2.1.

Clinical Protocol

In this study, which was compliant with the Health Insurance Portability and Accountability Act (HIPAA) and approved by the Columbia University Institutional Review Board, informed consent was obtained from 21 subjects. The subjects were instructed to stand in a comfortable position, while the breast interface was brought into contact and adjusted for each breast. The protocol involved 2 to 4 min of baseline imaging, followed by three trials of up to a 30-s breath-hold and a 90-s recovery. During the breath-hold, the subject was asked to avoid a large inhalation and to stop breathing, while maintaining pressure in the mouth and stomach. In the event that the subject could not complete the 30-s breath-hold, she was asked to indicate the end of the breath-hold by opening her mouth (four subjects). Three trials were performed in order to achieve one trial with minimal motion and acceptable breath-hold duration; in most subjects, the second trial was selected for reconstruction.

2.2.

DOT Instrumentation

All optical measurements were performed using a previously described continuous-wave digital DOT system designed for dynamic measurements of the breast.²⁴ The system uses four wavelengths of near-infrared light (765, 805, 827, and 905 nm) to illuminate the tissue and can acquire data from 32 sources and 64 detectors per breast with four wavelengths ($1.6\times {10}^4$ data points per image) at a rate of 1.7 Hz. The system images both breasts simultaneously using a 3-D configuration of optical fibers that surround and make direct contact with the breasts. A photograph of the system and fiber-breast interface is shown in Fig. 1.

Fig. 1

Photograph of the dynamic diffuse optical tomography (DOT) breast imaging system.

2.3.

Image Reconstruction Algorithm

Three-dimensional reconstructions were performed for the measurement data on a mesh of $\sim \mathrm{65,000}$ elements using a recently developed partial differential equation-constrained multispectral imaging method.^24,25 For this study, we use the diffusion approximation to the equation of radiative transfer to describe the light propagation in the breast, a scattering-dominated tissue.

For each subject and each breast, a 50-frame data set ($\sim 30\mathrm{s}$) acquired immediately prior to the onset of the breath-hold was averaged as a baseline. All chromophores were reconstructed relative to this baseline, and therefore images indicate a change in the concentration of oxy-hemoglobin $\mathrm{\Delta }[{\mathrm{HbO}}_2]\%$ or deoxy-hemoglobin $\mathrm{\Delta }[\mathrm{Hb}]\%$. Any channels with $<15\mathrm{dB}$ signal-to-noise ratio during the baseline period were excluded to avoid numerical instability and artifacts in the final reconstructed image. Further, we assumed typical breast tissue values for the baseline [${\mathrm{HbO}}_2$] and [Hb] as 18 and 9 μM, respectively.^26,27 Although these values may not be exact for all subjects, we are most concerned with the dynamic (therefore, relative) changes, and absolute chromophore values are not necessary for that analysis.^28,20 One hundred frame-time sequences corresponding to $\sim 60\mathrm{s}$ were reconstructed starting from the onset of the breath-hold and lasting through the recovery period.

2.4.

Image Quantification

All breast data was quantified using an automated MATLAB (Mathworks, Natick, Massachusetts) code to extract the average of a spherical region around the voxel of peak change ($\mathrm{\Delta }[\mathrm{Hb}]\%$ or $\mathrm{\Delta }[{\mathrm{HbO}}_2]\%$). The code automatically identifies the voxel of peak chromophore change for each image frame and takes the average of all voxels that fall within a sphere of radius 1 cm around that peak voxel [our designated region of interest (ROI)]. This technique has previously been used to quantify 3-D DOT images in preclinical studies.²⁹

To capture the differences in the overall hemodynamic response, while making use of the simultaneous measurement of optical properties from both breasts, we chose to also look at the correlation coefficient (CC) between the $\mathrm{\Delta }[\mathrm{Hb}]\%$ in the ROI of the left and the right breast during the 100 frames following the onset of the breath-hold [Eq. (1)].

