Abstract

Studying tissue hemodynamics following breast compression has the potential to reveal new contrast mechanisms for evaluating breast cancer. However, how compression will be distributed and, consequently, how hemodynamics will be altered inside the compressed breast remain unclear. To explore the effect of compression, 12 healthy volunteers were studied by applying a step compression increase (4.5–53.4 N) using an optical imaging system capable of concurrently measuring pressure distribution and hemodynamic responses. Finite element analysis was used to predict the distribution of internal fluid pressure (IFP) in breast models. Comparisons between the measured pressure distribution and the reconstructed hemodynamic images for the healthy volunteers indicated significant (p < 0.05) negative correlations. The findings from a breast cancer patient showed that IFP distribution during compression strongly correlates with the observed differential hemodynamic images. We concluded that dynamic breast compression results in non-uniform internal pressure distribution throughout the breast that could potentially drive directed blood flow. The encouraging results obtained highlight the promise of developing dynamic optical imaging biomarkers for breast cancer by interpreting differential hemodynamic images of breast tissue during compression in the context of measured pressure distribution and predicted IFP.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Breast cancer imposes a significant societal burden, with nearly 2.2 million women expected to be diagnosed and more than 600,000 expected deaths worldwide in 2020 [1]. Mammography screening has led to significant reductions in breast cancer mortality [2]. However, the positive predictive value of performing a breast biopsy following a BI-RADS 3 or 4 assessment after diagnostic workup (i.e., suspicious abnormality) is only 28.6% according to the latest Breast Cancer Surveillance Consortium update [3,4]. This means that nearly 3 in 4 biopsies come back negative for malignancy, resulting in excessive patient anxiety and increased healthcare costs [5].

Near-infrared diffuse optical spectroscopy (NIRS) and tomography (DOT) are novel functional imaging techniques that have been shown to be sensitive to cancer-related phenotypical changes in breast tissue [6]. These technologies take advantage of the low absorption of tissue in the 650 to 900 nm range [7], where NIR light can penetrate deeply to allow quantitative measurements of tissue components such as oxy- and deoxy-hemoglobin, water, and lipids. NIR tissue biomarkers such as the total hemoglobin concentration and tissue oxygenation can report on tumor proliferation, blood flow, and oxygen metabolism [810].

In addition to tissue chromophore contrast, malignant lesions are also known to have elevated stiffness due to altered vasculature, abnormal perfusion, high cellularity, increased collagen deposition in the extracellular matrix, and higher interstitial pressure [1114]. Several groups, including ourselves, have investigated the breast tissue hemodynamic changes in response to compression to define dynamic optical imaging biomarkers of breast cancer [1517], by observing differential behavior of lesion areas vs. surrounding normal tissues. So far, these investigations have been conducted on an empirical basis, without exploring the link between lesion biomechanical properties and the hemodynamic response.

To explore the relationship between the applied mechanical surface pressure (compression) and the resulting internal pressure distribution in soft tissue, Darling et al. [18] performed a series of finite element and experimental studies in tissue-simulating phantoms. Internal pressure distribution was simulated on cubic volumes with displacement boundary conditions placed on the lower and upper surfaces to mimic compression. These studies were used to predict the change in internal pressure in human breast tissue in response to external compression. In our paper, we attempt to connect the internal pressure distribution during dynamic breast compression with the internal variation in total hemoglobin concentration. The basis of these simulations comes from well-established mechanical science that can predict internal pressure and its distribution with good accuracy by solving boundary value problems. In this work, we present images of simultaneously measured pressure distribution using a pressure mapping system and reconstructed hemodynamics images using continuous-wave optical imaging. We demonstrate the relationship between pressure images and hemoglobin changes in a group of healthy volunteers. In addition, we show that the internal pressure distribution during an increasing compression maneuver correlates with the observed differential optical images in a previously reported breast cancer patient case.

2. Methods

2.1 System description

The breast compression and imaging device used in this study was derived from our previous dynamic DOT system reported in [16]. Figure 1 shows a schematic of the sensing head used for optical data collection and compression, together with a photograph showing a front view of the same device. The main parts of the mechanical system of the sensing head include a stepper motor used to compress/decompress the breast by changing the distance between a stationary breast support plate and a compression paddle. The support plate is horizontal and attached to the instrument cart, while the compression paddle has a fixed 10-degree tilt angle in the nipple-to-chest wall direction from the horizontal plane and mounted on a computer-controlled translation stage. The tilted configuration of the compression paddle was used to better conform to the breast contour and thereby to improve compression and patient comfort [19]. Two load cells attached to the compression paddle were used to measure the applied force by the compression paddle [20]. The measured force was used in a closed feedback loop to apply a pre-specified force on the upper surface of the breast. The closed-loop control mechanism includes three major elements: (1) the two load cells affixed to the compression paddle, (2) motor driver that provides power for control of the stepper motor, and (3) software for motion control, display, and data storage. The software supported two modes of operations: stress-relaxation studies and creep studies. In creep studies, the compression paddle would be engaged all the time by moving slightly up and down (adjusting deformation) to maintain a target stress (pressure). In stress-relaxation studies, which were implemented in this paper, the compression paddle was moved down until a predetermined force was reached and then held there throughout the measurement. During the stress-relaxation studies, the compression paddle will not engage in fine adjustment of deformation while the breast tissues gradually relax. Instead, readings were recorded during the reduction of force due to the tissue relaxation in this period of constant strain (deformation). To ensure participants’ safety, limit switches were used on the translation stage, and an emergency stop switch was given to participants under study. If the emergency stop switch were activated by the participant, the compression paddle would immediately return to the home position, thereby releasing the breast.

 figure: Fig. 1.

Fig. 1. (a) A schematic of the measuring head of the system showing the main parts of the compression mechanism, (b) A picture of the measuring head showing a breast (represented by a balloon) under compression between the breast support plate and the compression paddle.

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Given the natural plasticity of the breast, it is expected that compression maneuvers can influence the hemodynamic response. To appreciate the impact that externally applied forces can be expected to have on hemodynamics, we measured the pressure distribution at the lower surface of the breast using a pressure map sensor. As shown in Fig. 1, the pressure map sensor (Tekscan I-Scan, Model 5250, Boston, MA) was mounted on the lower support plate. Two linear encoders, one on the left side and the other on the right side of the breast, were used to accurately measure breast thickness, which was the distance between the breast support plate and the compression paddle towards the nipple end. A personal computer was used to acquire the measured force and breast thickness continuously and to control the movements of the stepper motor.

Diffuse optical tomography measurements were obtained using a TechEn CW6 continuous-wave NIRS (CW-NIRS) imager (TechEn Inc., Milford, MA). The instrument offers 32 sources, split evenly between 685 nm and 830 nm, and 32 detectors. We used 32 sources and 30 detectors (960 channels) to image the breast in transmission mode. Sources fibers were inserted in the support plate, and the detectors were inserted in the compression paddle, similar to the configuration described by Carp et al. [16]. The light sources were modulated at 32 individual frequencies to allow full simultaneous detection [16]. The modulation frequencies were between 6.4 kHz and 12.6 kHz, spaced every 200 Hz, and each source delivers ∼10 mW of light power to the breast surface. Avalanche photodiode detectors (Hamamatsu C5460-01) were used to acquire light transmitted through the breast. The detected signals were demodulated with 25 Hz bandwidth. Therefore, no significant overlap or cross-talk was detected between detectors if they were not being saturated [21]. Optical data were collected from the instrument at 25 frames per second. The signal-to-noise ratio was increases by averaging a set of 5 frames, to produce an imaging rate of 5 Hz, which allowed studying breast's hemodynamics with a sufficient temporal resolution before, during, and after compression. The sources covered a 10 cm by 6.7 cm area, while the detectors covered a 13 cm by 7.4 cm area.

Sensor measurements and CW6 data were logged using a custom MATLAB code for the duration of the compression imaging protocol. The Tekscan Pressure Measurement System software (Version 5.62I) recorded pressure maps at 5 Hz timestamped for synchronization between the mechanical and optical measures. By timestamping data, we can ensure the alignment of optical and pressure map data to within a fraction of a second.

2.2 Optical data processing and image reconstruction

Since we are interested in hemodynamic changes in breast tissue due to compression and CW optical imaging does not provide the ability to quantify absolute hemoglobin concentrations [22], the Normalized Difference Method (NDM) was used for image reconstruction [23]. The forward problem was solved by the use of a finite element method (FEM) on a suitable model. The model represents an approximation to the geometry of a typical breast when placed inside the sensing head. The values of the initial guess for image reconstruction were μs′ = 6.937 cm−1 and μa = 0.073 cm−1 for 685 nm, and μs = 4.855 cm−1 and μa = 0.06 cm−1 for 830 nm [24]. Figure 2(a) shows a 3D image of the FEM model used for image reconstruction, which represents an approximation to the geometry of a typical breast when compressed between the support plate and the compression paddle. The locations of the sources and detectors used for data collection are also marked. Based on our previous clinical study [25], the distribution of the sources and detectors was chosen to have a full breast coverage in most participants and also meet fiber optic cable routing constraints in a compact space. The optodes cover 12 cm in the medial-lateral direction and 7 cm in the anterior-posterior direction. The forward FEM model has 45,134 nodes and 271,099 elements, and the reconstruction mesh used for storing the tissue parameters in the inverse computation has 5,003 nodes and 25,976 elements [26]. To generate forward and inverse FEM models for each breast, the breast thickness measured by the two linear encoders was used to determine the thickness (height) of the model, and the pressure map from Tekscan sensor was used to determine the width and the depth of the model.

 figure: Fig. 2.

