and [tHb] (p = 0.0070).Fig. 8. Average point-to-point difference δ% of the lactating and non-lactating breast, respectively after milk extraction or a waiting period, for all the DOS parameters in the breast region outside the areolar region.Significant differences (p < 0.05) between groups are indicated by an asterisk (*).
For the non-lactating group, no differences in overall breast tissue composition were expected between the measurements taken before and after the waiting period.This was reflected in the δ% for [H 2 O] and [lipid].Larger differences were observed in the hemodynamic parameters, which were reflected in the [tHb] and LOI values.

DOS probing depth
Figure 9 shows the probing depth for each participant group in this study for a selection of three wavelengths within the evaluated continuous spectrum (650-1000 nm).The wavelengths were selected to represent approximate points at the beginning, middle, and end of the probed wavelength range.The probing depth showed significant differences between lactating and non-lactating breasts at 650 nm and 808 nm (p < 0.05), for both the areolar and non-areolar region.No significant differences were found in probing depth between the areolar and non-areolar region (p > 0.05), for both the lactating and non-lactating breast.For a fair comparison, data from the two participants that were obtained with a smaller source-detector distance than 28 mm were excluded in this analysis.
The probing depths of the two subjects measured with a 22 mm source-detector separation ranged between 9.5 -19.5 mm for the areola and 11.0-16.8mm for the non-areola at the three evaluated wavelengths.These probing depths fall within the range of the subjects who were measured with the 28 mm source-detector separation.Fig. 9. Probing depth at 650, 808 and 990 nm for the lactating and non-lactating breast.Significant differences (p < 0.05) between groups are indicated by an asterisk (*).

Discussion
In this study, we used DOS to study the optical and physiological differences between i) lactating and non-lactating breasts, ii) the areolar and non-areolar region within the breast, and iii) lactating breasts before and after milk extraction.The aim was to determine if DOS effectively assesses these differences in mammary tissue composition.Our results demonstrate the capability of DOS to accomplish this task, which is consistent with our hypotheses.and [tHb] in the lactating breast compared to the non-lactating breast.This indicates that the blood volume in the lactating breast is elevated compared to the non-lactating breast.This is in line with the mammary vascular expansion that occurs during pregnancy and leads to increased vasculature density during lactation [30].Further, we measured a non-significant increase in [H 2 O] and a decrease in [lipid] between the lactating and non-lactating breast.This reflects the expected increased water-to-lipid ratio due to increased glandular tissue volume in the lactating breast [16].The non-significance (p < 0.05) of this finding could be due to the large variation in glandular tissue content between women.StO 2 levels did not significantly differ between the groups and exhibited minimal variability within each group.This can be attributed to the similarity in StO 2 levels between glandular and adipose tissue [31].

Tissue composition
Our findings are in line with our previous case study with DOS on the process of post-lactational involution of the breast [12].There, we also demonstrated that [tHb] and [H 2 O] are higher, and [lipid] is lower in the lactating state in comparison to the non-lactating state of the breast.
In general, we note that there is a high variability in the DOS parameters in both the lactating and non-lactating groups.This can be attributed to a large inter-person variability in breast composition.Large differences in breast composition naturally exist due to, for example, differences in breast density [15].For this study, additional differences may also be caused by differences in the lactation period and menstrual cycle [32].Differences in lactation period relate to differences in the nutritional demand of the baby, leading to differences in milk production by the mother.However, it is currently unknown how exactly breast composition is related to milk production.While Ramsay et al. [14] did not find a relation between milk yield and the amount of glandular tissue, Arbour et al. [33] found that a minimum amount of glandular tissue is required for adequate milk production.
The breast tissue is highly responsive to hormonal changes that occur during the menstrual cycle, leading to differences in both blood volume and glandular tissue content [34][35][36][37].Most subjects within the lactating group had not reestablished menstruation yet at the time of the study, therefore cycle-dependent variations apply mainly to the non-lactating group.

Areolar versus non-areolar region
As expected, we found that the areolar region has a higher [H 2 O] and lower [lipid] than the non-areolar region.These differences are more prominent in the lactating breast.In addition, the areola of the lactating breast shows a higher blood volume than the non-areolar region of the lactating breast and the areolar region of the non-lactating breast.This corresponds with findings from previous studies [12,38] and can be attributed to highly vascularized tissue in the areolar region, which expands during lactation.Lastly, the scattering power of the areolar region is significantly (p < 0.05) higher than the non-areolar region.This can be attributed to the difference in scattering properties of fibrous and glandular tissue.The high glandular tissue content of the areolar region is associated with an increased scattering power due to the small size of the optical scatterers, cellular structures within the glandular tissue [39].
The higher observed [tHb], [H 2 O], scattering power and lower lipid content found in the areolar compared to the non-areolar region are in line with previous observations [12,38,40].