Furthermore, we sought to capture the unique hemodynamic signature of the tumor. To this end, we fitted exponential rise and fall functions to the breath-hold and recovery (60 s total) and minimized the root-mean squared error between the exponential functions and the actual data. Such RC-circuit-like functions are commonly used, e.g., in the field of plethysmography to model hemodynamic responses to cuff experiments,³⁰ and can in general be expressed as

Here, $t$ is the time from the onset of the breath-hold, ${\tau }_{\mathrm{r}}$ is the rise time constant, and ${\tau }_{\mathrm{f}}$ is the fall time constant. For each patient, $t_{\mathrm{BH}}$ is automatically determined as the point during the breath-hold where the $\mathrm{\Delta }[\mathrm{Hb}]\%$ reaches its maximum. The functions $f_{\mathrm{sd}}$ and $f_{\mathrm{su}}$ are step down and step up functions, respectively, defined as follows:

All exponential fitting were performed on normalized experimental data in order to characterize the shape of the curve without considering the amplitude of change, and for this reason, Eq. (2) is normalized to unity at time $t_{\mathrm{BH}}$.

2.5.

Study Population

Dynamic DOT measurements were performed on 21 subjects over the course of 1 year. Three of the subjects were healthy volunteers, while the other 18 had a benign or malignant mass. Thirteen of the 21 subjects were postmenopausal with a mean age of $54\pm 10\text{years}$ and a mean body-mass index (BMI) of $30\pm 4$. Fourteen subjects had a malignant mass in one breast, of which four were invasive ductal carcinomas (IDC), one was invasive lobular carcinoma (ILC), two were ductal carcinomas in situ (DCIS), and seven were a combination of IDC, ILC, and DCIS. Three subjects had a benign mass in one breast, and one subject had benign masses in both breasts. Three subjects with a malignant mass in one breast also had a contralateral breast with a benign mass. Of the eight benign masses, one was atypical ductal hyperplasia (ADH), four were fibroadenomas (FA), one was a cyst, one was sclerosing adenosis (SA), and one was unbiopsied. The average mass size was 1.6 cm ranging from 0.1 to 4 cm. Overall, there were $n=8$ breasts with benign masses and $n=14$ breasts with malignant masses. Unless explicitly mentioned, all of these breasts were included in our statistical analysis.

All the subjects in this study had prior mammograms for comparison. In most cases, ultrasound and dynamic contrast-enhanced magnetic resonance imaging images were also available and were used to verify the tumor location and size. Table 1 contains a summary of the subjects who participated in the study.

Table 1

Summary of subjects and pathologies.

2.6.

Statistical Analysis

To compare the three groups (healthy breasts, breasts with a benign mass, and breasts with malignant masses), we employed the Holm t-test.^31–33 This test applies an accept/reject criterion to a set of ordered-null hypotheses, starting with the smallest $p$-value and proceeding until it fails to reject a null hypothesis. The null hypothesis in our case is that there is no difference between the three groups, or in other words that the samples are drawn from the same population. Therefore, we start by calculating the uncorrected $p$-values with a student t-test for all $k=3$ pairwise comparisons (healthy-malignant, healthy-benign, and benign-malignant). The resulting $p$-values are ordered from the smallest to the largest with the smallest $p$-value considered first in a sequential step-down test procedure. For the $j$’th hypothesis test in this ordered sequence, the Holm’s test applies the Bonferroni criterion³² until one fails to reject the null hypothesis. Specifically, the uncorrected $p$-value for the $j$’th test is compared with ${\alpha }_{\mathrm{j}}={\alpha }_{\mathrm{T}}/(k-j+1)$. For the first comparison, $j=1$, the uncorrected $p$-value needs to be smaller than ${\alpha }_1={\alpha }_{\mathrm{T}}/(k-j+1)={\alpha }_{\mathrm{T}}/k$. If the smallest calculated $p$-value is less than ${\alpha }_1$, we reject the null hypothesis, and then compare the next smallest uncorrected $p$-value with ${\alpha }_2={\alpha }_T/(k-2+1)={\alpha }_T/(k-1)$, etc. With ${\alpha }_T=0.05$ (significance level of 95%) we get in our case ($k=3$), ${\alpha }_1=0.0167$, ${\alpha }_2=0.025$, and ${\alpha }_3=0.05$; and with ${\alpha }_T=0.01$ (significance level of 99%), we get ${\alpha }_1=0.0033$, ${\alpha }_2=0.005$, and ${\alpha }_3=0.01$. All $p$-values subsequently reported in this article should be compared with these $\alpha$-values for assessing significance. For a more detailed discussion of this approach to multiple group comparisons, see Refs. 31–32.33.

3.1.