Fig. 2. (a) The finite element mesh used for hemodynamic computations and biomechanics modeling with red and blue dots identify the location of the sources and detectors relative to the mesh, respectively. (b) The 3D modeled compression procedure showing the support plate and the tilted compression paddle. The yellow pentagrams shown in (a) represent the positions of the source and detector of the reference channel.

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Optical signals (source-detector measurement pairs) to be used in image reconstruction were selected based on three criteria: mean value more than 10 dB over our instrument’s noise level, the separation distance between source-detector pair less than 10 cm (to exclude long separation channels with abnormally high signal level potentially due to artifactual light paths), and good correlation with a reference channel. The noise floor of the instrument was determined using calibration phantom measurements. The noise floor was at the inflection point where the plot of the signal vs the source-detector separation distance changed from exponentially decaying to relatively constant. The signal level is arbitrary but repeatable. Correlation coefficients were calculated, during compression, between every channel and a reference channel that was located at a central location near the chest wall. The reference channel always had good contact, even for small breast sizes. Figure 2(a) shows the locations of the source and detector of the reference channel. Gross changes in optical signals with good SNR during compression were similar; increase during compression (the separation distance between the source and the detector decreases) and decrease during decompression. Therefore, good SNR signals have a relatively high correlation. We empirically found that a correlation coefficient with the reference channel greater than 0.8 was an adequate indicator of channels with good SNR. The correlation criterion was also capable of detecting channels with saturation. Some channels were susceptible to saturation during compression, especially with large deformation and small breast size. Saturation happened when the separation between the source and detector became too short for those channels during the compression deformation. Furthermore, the correlation criterion was efficient to flag channels with poor optode-tissue contact that could happen to channels close to the outer boundaries. The three criteria were efficient to automatically select signals with good SNR, without saturation, and with good contact.

2.3 Biomechanics modeling

The biomechanical modeling is used to produce an estimation of the interstitial fluid pressure (IFP, or thermodynamic pressure) after applying external pressure or deformation to the breast surface. Soft–tissue mechanical responses can be approximated with linear elasticity theory if the strains are small (<30%) [27]. For calculations of IFP, a solid material containing fluid cavities (poroelastic) is used to model breast tissue. The fluid cavities include blood content in the microvessels compartment (capillaries) [28]. Transient IFP changes affect fluid flow and cause fluid migration through breast tissue compartments [29]. The IFP change driven movements of blood in breast tissue were measured using our dynamic DOT system.

Applying external force to the surfaces of breast tissue produces non-uniform increase in IFP. To study the impact of applying external force to breast tissues, the pressure distribution inside the breast was modeled using Linear Elastic Finite Element Analysis. This modeling was approximated at a macroscopic level as a poroelastic substrate [29]. The conservation of mass and momentum equations were used to describe fluid migration in a poroelastic material with a linear elastic solid component:

$$\nabla \cdot \,\dot{u} - \nabla \cdot ({\kappa \nabla p} )+ \mathrm{\chi }p = 0$$
$$\nabla \cdot \sigma = \nabla \cdot \left( { - p{{\rm I}} + \lambda \nabla \cdot u{{\rm I}} + 2\mu \varepsilon } \right) + \rho g = 0$$
Where $\dot{\boldsymbol{u}}$ and u are the velocity and displacement of the solid phase, respectively; ∇ is the gradient operator; I is the identity tensor; ε and σ are the strain and stress tensors, respectively; ρ is the tissue density; g is the acceleration due to gravity; $\boldsymbol{\chi }$ is the average microfiltration rate; $\boldsymbol{\kappa }$ is the interstitial permeability; λ is the dynamic viscosity; and μ is the bulk viscosity. The motion of the fluid component in response to the applied force is governed by $\boldsymbol{\chi }$ and κ. Since our goal to evaluate the internal mechanical response to applied force immediately following a compression, and the tissue is now quasi-static, κ and χ are assumed to be zero. The time course of the modeled protocol additionally gives us $\dot{\textbf{u}}$ ≈ 0 (i.e., there is negligible creep while the compression paddle is held still). Therefore, Eq. (1) was safely neglected and Eq. (2) was used as the basis of the forward-modeling computation. The microscopic analog of Eq. (2) is equivalent to the following equation, which is the deformation law for Newtonian viscous fluid given by Stokes [30,31]:
$${\tau _{ij}} ={-} p{\delta _{ij}} + \lambda \,tr(\varepsilon )\,{\delta _{ij}} + \mu \left( {\frac{{\partial {\nu_i}}}{{\partial {x_j}}} + \frac{{\partial {\nu_j}}}{{\partial {x_i}}}} \right)$$
Where ijth is element index, ${\boldsymbol{\tau}_{\boldsymbol{ij}}}$ is the surface stress tensor, tr(ε) is the trace of the fluid strain tensor, ${\boldsymbol{\delta }_{\boldsymbol{ij}}}$ is the Kronecker delta, and v is the fluid velocity. For a steady-state analysis, components of the strain were used to replace the velocity gradients in Eq. (3) [18]. By taking the mean of the axial components (i.e., i = j) of the stress, the mechanical pressure $\tilde{p}$ can be defined as $\tilde{p} = {\raise0.5ex\hbox{$\scriptstyle { - tr(\tau )}$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 3$}}$. IFP can be related to principal strains and mechanical pressure as follows [18]:
$$IFP = \tilde{p} + \left( {\lambda + \frac{2}{3}\mu } \right)tr(\varepsilon )$$
To calculate IFP, finite element analysis was performed on models of breast tissue with Poisson’s ratio of 0.49 and mechanical properties appropriate for fibroglandular (Young’s modulus = 40 kPa), adipose (fat) tissue (20 kPa), and breast tumors (90 kPa) [18]. The geometric model considered is shown in Fig. 2(b), and it represents an approximation to the geometry of a typical breast when placed between the support plate and the compression paddle. The coordinates of the nodes were scaled in all three dimensions based on the outline of the breast derived from the Tekscan system and thickness measured from linear encoders.

We used a nonlinear finite element software called FeBio to compute the mechanical pressure and principal strains [32]. The values of λ = 450 Pa and μ = 50 kPa, consistent with the range reported by Eiben et al. [33], were used. IFP was calculated by Eq. (4). Two boundary conditions that are frequently used by other researchers [3436] were applied to the FEM model in FeBio to constrain the rigid body motion and model the attachment of the breast to the rest of the body. The first boundary condition is a constrained anterior-posterior displacement on the posterior surface of the model to allow a sliding contact between the breast and the underlying ribcage. The second one is the interaction between the breast and both the compression paddle and the support plate, which is considered as a rigid-wall contact; the breast tissues were defined as deformable bodies, and the compression paddle and support plate were considered as rigid bodies. The later condition was necessary to prevent tissue from penetrating the support plate and the compression paddle. Compression was simulated by applying fixed force in the range from 4.45 to 53.4 N, consistent to those applied to healthy volunteers, or deforming the breast and decreasing its thickness (prescribed displacement) in the range of 0 to 2 cm. This deformation range was determined based on the decrease of breast thickness measured from our human study (See section 2.4). Finally, the effect of gravity was simulated by a body force acting on each element with 9.8 m/s2 acceleration in the caudal (downward) direction.

2.4 Measurement protocol

We conducted measurements on 13 healthy female volunteers to evaluate the correlation between the measured spatial distribution of pressure and hemodynamic responses during breast compression. The age range was 24 to 63 (33 ± 13) years old, and the body-mass-index (BMI) range was 22.3 to 32.3 (25.9 ± 4.2) kg/m2. All measurements were conducted under a protocol approved by the Partners Institutional Review Board (IRB, protocol # 2007P001503). Written informed consent and a short survey were obtained from each research participant. Blood pressure, weight, height, and pulse rate were also measured before the initiation of the study imaging procedure. Then, participants were seated in a chair positioned sufficiently close to the imager to allow for positioning of the breast on the support plate and comfortably support the breast. The height of the chair was adjusted for every subject, to ensure subject comfort. Participants were asked to minimize movements during the compression imaging session.