Before versus after milk extraction
In the lactating group, our results show the expected positive change in [tHb] after milk extraction.These results are consistent with those of Itoh et al. [20,21] and suggest a rise in blood volume shortly after milk expression.This rise in blood volume can be explained by reperfusion of blood vessels following temporary occlusion by milk duct dilatation during milk extraction [20].
In the non-lactating group, minimal change was expected during the 10-minute resting period.This expectation is met for [H 2 O] and [lipid], however, not for [HbO 2 ] and [tHb].This could be due to vasoconstriction of superficial blood vessels caused by cooling of the prolonged uncovered breast and/or extended rest.It is therefore recommended to include a simultaneous measure of breast skin temperature in future DOS studies on lactation physiology.

DOS probing depth
We simulated the DOS probing depth in lactating and non-lactating breasts, to compare the penetration depth and probed physiological structures.Our simulations demonstrate a median probing depth range of 12 to 20 mm for all subjects and for all investigated wavelengths.This aligns with the expectation that the DOS probing depth approximately reaches half the source-detector distance of 28 mm [41].
The lactating breast shows a shallower DOS probing depth, especially in the areolar region, compared to the areolar region of the non-lactating breast.This can be attributed to the increased amount of absorption in the lactating breast (Fig. 3(A)), which can be ascribed to a larger presence of glandular tissue.Despite these differences, the variation in probing depth between lactating and non-lactating breasts remains within a range of maximally 4 mm.We argue that this difference is sufficiently small to allow a fair comparison of DOS results between the lactating and non-lactating breast.

Outlook
This study demonstrates the potential of DOS to study lactation physiology by mapping mammary tissue composition.Due to the explorative nature of this work, the sample size of this study is limited to only fourteen lactating and eight non-lactating subjects.Therefore, the outcomes of this study should not be used for generalization to the entire population.In this study only the upper outer quadrant of one breast was studied for each research participant.However, breasts may not be fully symmetric in terms of composition.Considering that this is a pilot study to show the feasibility of DOS in lactation research, only one quadrant suffices to provide enough information.Our future research will focus on studying the whole breast of a larger study population, to establish a framework for healthy lactating breast physiology.Ultimately, this framework can serve as a basis to compare healthy lactation physiology to the lactation physiology of individuals exhibiting breastfeeding problems.In the case of lactation insufficiency, the use of DOS will be particularly valuable to assess the dependency of milk production on glandular tissue content, blood volume and LOI.

Conclusion
In this study, we demonstrated the effectiveness of DOS in studying mammary lactation physiology.First, we showed that lactating breasts have a larger blood content compared to non-lactating breasts.Second, we showed that the areolar region of the lactating breast has a higher blood content and LOI than the non-areolar region.Last, we showed that the lactating breast has a higher blood content following milk extraction compared to before milk extraction.This study contributes to the overall knowledge of mammary lactation physiology and serves as a foundation for future research and diagnostics in breastfeeding problems.

Fig. 1 :
Fig. 1: A. DOS probe design B. Demonstration of measurement setup for breast imaging with handheld DOS probe

Fig. 1 .
Fig. 1. A. DOS probe design B. Demonstration of measurement setup for breast imaging with handheld DOS probe.

Fig. 2 .
Fig. 2. DOS measurement grid pattern on a breast.The size of the areolar region varied per participant.

Fig. 2 .
Fig. 2. DOS measurement grid pattern on a breast.The size of the areolar region varied per participant.

Fig. A .
Fig. A. Example of MC simulated σ µ a (simulated µ a = 0.0156 mm −1 , simulated µ s ' = 0.886 mm −1 at λ = 808 nm), X and O denote the source and detector location respectively.B. The corresponding cumulative absorption sensitivity over all lateral positions, Σµ a (z).The red dotted line represents the probing depth.

Fig. 4 .
Fig. 4. Median optical properties (pre-measurements: before milk extraction/waiting period) of the lactating and non-lactating breast.A. Absorption coefficient µ a .B. Reduced scattering coefficient µ s ′ .The error bar represents the interquartile range of the data.For visibility purposes, only the error bars at four wavelengths are shown within the continuous spectrum.

Fig. 7 .
Fig.7.Chromophore concentration difference in breast tissue chromophore distributions of the areolar and non-areolar region of lactating and non-lactating breasts (pre-measurements: before milk extraction/waiting period).Significant differences (p < 0.05) between groups are indicated by an asterisk (*).

Funding.
HORIZON EUROPE European Research Council (101040376); University of Notre Dame.