Mid-Recovery Tumor Visualization

Figure 3(a) shows DOT coronal slices through the left and the right breast from a 57-year-old postmenopausal woman [identified in Table 1 as Subject 17 (S17)] for multiple time points during the breath-hold and the recovery sequence. The tumor, an invasive ductal and lobular carcinoma located at the 11o’clock position in the right breast, is most visible during the mid-recovery time point (15 s after resuming normal breathing) by a substantial (10%) enhancement in $\mathrm{\Delta }[\mathrm{Hb}]\%$ [Fig. 3(b)]. Similarly, one can also observe an increase in $\mathrm{\Delta }[{\mathrm{HbO}}_2]\%$ [Fig. 3(c)], although at only 2%, this increase is smaller than that of $\mathrm{\Delta }[\mathrm{Hb}]\%$. The ipsilateral breast [Fig. 3(a), left] shows a more moderate 4% increase in $\mathrm{\Delta }[\mathrm{Hb}]\%$ that was typically observed in healthy breasts.

Fig. 3

(a) Coronal slices looking at the $\mathrm{\Delta }[\mathrm{Hb}]\%$ in the left (top) and right (bottom) breast at four different time points over the course of the breath-hold: Baseline ($t=0\mathrm{s}$), mid-breath hold ($t=20\mathrm{s}$), mid-recovery ($t=45\mathrm{s}$), and end recovery ($t=60\mathrm{s}$) There is an invasive carcinoma at 11 o’clock in the right breast (S17), which is most visible during the mid-recovery time point ($t=45\mathrm{s}$, 15 s after resuming normal breathing at $t=30\mathrm{s}$). Coronal slices showing (b) $\mathrm{\Delta }[\mathrm{Hb}]\%$ and (c) $\mathrm{\Delta }[{\mathrm{HbO}}_2]\%$ demonstrate that while an enhancement of $\mathrm{\Delta }[{\mathrm{HbO}}_2]\%$ is seen in the tumor region, the contrast is not as great as in $\mathrm{\Delta }[\mathrm{Hb}]\%$.

The increase in $\mathrm{\Delta }[\mathrm{Hb}]\%$ in the tumor region at the mid-recovery time point is observed across multiple pathologies including IDC, ILC, and DCIS, but not in healthy breasts, as shown in Fig. 4. An enhancing region can be seen in the correct location for each of the cancerous pathologies [Figs. 4(a)–4(d)], but no enhancing regions are visible in the case of a benign pathology [Fig. 4(e)] or in a healthy subject [Fig. 4(f)].

Fig. 4

Coronal slices through the breast showing the $\mathrm{\Delta }[\mathrm{Hb}]\%$ for the left and the right breast at the time point 15 s into the recovery period. The cases shown include (a) an invasive ductal carcinomas (IDC) at 1:00 in the right breast (S4); (b) an IDC and invasive lobular carcinoma (ILC) at 2:30 in the left breast (S9); (c) an ILC at 10:00 in the right breast; (d) ductal carcinoma in situ at 2:00 in the left breast (S16); (e) atypical ductal hyperplasia (ADH) at 11:00 in the left breast (S21); and (f) a healthy subject with no breast nodules (S3).

3.2.

Quantification of Mid-Recovery $\mathrm{\Delta }[\mathrm{Hb}]\%$

To quantify the changes in $\mathrm{\Delta }[\mathrm{Hb}]\%$ in the region of the tumor at the mid-recovery time point, we performed a statistic analysis of all subjects. Figure 5(a) shows the average $\mathrm{\Delta }[\mathrm{Hb}]\%$ for healthy breasts ($n=6$), breasts with benign masses ($n=8$), and breasts with malignant masses ($n=14$). The values of $\mathrm{\Delta }[\mathrm{Hb}]\%$ were calculated by averaging over a 1-cm-radius sphere surrounding the peak $\mathrm{\Delta }[\mathrm{Hb}]\%$ in each patient. At the mid-recovery time point, the healthy breasts have almost returned to the baseline ($\text{mean}=1.6\%\pm 0.5\%$), while the malignant regions still have some $\mathrm{\Delta }[\mathrm{Hb}]\%$ lingering through the recovery period ($\text{mean}=6.8\%\pm 3.6\%$). The values for breasts with benign masses ($\text{mean}=4.9\%\pm 2.7\%$) fall between the values observed for healthy breast and a breast bearing a malignant mass. There is a significant difference in $\mathrm{\Delta }[\mathrm{Hb}]\%$ between healthy breasts and breasts with a malignant mass ($p=0.0002$) as well as between the healthy and benign breasts ($p=0.014$), but not between breasts bearing a benign mass and a malignant mass ($p=0.19$).