Each breast was centrally positioned onto the lower support plate. Since sufficient contact between the compression paddle and the top of the breast, the prerequisite for parallel-plate DOT, could not be achieved without applying some pressure, no optical measurements were taken pre-compression. The optical measurements were initiated only when a craniocaudal compression force of 4.45 N (1 lbf) was achieved by lowering the compression paddle. The baseline hemodynamics were recorded for 60 seconds while maintaining the position of the compression paddle. Next, a craniocaudal compression of 53.4 N (12 lbf) force was applied. The time needed for lowering the compression paddle to increase the compression force from 4.45 N to 53.4 N varied between 2 to 5 seconds. The variations in the compression time between participants were due to variations in breast size and stiffness. Once the 53.4 N compression was achieved, the compression paddle was stopped for another 60 sec to measure hemodynamics at the increased compression level. This is followed by a relaxation process wherein force is returned to the baseline level of 4.45 N for a period of 1 minute. The maximum compression force of 12 lbf was tolerable by most patients. Only one participant was excluded from the subsequent analysis because she could not tolerate the 12 lbf (53.4 N) compression force.

To show that the internal pressure distribution during an increasing compression maneuver correlates with the observed differential optical images, a reported breast cancer patient case from our previous work was used for modeling IFP distribution. The patient was a 47-year old with a 1.5 cm diameter invasive ductal carcinoma. The compression protocol for the cancer patient involved half-mammographic compression 21.8 N (4.9 lbf) followed by full-mammographic compression 44.5 N (10 lbf). Optical images were reconstructed the same way as described in Ref. [15] using volumetric fractions of adipose, fibro-glandular, and inclusion as structural priors implemented in our in-house standard diffusion approximation for light transport FEM solver Redbird [37]. The compositional structure of adipose and fibroglandular priors were derived from digital breast tomosynthesis (DBT) images of the patient using a dual-Gaussian segmentation algorithm [38], and a lesion prior was obtained from the tumor markings on the patient’s DBT images provided by an experienced breast radiologist [15]. Biomechanical simulations were performed the same way as described in section 2.3 using the patient image-derived compositional distributions of adipose, lesion, and fibroglandular tissues.

3. Results

To show the effect of increasing the applied force from 4.45 N to 53.4 N (1 lbf to 12 lbf) on the hemodynamics of breast tissue, representative spatial maps of the change in pressure (Δp) measured by the Tekscan pressure sensor placed on the bottom supporting plate along with spatial maps of the changes in total hemoglobin concentration (ΔHbT) vertically averaged within a region covering the bottom fifth of the breast volume are shown in Fig. 3. The images are for the left and right breasts of a 24-year old healthy volunteer. It can be seen that there is an inverse relationship between ΔHbT and Δp spatial maps, the largest drops in HbT occurring at or near the positions where Δp is the largest. The relationship between the ΔHbT and Δp spatial maps reveals that ΔHbT patterns reflect redistributions of blood in response to changes in the internal pressure distribution. Particularly, the striking inverse relationship between ΔHbT and Δp suggests the movement of blood due to the pressure gradients.

 figure: Fig. 3.

Fig. 3. Spatial maps of pressure distribution and total hemoglobin (ΔHbT) responses to applied pressure. (a) The change in pressure distribution going from 4.45 N (1 lbf) to 53.4 N (12 lbf) compression force measured by Tekscan pressure sensor placed on the bottom supporting plate, (b) Axial views of the decrease in total hemoglobin concentration (ΔHbT) in the lower part of the breast after applying the 53.4 N compression. The images are from a 24-year old healthy participant with a BMI of 23.6.

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The mean and standard deviation of ΔHbT and Δp across all healthy participants were 1.03 ± 1.29 µM and 7.42 ± 6.41 kPa, respectively. Given the heterogeneity of the ΔHbt and ΔP images across participants, and that boundaries react differently from the center of the breast within each participant, the standard deviation values were very large. We quantified the relationship between Δp and ΔHbT spatial maps by calculating the 2D correlation coefficients between them for the left breast and the right breast individually. From the reconstructed HbT images, the changes in total hemoglobin (ΔHbT) were found after applying the 12 lbf compression force. Then, the calculated ΔHbT of the lower fifth of the breast volume were averaged vertically across this region to generate 2D ΔHbT spatial maps. The lower fifth of the breast volume (closer to the supporting plate) was chosen because the Tekscan pressure sensor was mounted on the bottom plate. Finally, 2D correlation was calculated between the Tekscan Δp distribution with the averaged ΔHbT map using the Pearson correlation method across all values in the maps, arranged in a paired fashion. Table 1 presents the correlation coefficient (r) for the 12 subjects included in the study. In addition, the p-value for each correlation was calculated using the Student's t distribution method under the null hypothesis that there is no correlation between Δp and ΔHbT images. The correlations were negative and significant (p < 0.05) for 20 out of 24 individual breast recordings (2 breasts x 12 subjects). The negative correlation between Δp and ΔHbT reported suggests that increasing localized pressure in a region leads to decreasing HbT in that region. The somewhat low values of the correlation coefficients may be due to the spatial offsets in peak change between IFP and HbT for each subject. The offset ranged from 0 to 3 cm in the axial plane. The acquisition of the pressure map on the bottom plate vs the volume averaged ΔHbT may have also played a role in reducing correlation coefficients.

Tables Icon

Table 1. The 2D correlation coefficients and p-value between Δp and ΔHbT images after applying 12 lbf compression.

The correlations coefficients were close to zero and insignificant in three subjects: left breast of subject 5, left breast of subject 7, both breasts of subject 9. Inspection of the raw data for these subjects reveals that there was a motion artifact while applying the 53.4 N compression on the left breast of subject 7, and substantial stress relaxation after the 53.4 N compression on the left breast of subject 5 (which could indicate slipping of the left breast during compression). For subject 9, the breast size was very small (left and right breasts).

To help explain the hemodynamic responses of breast tissue to changes in compression, biomechanical simulations were performed to predict the distribution of ΔIFP by increasing the compression force from 22.2 N (5 lbf) to 44.5 N (10 lbf). The simulated compression is the same compression protocol, i.e., from half to full compression, performed on the cancer case shown in Fig. 5. To investigate the ΔIFP distribution in various scenarios, we embedded a lesion-mimicking inclusion of 90 kPa Young’s modulus with a radius of 1, 1.5, or 2 cm in two different background tissue with biomechanical properties mimicking those of adipose (20 kPa) and fibro-glandular (40 kPa) tissues, respectively. Compressions were simulated by increasing the applied force from 5 lbf to 10 lbf (one-step 22.2 N increment) on the top of the models. The ΔIFP distributions from fibroglandular-mimicking and adipose-mimicking models are presented (axial view) in the upper images and lower images in Fig. 4, respectively. Inspection of the images reveals that higher ΔIFP was occurring at or near the positions of the inclusion. Also, ΔIFP is smaller in small-sized inclusions compared to large-sized inclusions within the same background tissue. For the same lesion size, higher values of ΔIFP are observed in breast models where there are bigger differences in Young's modulus of the inclusion compared to the rest of the model. For instance, the contrast of ΔIFP for inclusion is high in the adipose-simulating models because the ratio of Young's modulus of inclusion (90 kPa) to adipose (20 kPa) is larger than the ratio of Young's modulus of inclusion (90 kPa) to fibroglandular (40 kPa). These localized regions of high ΔIFP near inclusions produce pressure gradients within the breast tissue, which can produce directed blood flow from high-pressure to low-pressure regions (in the direction of pressure gradients). Hence the spatial pattern of blood redistribution is greatly affected by the presence of inclusions of a different stiffness, as would be the case for tumors, for example.

 figure: Fig. 4.

Fig. 4. Spatial maps of calculated ΔIFP distribution as the applied force increased from 5 lbf to 10 lbf on heterogeneous models with inclusions . The upper row in the figure from left to right presents images for fibroglandular models with 90 kPa inclusions with 1, 1.5, and 2 cm radius, respectively. The lower row of figures from left to right present images from adipose models with 90 kPa inclusions with 1, 1.5, and 2 cm radius, respectively. The results are calculated using models with a volume equal to 400-ml. Dashed circles represent the boundary of the inclusions.

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 figure: Fig. 5.

Fig. 5. Spatial maps of changes in (a) simulated ΔIFP and (b) reconstructed HbT from optical measurements taken as the compression increase from half 21.8 N to full 44.5 N mammographic force of a 47-year old cancer patient with a Grade 3 invasive ductal carcinoma (IDC) measuring 1.8 × 1.2 × 1.1 cm3. The dotted-line in (a) and (b) denotes the location of the tumor as marked by our collaborating radiologist. Anatomical information of adipose, fibroglandular, and tumor tissue compositions was derived from DBT x-ray images of the patient. The elastic moduli used to model adipose, fibroglandular, and tumors tissues for IFP simulation were 20, 40, and 90 kPa, respectively.

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Figure 5(a) shows a spatial map (axial view) of the increase in internal IFP (ΔIFP) for a model of the cancer patient’s breast with an invasive ductal carcinoma during the compression protocol. The protocol consisted of half mammographic compression of 21.8 N held for 107 seconds, followed by full mammographic compression at 44.5 N held for 32 seconds [15]. The compression force was manually increased from half to full compression in 30 seconds. The spatial map of the increase in IFP (ΔIFP) was simulated based on the compositional structure of adipose and fibroglandular derived from digital breast tomosynthesis images of the cancer patient. Figure 5(b) shows the corresponding spatial map of the decrease in HbT (ΔHbT) after applying full compression. The spatial map of ΔHbT was reconstructed from optical measurements using our in-house standard diffusion approximation for light transport FEM solver Redbird. It is shown that the highest increase in IFP is predicted to occur at the location of the tumor (∼ 80 mmHg). As a result, the greatest decrease in HbT also is predicted to occur at the tumor location. Clearly, the internal pressure distribution during an increasing compression maneuver is inversely correlated with ΔHbT, similar as observed in healthy volunteers.

The average HbT at half-compression in the tumor was approximately 50 µM, which is about three times that in the rest of breast tissue (17 µM). As the compression was increased from half to full compression force, the averaged ΔHbT in the tumor and the rest of the breast tissue were −15 µM and −0.85 µM, respectively. The averaged ΔIFP, as the compression was increased from half to full compression force, for the tumor and the rest of the breast tissue were 83.5 mmHg and 28.8 mmHg, respectively. Although the ratio of averaged ΔIFP between tumor and the rest of breast tissue RΔIFP was 2.9 (83.5/28.8), the ratio of averaged ΔHbT between tumor and the rest of breast tissue RΔHbT was 17.6 (15/.85), approximately 6 times of RΔIFP. This result indicates the potential of enhanced HbT contrast by applying a baseline compression (e.g., half compression) followed by a higher-level compression (e.g., full compression). Other factors that may influence IFP are breast size, its mechanical properties (Young's modulus), and the amount of deformation. Additional computations of the average IFP were carried out on homogeneous models with different volumes, two elastic moduli 20 and 40 kPa, and progressive deformations (0–2.7 cm). Results shown in Fig. 6(a) demonstrate generally decreasing IFP with increasing breast size. Decreasing the elastic modulus of the breast model from 40 to 20 kPa decreases IFP by about 50%. On the other hand, results shown in Fig. 6(b) demonstrate the effect of the elastic modulus on IFP amplitudes is small for small deformation and increases as the deformation increases.

 figure: Fig. 6.

Fig. 6. Average IFP over an 8-cm3 cube located at the center of the breast volume for homogenous fibroglandular and adipose models as a function of (a) breast volume and (b) decrease in breast thickness. The error bars are the standard deviation of IFP across all nodes (n ranged from 29 to 230) in the central 8-cm3 volume. The decrease in breast thickness to simulate compression in (a) was 1 cm. The breast volume used in (b) was 400 ml.

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4. Discussion

Application of mechanical compression to the breast as a strategy to reveal enhanced optical contrast is gaining increasing attention as a useful approach for the detection of tumors and monitoring neoadjuvant chemotherapy [17,3944]. While it is evident that externally applied force will produce a complex IFP distribution within the breast, affecting the hemodynamic contrast, it is much less clear how IFP will be distributed inside the compressed breast, and how IFP will affect blood content, quantified by HbT, in the breast tissue. In this work, we sought to further explore the relationship between IFP and hemodynamics, with the goal to help design controlled compressions that exploit known physiological abnormalities of tumors, hence enhancing the detectability of breast cancer using diffuse optical tomography. In general, the main parameters of compressions that can be designed to produce distinctive hemodynamic responses are force amplitude, duration, and sequence. We have explored the implementation of a wide range of compression protocols that varied in duration, sequence and amplitude of applied pressure. In this paper, we have shown the hemodynamic responses to a step increase compression protocol in a group of healthy volunteers and in a breast cancer patient case.

The amplitude of IFP can be increased and decreased based on the amplitude of the applied external force. Our group had presented evidence that the amplitude of compression affects blood distribution in different vascular compartments [20]. For example, high amplitude of compression can result in removing blood from almost all vascular compartments, including arteries, while low amplitude of compression may only result in removing blood from veins and capillaries (<30 mmHg) [45]. For instance, interstitial pressure in breast carcinomas is known to increase (interstitial hypertension) compared to healthy breast tissue [46,47]. Therefore, it is crucial to optimize the amplitude of IFP and measure its distribution in order to produce the highest contrast in compression-induced changes of the hemodynamics between normal breast tissues and tumors.

The second parameter is the sequence of compression when the breast is compressed several times; compression, decompression, compression, decompression, etc. It is expected that the mechanical and hemodynamic responses of the breast to be different in the first compression compared to the following compressions, even for the same amplitude and duration of compression. The reasons for this behavior are the hysteresis and viscoelastic properties of breast tissue [48]. During compression, breast tissue recovers part of its volume when compression is released due to its elasticity. However, breast volume and shape do not return to their initial uncompressed levels (results not shown), indicating the collagen matrix remains stretched. Thus, less elastic resistance and a different relative amount of blood will be removed after subsequent compressions [49].

The pressure distribution in Fig. 3 was not uniformly distributed throughout the breast; pressure was high in some parts of the breast while low or negligible elsewhere. The size, shape, and location of high-pressure areas were different between the left and right breasts of the same subject, and between different subjects (not shown in the figure). Often, high-pressure regions were seen in the lateral and central areas of the breast. Non-uniform pressure distribution was also reported by Dustler et al. [50]. They used pressure sensors underneath the compression plate of an x-ray mammography machine to visualize the distribution of pressure over a compressed breast in the mediolateral oblique projection. Pressure measurements were taken under approximately 95 N and 54 N force of mammographic compression [51]. The low compression in their study was similar to the full compression force (53.4 N) used in our study. There are two factors that influence the measured pressure distribution during breast compression: thickness and stiffness across the breast [50]. It is reasonable that the above two factors affect pressure distribution and make it non-uniformly distributed because the breast is, in fact, highly heterogeneous [52]. The results suggest that compression between two plates do not produce uniform internal pressure distribution. Two strategies can be implemented to improve the uniformity of internal pressure distribution when executing external compression: using a tilted compression paddle or applying fine compression using multiple elements, such as using fingers [39]. The tilted configuration conforms to the breast contour and improves compression [19]. While a fixed 10-degree tilt angle of the compression paddle was used here, the tilt-angle could be adjusted to better conform to each breast shape and even out internal pressure distribution. Although the fine compression using fingers is doable, the complexities that it adds to the data collection space (e.g., spatial dependence of applied force, its magnitude, and its time dependence) can present a daunting task to define tractable measurement strategies that are effective [39], not to mention the challenges in subsequent analysis as well as in ensuring reproducibility across subjects or in longitudinal study.

Results in Fig. 4 and Fig. 5 have shown that the change of IFP near inclusions (tumors) was enhanced after applying mechanical compression. These results are consistent with a previous study done by Darling et al. using linear elastic finite element analysis [18]. In addition, an association between the inclusion size and ΔIFP inside the tumor can be observed from Fig. 4; the value of ΔIFP inside the tumor increases as the tumor size increases. In Fig. 5, the most decrease in HbT occurs at the location of the tumor, reinforcing previous findings of the increased stiffness and HbT concentration in breast cancer tumors [11,12,15]. In the cancer case presented, the half compression applied was above the arterial pressure of the patient. Therefore, most vascular compartments, including arteries, were collapsed in normal breast tissue. However, because the tumor was stiff enough, the vascular compartment at the tumor location was protected from total collapse. By increasing the compression force to full compression (44.5 N), the remaining blood in the non-collapsed vessels at the tumor was expelled to produce a high ΔHbT contrast between normal and tumor as shown in Fig. 5(b). For instance, RΔHbT was approximately 6 times RΔIFP.

Based on these results, to optimize the effect of ΔIFP on producing enhanced ΔHbT responses between normal and tumor tissue, it may be best to first apply an initial compression to divert most blood from normal tissue, and then a higher-level compression to divert the remaining blood in cancerous tissue. The encouraging results obtained highlight the promise that well-designed compression protocol can produce distinct dynamic responses among normal and cancerous breast tissue. In theory, the ratio RΔHbT/RΔIFP during compression may be used as a biomarker to reveal information about the increased stiffness of breast tumors. Decreases in this ratio may be used for assessment of tumor response to neoadjuvant chemotherapy. In a similar scenario, where tumor vs. normal tissue dynamic responses to slow pressure relaxation were monitored, it has been reported that the hemodynamic responses of tumor tissue to compression converged toward normal tissue in neoadjuvant chemotherapy responders, while the hemodynamic responses of tumor tissue to compression was different, and unchanged in neoadjuvant chemotherapy non-responders [42].