Fig. 5

Statistical analysis of the differences in $\mathrm{\Delta }[\mathrm{Hb}]\%$ between healthy ($n=6$), benign ($n=8$), and tumor-bearing ($n=14$) breasts 15 s after the end of a breath-hold. (a) Mean value and standard deviations of the average $\mathrm{\Delta }[\mathrm{Hb}]\%$ in a 1-cm-sphere around the point of peak hemoglobin change. In (b), the $\mathrm{\Delta }[\mathrm{Hb}]\%$ was normalized to the peak change in either breast over the course of the breath-hold for each patient. This provides a more uniform metric across patients. Error bars represent the standard deviation across subjects (*$p<0.05$, **$p<0.01$)

To standardize the technique for better comparison across subjects, we normalized each breast to the maximum $\mathrm{\Delta }[\mathrm{Hb}]\%$ in the ROI over the course of the breath-hold in either breast for each subject [Fig. 5(b)]. Similar to the results found in Fig. 5(a), the healthy breasts and breasts with a benign mass have much smaller normalized $\mathrm{\Delta }[\mathrm{Hb}]\%$ [$\text{mean}(\text{healthy})=0.17\pm 0.1$, $\mathrm{mean}(\text{benign})=0.31\pm 0.22$], while the malignant-mass bearing breasts have a larger fraction of deoxy-hemoglobin remaining in the tumor region at mid-recovery time point [$\text{mean}(\text{malignant})=0.45\pm 0.27$]. With this normalization, we find that there is a significant difference between the healthy and the tumor-bearing breasts ($p=0.004$), but not between benign and healthy breasts ($p=0.12$) or benign and malignant breasts ($p=0.22$).

3.3.

Correlation Between Breasts

Subjects with two healthy breasts showed a high correlation between the hemodynamic response to the breath-hold in both the left and the right breasts [$\text{mean}({\mathrm{CC}}_{\text{healthy}})=0.96\pm 0.02$]. This correlation is somewhat lower in breasts with a benign mass [$\text{mean}({\mathrm{CC}}_{\text{benign}})=0.89\pm 0.02$] and, on average, much lower for breasts with a malignant mass [$\text{mean}({\mathrm{CC}}_{\text{malignant}})=0.75\pm 0.23$]. Using the Holm’s test, the differences between healthy subjects and patients with benign and malignant masses is statistically significant ($p=0.010$ and $p=0.015$, respectively), while the $p$-value for the comparison of patients with benign and malignant masses is slightly above the 0.05 threshold with 95% significance ($p=0.060$). (Note that to study the correlation between tumor bearing and healthy breast, we excluded the four patients who had lesions in both breasts.)

3.4.

Exponential Fitting of Breast Hemodynamics

Finally, Fig. 6 shows the results of our statistical analysis concerning the fall and the rise times of the $\mathrm{\Delta }[\mathrm{Hb}]\%$ signal when exponential functions are fitted [see Eq. (2)]. The average rise-time constant ${\tau }_r$ for the malignant tumor-bearing breasts (${\tau }_r=25.2\mathrm{s}$) appears to be smaller than for the healthy breasts (${\tau }_r=39.7\mathrm{s}$); however, because of the large standard deviation, the differences are not statistically significant ($p=0.33$) [Fig. 6(a)]. The difference in the average fall-time constants between healthy and tumor-bearing breasts is more pronounced [Fig. 6(b)]. On average, healthy breasts have a faster washout rate (${\tau }_f=14.3\mathrm{s}$) compared with malignant-tumor-bearing breasts (${\tau }_f=29.9\mathrm{s}$) ($p=0.09$), which agrees with the selection of the 15-s time point following the end of the breath-hold as a key time point for tumor visualization. The trends in uptake and washout rate provide insight into the hemodynamic responses of healthy and diseased tissues. A study with more healthy subjects and a larger number of breast cancer patients may shed more light on the significance of uptake and washout constants as biomarkers.

Fig. 6

Mean and standard deviations of the (a) rise-time (${\tau }_r$) and (b) fall-time (${\tau }_f$) constants for the exponential fit for healthy breasts ($n=6$), breasts with a benign mass ($n=8$), and breasts with a malignant mass ($n=14$).

3.5.