Based on Fig. 6, the stiffness and size of the breast should be taken into consideration to determine the level of compression. As the amplitude of deformation increases, so does the average IFP (Fig. 6(b)). The role of the breast geometry is that for the same breast stiffness, the average IFP decreases as the breast size increases (Fig. 6(a)) under constant amplitude of deformation. And the role of mechanical properties is that the average IFP increases as the stiffness (Young's modulus) of the breast tissue increase for all amplitudes of deformation and breast sizes (Fig. 6(a) and (b)). These results are consistent with a previous study done on gelatin phantoms [18].

The composition of human breast and its mechanical properties are strongly influenced by menstrual cycle and menopausal status [53]. For instance, the stiffness of fibroglandular tissue two weeks into the menstrual cycle is approximately two times of that at 5 days after the onset of menses [54]. On the other hand, the stiffness of adipose tissue does not significantly change during the menstrual cycle [54]. Therefore, the average IFP induced by applying external force on a breast is expected to be the greatest at two weeks into the menstrual cycle (ovulation). There are also notable differences in tissue stiffness and blood content between pre- and post-menopausal women. The HbT in breast tissue, as well as the ratio of HbT between fibroglandular and adipose tissues, tend to be less in postmenopausal subjects [5557]. The contrast of IFP for tumors during compression in postmenopausal cancer patients is expected to be higher than that in premenopausal cancer patients. Therefore, the tumor hemodynamic response to compression is likely to stand out even better in postmenopausal patients. Two out of the 13 healthy volunteers imaged in this study were postmenopausal.

One limitation of this work is that getting the most accurate results of the internal pressure distribution requires modeling breast tissue as a visco- and poro-elastic material with accurate visco- and poro-elastic coefficients and detailed breast geometry. While the poroelastic model is conceptually appealing, the stability and ultimate utility of the solutions obtained can prove rather unsatisfactory in the absence of accurate physical modeling and detailed knowledge of the boundary conditions (internal and external). A practical approach is to use magnetic resonance imaging, x-ray mammography, or digital breast tomosynthesis in a coregistered multimodal setting to accurately model the internal boundary conditions and the breast shape during compression, which we have developed recently [15].

Another limitation of this work is that optical image reconstruction was performed using a model with an approximate geometry of a typical breast when placed inside the sensing head. The coordinates of the nodes in the FEM model were scaled in all three dimensions before running the optical imaged reconstruction based on the outline of the breast derived from the Tekscan system and thickness measured from linear encoders. Although the sizes of breasts were accurately captured by the measured pressure distribution, the side contours of the breast were estimated based on a reasonable assumption that breasts typically conform similarly when compressed between two plates. The errors in estimating breast shapes and assuming homogeneity of breast tissues could introduce inaccuracy of the spatial details in the reconstructed optical images. For instance, inspection of the spatial maps of pressure and HbT presented in Fig. 3, reveals that there is a substantial spatial offset (∼ 1 cm) in peak change between pressure and HbT in the left breast. The spatial offset decreases 2D correlation between spatial maps. In fact, the images presented in Fig. 3 are for patient #6 in Table 1, whose correlation coefficient in the left breast (−0.356) is less than that of the right breast (−0.564). The maximum spatial offset of the rest of participants (not shown) was 3 cm. We found that the spatial offset was the main reason of the low/modest r values in Table 1. Nevertheless, it was reported by Deng et al. that the impact of breast boundary inaccuracies on reconstructed optical images was minimal as long as the boundary was not close to the DOT field of view [58]. Furthermore, NDM has been shown to have remarkable stability while varying breast size [23,39].

5. Conclusion

To the best of our knowledge, we are the first to quantify the relationship between spatial hemodynamic responses and pressure distribution during compression on human breasts. The significant inverse relationship and negative correlation between pressure distribution and hemodynamic images after applying compression emphasizes the role of pressure distribution in directing hemodynamics inside heterogeneous breast tissues. We found that breast size and stiffness affect the average internal pressure, which should be carefully considered when determining the level of compression. The location of the highest hemodynamic response as compression was increased in one patient with a breast malignant tumor overlaps with the location of the highest increase in internal pressure. The details of the internal pressure distribution can be used to predict hemodynamic responses to external compressions. While studies on more breast cancer patients are needed, the contrast in both predicted and measured hemodynamic responses influenced by the presence of disease could potentially serve as a basis for detecting breast cancer and monitoring response to therapy.

Funding

National Institutes of Health (K01EB027726, R01CA187595); Jordan University of Science and Technology (4-2018).

Acknowledgments:

This research is supported in part by NIH grants R01CA187595 (SAC) and K01EB027726 (BD) as well as funding from the Deanship of Research in Jordan University of Science and Technology, Irbid, Jordan, Grant number 4-2018.

Disclosures

The authors declare no conflicts of interest.

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References

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  1. “Global Cancer Observatory,” http://gco.iarc.fr/ .
  2. K. C. Oeffinger, E. T. H. Fontham, R. Etzioni, A. Herzig, J. S. Michaelson, Y.-C. T. Shih, L. C. Walter, T. R. Church, C. R. Flowers, S. J. LaMonte, A. M. D. Wolf, C. DeSantis, J. Lortet-Tieulent, K. Andrews, D. Manassaram-Baptiste, D. Saslow, R. A. Smith, O. W. Brawley, R. Wender, and A. C. Society, “Breast Cancer Screening for Women at Average Risk: 2015 Guideline Update From the American Cancer Society,” JAMA 314(15), 1599–1614 (2015).
    [Crossref]
  3. C. D. Lehman, R. F. Arao, B. L. Sprague, J. M. Lee, D. S. M. Buist, K. Kerlikowske, L. M. Henderson, T. Onega, A. N. A. Tosteson, G. H. Rauscher, and D. L. Miglioretti, “National Performance Benchmarks for Modern Screening Digital Mammography: Update from the Breast Cancer Surveillance Consortium,” Radiology 283(1), 49–58 (2017).
    [Crossref]
  4. American College of Radiology and BI-RADS Committee, ACR BI-RADS Atlas: Breast Imaging Reporting and Data System (American College of Radiology, 2013).
  5. C. Gunn, B. Bokhour, T. Battaglia, R. Silliman, and A. Hanchate, “False-positive mammography and its association with health service use,” Am. J. Manag. Care 24, 131–138 (2018).
  6. S. Fantini and A. Sassaroli, “Near-Infrared Optical Mammography for Breast Cancer Detection with Intrinsic Contrast,” Ann. Biomed. Eng. 40(2), 398–407 (2012).
    [Crossref]
  7. F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198(4323), 1264–1267 (1977).
    [Crossref]
  8. S. H. Chung, M. D. Feldman, D. Martinez, H. Kim, M. E. Putt, D. R. Busch, J. Tchou, B. J. Czerniecki, M. D. Schnall, M. A. Rosen, A. DeMichele, A. G. Yodh, and R. Choe, “Macroscopic optical physiological parameters correlate with microscopic proliferation and vessel area breast cancer signatures,” Breast Cancer Res. 17(1), 72 (2015).
    [Crossref]
  9. Q. Zhu, S. H. Kurtzma, P. Hegde, S. Tannenbaum, M. Kane, M. Huang, N. G. Chen, B. Jagjivan, and K. Zarfos, “Utilizing optical tomography with ultrasound localization to image heterogeneous hemoglobin distribution in large breast cancers,” Neoplasia (N. Y., NY, U. S.) 7(3), 263–270 (2005).
    [Crossref]
  10. S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4(5), 513–526 (2005).
    [Crossref]
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    [Crossref]
  12. R. K. Jain, “Normalizing tumor microenvironment to treat cancer: bench to bedside to biomarkers,” J. Clin. Oncol. 31(17), 2205–2218 (2013).
    [Crossref]
  13. R. K. Jain, “Delivery of molecular and cellular medicine to solid tumors,” Adv. Drug Delivery Rev. 64, 353–365 (2002).
    [Crossref]
  14. R. K. Jain, “Normalizing tumor vasculature with anti-angiogenic therapy: a new paradigm for combination therapy,” Nat. Med. 7(9), 987–989 (2001).
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2018 (3)

B. Deng, M. Lundqvist, Q. Fang, and S. A. Carp, “Impact of errors in experimental parameters on reconstructed breast images using diffuse optical tomography,” Biomed. Opt. Express 9(3), 1130–1150 (2018).
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C. Gunn, B. Bokhour, T. Battaglia, R. Silliman, and A. Hanchate, “False-positive mammography and its association with health service use,” Am. J. Manag. Care 24, 131–138 (2018).

E. García, Y. Diez, O. Diaz, X. Lladó, R. Martí, J. Martí, and A. Oliver, “A step-by-step review on patient-specific biomechanical finite element models for breast MRI to x-ray mammography registration,” Med. Phys. 45(1), e6–e31 (2018).
[Crossref]

2017 (3)

B. B. Zimmermann, B. Deng, B. Singh, M. Martino, J. Selb, Q. Fang, A. Y. Sajjadi, J. Cormier, R. H. Moore, D. B. Kopans, D. A. Boas, M. A. Saksena, and S. A. Carp, “Multimodal breast cancer imaging using coregistered dynamic diffuse optical tomography and digital breast tomosynthesis,” J. Biomed. Opt. 22(4), 046008 (2017).
[Crossref]

A. Y. Sajjadi, S. J. Isakoff, B. Deng, B. Singh, C. M. Wanyo, Q. Fang, M. C. Specht, L. Schapira, B. Moy, A. Bardia, D. A. Boas, and S. A. Carp, “Normalization of compression-induced hemodynamics in patients responding to neoadjuvant chemotherapy monitored by dynamic tomographic optical breast imaging (DTOBI),” Biomed. Opt. Express 8(2), 555–569 (2017).
[Crossref]

C. D. Lehman, R. F. Arao, B. L. Sprague, J. M. Lee, D. S. M. Buist, K. Kerlikowske, L. M. Henderson, T. Onega, A. N. A. Tosteson, G. H. Rauscher, and D. L. Miglioretti, “National Performance Benchmarks for Modern Screening Digital Mammography: Update from the Breast Cancer Surveillance Consortium,” Radiology 283(1), 49–58 (2017).
[Crossref]

2016 (2)

M. D. Yoko Hoshi and Y. Yamada, “Overview of diffuse optical tomography and its clinical applications,” J. Biomed. Opt. 21(9), 091312 (2016).
[Crossref]

N. G. Ramião, P. S. Martins, R. Rynkevic, A. A. Fernandes, M. Barroso, and D. C. Santos, “Biomechanical properties of breast tissue, a state-of-the-art review,” Biomech. Model. Mechanobiol. 15(5), 1307–1323 (2016).
[Crossref]

2015 (3)

K. C. Oeffinger, E. T. H. Fontham, R. Etzioni, A. Herzig, J. S. Michaelson, Y.-C. T. Shih, L. C. Walter, T. R. Church, C. R. Flowers, S. J. LaMonte, A. M. D. Wolf, C. DeSantis, J. Lortet-Tieulent, K. Andrews, D. Manassaram-Baptiste, D. Saslow, R. A. Smith, O. W. Brawley, R. Wender, and A. C. Society, “Breast Cancer Screening for Women at Average Risk: 2015 Guideline Update From the American Cancer Society,” JAMA 314(15), 1599–1614 (2015).
[Crossref]

B. Deng, D. H. Brooks, D. A. Boas, M. Lundqvist, and Q. Fang, “Characterization of structural-prior guided optical tomography using realistic breast models derived from dual-energy x-ray mammography,” Biomed. Opt. Express 6(7), 2366–2379 (2015).
[Crossref]

S. H. Chung, M. D. Feldman, D. Martinez, H. Kim, M. E. Putt, D. R. Busch, J. Tchou, B. J. Czerniecki, M. D. Schnall, M. A. Rosen, A. DeMichele, A. G. Yodh, and R. Choe, “Macroscopic optical physiological parameters correlate with microscopic proliferation and vessel area breast cancer signatures,” Breast Cancer Res. 17(1), 72 (2015).
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2013 (2)

2012 (3)

M. Dustler, I. Andersson, H. Brorson, P. Fröjd, S. Mattsson, A. Tingberg, S. Zackrisson, and D. Förnvik, “Breast compression in mammography: pressure distribution patterns,” Acta Radiol. 53(9), 973–980 (2012).
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S. Fantini and A. Sassaroli, “Near-Infrared Optical Mammography for Breast Cancer Detection with Intrinsic Contrast,” Ann. Biomed. Eng. 40(2), 398–407 (2012).
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S. A. Maas, B. J. Ellis, G. A. Ateshian, and J. A. Weiss, “FEBio: finite elements for biomechanics,” J. Biomech. Eng. 134(1), 011005 (2012).
[Crossref]

2011 (4)

C. M. L. Hsu, M. L. Palmeri, W. P. Segars, A. I. Veress, and J. T. Dobbins, “An analysis of the mechanical parameters used for finite element compression of a high-resolution 3D breast phantom,” Med. Phys. 38(10), 5756–5770 (2011).
[Crossref]

R. Al abdi, H. L. Graber, Y. Xu, and R. L. Barbour, “Optomechanical imaging system for breast cancer detection,” J. Opt. Soc. Am. A 28(12), 2473–2493 (2011).
[Crossref]

P. Schedin and P. J. Keely, “Mammary Gland ECM Remodeling, Stiffness, and Mechanosignaling in Normal Development and Tumor Progression,” Cold Spring Harbor Perspect. Biol. 3(1), a003228 (2011).
[Crossref]

Q. Fang, J. Selb, S. A. Carp, G. Boverman, E. L. Miller, D. H. Brooks, R. H. Moore, D. B. Kopans, and D. A. Boas, “Combined Optical and X-ray Tomosynthesis Breast Imaging,” Radiology 258(1), 89–97 (2011).
[Crossref]

2010 (1)

T.-C. Shih, J.-H. Chen, D. Liu, K. Nie, L. Sun, M. Lin, D. Chang, O. Nalcioglu, and M.-Y. Su, “Computational Simulation of Breast Compression Based on Segmented Breast and Fibroglandular Tissues on Magnetic Resonance Images,” Phys. Med. Biol. 55(14), 4153–4168 (2010).
[Crossref]

2009 (3)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Engng. 25(6), 711–732 (2009).
[Crossref]

Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
[Crossref]

S. Jiang, B. W. Pogue, A. M. Laughney, C. A. Kogel, and K. D. Paulsen, “Measurement of pressure-displacement kinetics of hemoglobin in normal breast tissue with near-infrared spectral imaging,” Appl. Opt. 48(10), D130–D136 (2009).
[Crossref]

2008 (1)

2007 (3)

A. L. Kellner, T. R. Nelson, L. I. Cerviño, and J. M. Boone, “Simulation of mechanical compression of breast tissue,” IEEE Trans. Biomed. Eng. 54(10), 1885–1891 (2007).
[Crossref]

A. L. Darling, P. K. Yalavarthy, M. M. Doyley, H. Dehghani, and B. W. Pogue, “Interstitial fluid pressure in soft tissue as a result of an externally applied contact pressure,” Phys. Med. Biol. 52(14), 4121–4136 (2007).
[Crossref]

R. X. Xu, D. C. Young, J. J. Mao, and S. P. Povoski, “A prospective pilot clinical trial evaluating the utility of a dynamic near-infrared imaging device for characterizing suspicious breast lesions,” Breast Cancer Res. 9(6), R88 (2007).
[Crossref]

2006 (3)

R. Leiderman, P. Barbone, A. Oberai, and J. Bamber, “Coupling between elastic strain and interstitial fluid flow: Ramifications for poroelastic imaging,” Phys. Med. Biol. 51(24), 6291–6313 (2006).
[Crossref]

S. A. Carp, T. Kauffman, Q. Fang, E. Rafferty, R. Moore, D. Kopans, and D. Boas, “Compression-induced changes in the physiological state of the breast as observed through frequency domain photon migration measurements,” J. Biomed. Opt. 11(6), 064016 (2006).
[Crossref]

M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt. 11(5), 054007 (2006).
[Crossref]

2005 (2)

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4(5), 513–526 (2005).
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Q. Zhu, S. H. Kurtzma, P. Hegde, S. Tannenbaum, M. Kane, M. Huang, N. G. Chen, B. Jagjivan, and K. Zarfos, “Utilizing optical tomography with ultrasound localization to image heterogeneous hemoglobin distribution in large breast cancers,” Neoplasia (N. Y., NY, U. S.) 7(3), 263–270 (2005).
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2004 (2)

B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J. Biomed. Opt. 9(3), 541–552 (2004).
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C.-H. Heldin, K. Rubin, K. Pietras, and A. Ostman, “High interstitial fluid pressure - an obstacle in cancer therapy,” Nat. Rev. Cancer 4(10), 806–813 (2004).
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2003 (1)

J. Lorenzen, R. Sinkus, M. Biesterfeldt, and G. Adam, “Menstrual-Cycle Dependence of Breast Parenchyma Elasticity: Estimation With Magnetic Resonance Elastography of Breast Tissue During the Menstrual Cycle,” Invest. Radiol. 38(4), 236–240 (2003).
[Crossref]

2002 (1)

R. K. Jain, “Delivery of molecular and cellular medicine to solid tumors,” Adv. Drug Delivery Rev. 64, 353–365 (2002).
[Crossref]

2001 (4)

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of Absorption and Scattering Contrast for Near-Infrared Optical Mammography,” Acad. Radiol. 8(3), 211–218 (2001).
[Crossref]

Y. Pei, H. L. Graber, and R. L. Barbour, “Influence of Systematic Errors in Reference States on Image Quality and on Stability of Derived Information for dc Optical Imaging,” Appl. Opt. 40(31), 5755–5769 (2001).
[Crossref]

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. 98(8), 4420–4425 (2001).
[Crossref]

R. K. Jain, “Normalizing tumor vasculature with anti-angiogenic therapy: a new paradigm for combination therapy,” Nat. Med. 7(9), 987–989 (2001).
[Crossref]

1977 (1)

F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198(4323), 1264–1267 (1977).
[Crossref]

1966 (1)

A. C. Guyton, J. Prather, K. Scheel, and J. Mcgehee, “Interstitial Fluid Pressure,” Circ. Res. 19(6), 1022–1030 (1966).
[Crossref]

Abdi, R. A.