False Negative and False Positive Cases

In four tumor-bearing breasts, we were unable to visualize the tumor at the mid-recovery time point. Two of these cases (S6 and S13) involved large-breasted subjects with tumors near the chest wall. In these cases, it is possible that the fiber interface did not make adequate contact with the region of the breast that contained the tumor. As a result, the fiber interface was primarily imaging the healthy portion of the breast. In the third case (S16), suspicious nodules with tumor-like profiles were observed in the contralateral breast. These nodules were unbiopsied, so it is not clear how our finding relates to the pathology. In the fourth case (S14), the subject had very dense breasts, as indicated on the medical records.

In one of the breasts with a benign mass (S19), our imaging showed an enhancement in $\mathrm{\Delta }[\mathrm{Hb}]\%$ in the location indicated by the medical records. The mass has not been biopsied, and the subject is scheduled for a follow-up visit in 6 months.

4.1.

Origins of Dynamic Tumor Contrast

In this study, we demonstrated that there are hemodynamic biomarkers of breast cancer that can be detected with dynamic optical tomography imaging during a breath-hold. Respiratory maneuvers, such as a breath-hold or valsalva maneuver, have been previously explored in brain DOT imaging, where an increased blood volume is observed in the region overlying valveless cerebral veins that experience hypertension during the respiratory maneuver.³⁴ While the effect of respiratory maneuvers is not well studied in the breast, increased blood volume has been reported in some case studies involving one to two patients using DOT imaging of the breast during a valsalva maneuver or breath-hold.^20,35 These respiratory maneuvers are believed to cause increased intrathoracic pressure that is transmitted through the vascular tree resulting in increased arterial and venous pressure.³⁶ In addition to the increased blood volume during the maneuver, these studies have also reported that the change in [Hb] in the breast appears to be more sensitive to respiratory maneuvers, similar to our observations.

The source of dynamic contrast comes from differences in the architecture and the structure between normal and tumor vasculatures. Growing tumors require increased vasculature in order to supply nutrients and oxygen, while also removing waste products from the expanding tumor. Once tumors surpass approximately 200 μm, the tumor cells can no longer rely on diffusion from the nearby vessels, and therefore must recruit new blood vessels by releasing proangiogenic growth factors. The newly formed vasculature is tortuous, disorganized, and hyperpermeable.²³ There are many shunts and stunted vessels that disrupt the normal artery-capillary-vein vascular hierarchy. Due to this disorganized structure, despite increased vasculature, the tumor perfusion remains poor. Poor perfusion combined with the high-metabolic activity of tumor cells causes tumors to be more hypoxic than the surrounding healthy tissue.³⁷

In our study, the hemodynamic response of the tumor tissue differed from that of the healthy tissue. In healthy subjects, we saw a rise in [Hb] levels during the breath-hold, followed by a rapid return to the baseline levels upon the resumption of normal breathing. In tumor regions of the breast, we observed an increase in [Hb] levels during the breath-hold, followed by a much slower return to the baseline than in healthy subjects. We believe that this sluggish return to the baseline is due to the combined effect of the disorganized vasculature that affects blood flow in the tumor region and the hypoxic nature of oxygen-hungry tumors. Our results confirm and extend the results of case studies involving one or two patients looking at respiratory dynamics using DOT that reported a phase delay in the transient response of tumor tissue¹⁷ and a sluggish recovery in [Hb] levels following a breath-hold.²⁰ Similar effects have also been seen in pressure-induced dynamic optical imaging, where an increased [Hb] is a hallmark of the tumor region during compression.¹⁸

4.2.

Study Limitations

There are a number of clinical advantages of using dynamic DOT, which include the lack of compression during imaging, direct fiber contact with the breast which means no coupling fluid is required, and the use of endogenous contrast. The main disadvantage involves the variability in breath-holds performed by subjects. One of the four false negative subjects also suffered from asthma (S6), where poor breath-hold execution likely affected the DOT results. Asthma should be considered as a contraindication to future breath-hold studies.

Two subjects had large breasts (DDD and D size cups) with tumors located close to the chest wall (10 and 13 cm from the nipple). In those cases, we had difficulty in getting the tumor region into our optical breast interface due to the size of the breast, resulting in poor visualization of the tumor region. This issue can be addressed with more sophisticated designs for bringing the optical fibers in contact with the breast.

While this work included benign masses for analysis, its primary focus was in differentiating healthy tissue from malignant masses. Due to the variety of benign masses sampled and coupled with small sample size, it was not possible to infer strong statistical value from some of the benign subject data. While the work here shows some promising trends in the benign masses (typically falling in between healthy and malignant values), it is clear that a larger, more controlled study would be necessary to fully explore these findings.