R. A. Abdi, G. Feuer, H. L. Graber, S. Saha, R. L. Barbour, and R. L. Barbour, “Optomechanical Imaging: Biomechanic and Hemodynamic Responses of the Breast to Controlled Articulation,” in Biomedical Optics and 3-D Imaging (2012), Paper BSu3A.92 (Optical Society of America, 2012), p. BSu3A.92.

Adam, G.

J. Lorenzen, R. Sinkus, M. Biesterfeldt, and G. Adam, “Menstrual-Cycle Dependence of Breast Parenchyma Elasticity: Estimation With Magnetic Resonance Elastography of Breast Tissue During the Menstrual Cycle,” Invest. Radiol. 38(4), 236–240 (2003).
[Crossref]

Al abdi, R.

Andersson, I.

M. Dustler, I. Andersson, H. Brorson, P. Fröjd, S. Mattsson, A. Tingberg, S. Zackrisson, and D. Förnvik, “Breast compression in mammography: pressure distribution patterns,” Acta Radiol. 53(9), 973–980 (2012).
[Crossref]

Andrews, K.

K. C. Oeffinger, E. T. H. Fontham, R. Etzioni, A. Herzig, J. S. Michaelson, Y.-C. T. Shih, L. C. Walter, T. R. Church, C. R. Flowers, S. J. LaMonte, A. M. D. Wolf, C. DeSantis, J. Lortet-Tieulent, K. Andrews, D. Manassaram-Baptiste, D. Saslow, R. A. Smith, O. W. Brawley, R. Wender, and A. C. Society, “Breast Cancer Screening for Women at Average Risk: 2015 Guideline Update From the American Cancer Society,” JAMA 314(15), 1599–1614 (2015).
[Crossref]

Antaki, J. F.

C. M. Robbins, J. Yang, J. F. Antaki, and J. M. Kainerstorfer, “Hand-held multi-wavelength spatial frequency domain imaging for breast cancer imaging,” in Optical Tomography and Spectroscopy of Tissue XIII (International Society for Optics and Photonics, 2019), Vol. 10874, p. 108740U.

Arao, R. F.

C. D. Lehman, R. F. Arao, B. L. Sprague, J. M. Lee, D. S. M. Buist, K. Kerlikowske, L. M. Henderson, T. Onega, A. N. A. Tosteson, G. H. Rauscher, and D. L. Miglioretti, “National Performance Benchmarks for Modern Screening Digital Mammography: Update from the Breast Cancer Surveillance Consortium,” Radiology 283(1), 49–58 (2017).
[Crossref]

Ateshian, G. A.

S. A. Maas, B. J. Ellis, G. A. Ateshian, and J. A. Weiss, “FEBio: finite elements for biomechanics,” J. Biomech. Eng. 134(1), 011005 (2012).
[Crossref]

Azar, F. S.

F. S. Azar, “A deformable finite element model of the breast for predicting mechanical deformations under external perturbations,” Diss. Available ProQuest 1–208 (2001).

Bamber, J.

R. Leiderman, P. Barbone, A. Oberai, and J. Bamber, “Coupling between elastic strain and interstitial fluid flow: Ramifications for poroelastic imaging,” Phys. Med. Biol. 51(24), 6291–6313 (2006).
[Crossref]

Barbone, P.

R. Leiderman, P. Barbone, A. Oberai, and J. Bamber, “Coupling between elastic strain and interstitial fluid flow: Ramifications for poroelastic imaging,” Phys. Med. Biol. 51(24), 6291–6313 (2006).
[Crossref]

Barbour, R. L.

R. Al abdi, H. L. Graber, Y. Xu, and R. L. Barbour, “Optomechanical imaging system for breast cancer detection,” J. Opt. Soc. Am. A 28(12), 2473–2493 (2011).
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S. A. Carp, J. Selb, Q. Fang, R. Moore, D. B. Kopans, E. Rafferty, and D. A. Boas, “Dynamic functional and mechanical response of breast tissue to compression,” Opt. Express 16(20), 16064–16078 (2008).
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Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
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B. Deng, D. H. Brooks, D. A. Boas, M. Lundqvist, and Q. Fang, “Characterization of structural-prior guided optical tomography using realistic breast models derived from dual-energy x-ray mammography,” Biomed. Opt. Express 6(7), 2366–2379 (2015).
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Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
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A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of Absorption and Scattering Contrast for Near-Infrared Optical Mammography,” Acad. Radiol. 8(3), 211–218 (2001).
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N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. 98(8), 4420–4425 (2001).
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Carp, S. A.

B. Deng, M. Lundqvist, Q. Fang, and S. A. Carp, “Impact of errors in experimental parameters on reconstructed breast images using diffuse optical tomography,” Biomed. Opt. Express 9(3), 1130–1150 (2018).
[Crossref]

B. B. Zimmermann, B. Deng, B. Singh, M. Martino, J. Selb, Q. Fang, A. Y. Sajjadi, J. Cormier, R. H. Moore, D. B. Kopans, D. A. Boas, M. A. Saksena, and S. A. Carp, “Multimodal breast cancer imaging using coregistered dynamic diffuse optical tomography and digital breast tomosynthesis,” J. Biomed. Opt. 22(4), 046008 (2017).
[Crossref]

A. Y. Sajjadi, S. J. Isakoff, B. Deng, B. Singh, C. M. Wanyo, Q. Fang, M. C. Specht, L. Schapira, B. Moy, A. Bardia, D. A. Boas, and S. A. Carp, “Normalization of compression-induced hemodynamics in patients responding to neoadjuvant chemotherapy monitored by dynamic tomographic optical breast imaging (DTOBI),” Biomed. Opt. Express 8(2), 555–569 (2017).
[Crossref]

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[Crossref]

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[Crossref]

Q. Fang, S. A. Carp, J. Selb, G. Boverman, Q. Zhang, D. B. Kopans, R. H. Moore, E. L. Miller, D. H. Brooks, and D. A. Boas, “Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression,” IEEE Trans. Med. Imaging 28(1), 30–42 (2009).
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S. A. Carp, J. Selb, Q. Fang, R. Moore, D. B. Kopans, E. Rafferty, and D. A. Boas, “Dynamic functional and mechanical response of breast tissue to compression,” Opt. Express 16(20), 16064–16078 (2008).
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A. Kabeer, M. A. Saksena, J. Cormier, S. A. Carp, and B. Deng, “Compression-induced hemodynamic features of tumors in breast cancer patients undergoing neoadjuvant therapy: a longitudinal case study,” in Biophotonics Congress: Biomedical Optics 2020 (Translational, Microscopy, OCT, OTS, BRAIN) (2020), Paper JTh2A.7 (Optical Society of America, 2020), p. JTh2A.7.

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H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Engng. 25(6), 711–732 (2009).
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N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. 98(8), 4420–4425 (2001).
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A. L. Kellner, T. R. Nelson, L. I. Cerviño, and J. M. Boone, “Simulation of mechanical compression of breast tissue,” IEEE Trans. Biomed. Eng. 54(10), 1885–1891 (2007).
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S. H. Chung, M. D. Feldman, D. Martinez, H. Kim, M. E. Putt, D. R. Busch, J. Tchou, B. J. Czerniecki, M. D. Schnall, M. A. Rosen, A. DeMichele, A. G. Yodh, and R. Choe, “Macroscopic optical physiological parameters correlate with microscopic proliferation and vessel area breast cancer signatures,” Breast Cancer Res. 17(1), 72 (2015).
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K. C. Oeffinger, E. T. H. Fontham, R. Etzioni, A. Herzig, J. S. Michaelson, Y.-C. T. Shih, L. C. Walter, T. R. Church, C. R. Flowers, S. J. LaMonte, A. M. D. Wolf, C. DeSantis, J. Lortet-Tieulent, K. Andrews, D. Manassaram-Baptiste, D. Saslow, R. A. Smith, O. W. Brawley, R. Wender, and A. C. Society, “Breast Cancer Screening for Women at Average Risk: 2015 Guideline Update From the American Cancer Society,” JAMA 314(15), 1599–1614 (2015).
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Cormier, J.

B. B. Zimmermann, B. Deng, B. Singh, M. Martino, J. Selb, Q. Fang, A. Y. Sajjadi, J. Cormier, R. H. Moore, D. B. Kopans, D. A. Boas, M. A. Saksena, and S. A. Carp, “Multimodal breast cancer imaging using coregistered dynamic diffuse optical tomography and digital breast tomosynthesis,” J. Biomed. Opt. 22(4), 046008 (2017).
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A. Kabeer, M. A. Saksena, J. Cormier, S. A. Carp, and B. Deng, “Compression-induced hemodynamic features of tumors in breast cancer patients undergoing neoadjuvant therapy: a longitudinal case study,” in Biophotonics Congress: Biomedical Optics 2020 (Translational, Microscopy, OCT, OTS, BRAIN) (2020), Paper JTh2A.7 (Optical Society of America, 2020), p. JTh2A.7.

Czerniecki, B. J.

S. H. Chung, M. D. Feldman, D. Martinez, H. Kim, M. E. Putt, D. R. Busch, J. Tchou, B. J. Czerniecki, M. D. Schnall, M. A. Rosen, A. DeMichele, A. G. Yodh, and R. Choe, “Macroscopic optical physiological parameters correlate with microscopic proliferation and vessel area breast cancer signatures,” Breast Cancer Res. 17(1), 72 (2015).
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H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Engng. 25(6), 711–732 (2009).
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A. Mîra, Y. Payan, A.-K. Carton, P. M. de Carvalho, Z. Li, V. Devauges, and S. Muller, “Simulation of breast compression using a new biomechanical model,” in Medical Imaging 2018: Physics of Medical Imaging (International Society for Optics and Photonics, 2018), Vol. 10573, p. 105735A.

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H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Engng. 25(6), 711–732 (2009).
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A. L. Darling, P. K. Yalavarthy, M. M. Doyley, H. Dehghani, and B. W. Pogue, “Interstitial fluid pressure in soft tissue as a result of an externally applied contact pressure,” Phys. Med. Biol. 52(14), 4121–4136 (2007).
[Crossref]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4(5), 513–526 (2005).
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B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J. Biomed. Opt. 9(3), 541–552 (2004).
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S. H. Chung, M. D. Feldman, D. Martinez, H. Kim, M. E. Putt, D. R. Busch, J. Tchou, B. J. Czerniecki, M. D. Schnall, M. A. Rosen, A. DeMichele, A. G. Yodh, and R. Choe, “Macroscopic optical physiological parameters correlate with microscopic proliferation and vessel area breast cancer signatures,” Breast Cancer Res. 17(1), 72 (2015).
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B. Deng, M. Lundqvist, Q. Fang, and S. A. Carp, “Impact of errors in experimental parameters on reconstructed breast images using diffuse optical tomography,” Biomed. Opt. Express 9(3), 1130–1150 (2018).
[Crossref]

B. B. Zimmermann, B. Deng, B. Singh, M. Martino, J. Selb, Q. Fang, A. Y. Sajjadi, J. Cormier, R. H. Moore, D. B. Kopans, D. A. Boas, M. A. Saksena, and S. A. Carp, “Multimodal breast cancer imaging using coregistered dynamic diffuse optical tomography and digital breast tomosynthesis,” J. Biomed. Opt. 22(4), 046008 (2017).
[Crossref]

A. Y. Sajjadi, S. J. Isakoff, B. Deng, B. Singh, C. M. Wanyo, Q. Fang, M. C. Specht, L. Schapira, B. Moy, A. Bardia, D. A. Boas, and S. A. Carp, “Normalization of compression-induced hemodynamics in patients responding to neoadjuvant chemotherapy monitored by dynamic tomographic optical breast imaging (DTOBI),” Biomed. Opt. Express 8(2), 555–569 (2017).
[Crossref]

B. Deng, D. H. Brooks, D. A. Boas, M. Lundqvist, and Q. Fang, “Characterization of structural-prior guided optical tomography using realistic breast models derived from dual-energy x-ray mammography,” Biomed. Opt. Express 6(7), 2366–2379 (2015).
[Crossref]

A. Kabeer, M. A. Saksena, J. Cormier, S. A. Carp, and B. Deng, “Compression-induced hemodynamic features of tumors in breast cancer patients undergoing neoadjuvant therapy: a longitudinal case study,” in Biophotonics Congress: Biomedical Optics 2020 (Translational, Microscopy, OCT, OTS, BRAIN) (2020), Paper JTh2A.7 (Optical Society of America, 2020), p. JTh2A.7.

DeSantis, C.

K. C. Oeffinger, E. T. H. Fontham, R. Etzioni, A. Herzig, J. S. Michaelson, Y.-C. T. Shih, L. C. Walter, T. R. Church, C. R. Flowers, S. J. LaMonte, A. M. D. Wolf, C. DeSantis, J. Lortet-Tieulent, K. Andrews, D. Manassaram-Baptiste, D. Saslow, R. A. Smith, O. W. Brawley, R. Wender, and A. C. Society, “Breast Cancer Screening for Women at Average Risk: 2015 Guideline Update From the American Cancer Society,” JAMA 314(15), 1599–1614 (2015).
[Crossref]

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A. Mîra, Y. Payan, A.-K. Carton, P. M. de Carvalho, Z. Li, V. Devauges, and S. Muller, “Simulation of breast compression using a new biomechanical model,” in Medical Imaging 2018: Physics of Medical Imaging (International Society for Optics and Photonics, 2018), Vol. 10573, p. 105735A.

Diamond, S. G.

M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt. 11(5), 054007 (2006).
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A. L. Darling, P. K. Yalavarthy, M. M. Doyley, H. Dehghani, and B. W. Pogue, “Interstitial fluid pressure in soft tissue as a result of an externally applied contact pressure,” Phys. Med. Biol. 52(14), 4121–4136 (2007).
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Figures (6)

Fig. 1.
Fig. 1. (a) A schematic of the measuring head of the system showing the main parts of the compression mechanism, (b) A picture of the measuring head showing a breast (represented by a balloon) under compression between the breast support plate and the compression paddle.
Fig. 2.
Fig. 2. (a) The finite element mesh used for hemodynamic computations and biomechanics modeling with red and blue dots identify the location of the sources and detectors relative to the mesh, respectively. (b) The 3D modeled compression procedure showing the support plate and the tilted compression paddle. The yellow pentagrams shown in (a) represent the positions of the source and detector of the reference channel.
Fig. 3.
Fig. 3. Spatial maps of pressure distribution and total hemoglobin (ΔHbT) responses to applied pressure. (a) The change in pressure distribution going from 4.45 N (1 lbf) to 53.4 N (12 lbf) compression force measured by Tekscan pressure sensor placed on the bottom supporting plate, (b) Axial views of the decrease in total hemoglobin concentration (ΔHbT) in the lower part of the breast after applying the 53.4 N compression. The images are from a 24-year old healthy participant with a BMI of 23.6.
Fig. 4.
Fig. 4. Spatial maps of calculated ΔIFP distribution as the applied force increased from 5 lbf to 10 lbf on heterogeneous models with inclusions . The upper row in the figure from left to right presents images for fibroglandular models with 90 kPa inclusions with 1, 1.5, and 2 cm radius, respectively. The lower row of figures from left to right present images from adipose models with 90 kPa inclusions with 1, 1.5, and 2 cm radius, respectively. The results are calculated using models with a volume equal to 400-ml. Dashed circles represent the boundary of the inclusions.
Fig. 5.
Fig. 5. Spatial maps of changes in (a) simulated ΔIFP and (b) reconstructed HbT from optical measurements taken as the compression increase from half 21.8 N to full 44.5 N mammographic force of a 47-year old cancer patient with a Grade 3 invasive ductal carcinoma (IDC) measuring 1.8 × 1.2 × 1.1 cm3. The dotted-line in (a) and (b) denotes the location of the tumor as marked by our collaborating radiologist. Anatomical information of adipose, fibroglandular, and tumor tissue compositions was derived from DBT x-ray images of the patient. The elastic moduli used to model adipose, fibroglandular, and tumors tissues for IFP simulation were 20, 40, and 90 kPa, respectively.
Fig. 6.
Fig. 6. Average IFP over an 8-cm3 cube located at the center of the breast volume for homogenous fibroglandular and adipose models as a function of (a) breast volume and (b) decrease in breast thickness. The error bars are the standard deviation of IFP across all nodes (n ranged from 29 to 230) in the central 8-cm3 volume. The decrease in breast thickness to simulate compression in (a) was 1 cm. The breast volume used in (b) was 400 ml.

Tables (1)

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Table 1. The 2D correlation coefficients and p-value between Δp and ΔHbT images after applying 12 lbf compression.

Equations (4)

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u ˙ ( κ p ) + χ p = 0
σ = ( p I + λ u I + 2 μ ε ) + ρ g = 0
τ i j = p δ i j + λ t r ( ε ) δ i j + μ ( ν i x j + ν j x i )
I F P = p ~ + ( λ + 2 3 μ ) t r ( ε )

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