# Characterizing Errors in Pharmacokinetic Parameters from Analyzing Quantitative Abbreviated DCE-MRI Data in Breast Cancer

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{8}

^{9}

^{10}

^{11}

^{12}

^{13}

^{14}

^{*}

## Abstract

**:**

^{trans}(volume transfer constant) and v

_{e}(extravascular/extracellular volume fraction), when compared to the full time course data. SKT analysis of simulated abbreviated time courses (ATCs) based on the imaging parameters from two available datasets (collected with a 3T MRI scanner) at a temporal resolution of 15 s (N = 15) and 7.23 s (N = 15) found a concordance correlation coefficient (CCC) greater than 0.80 for ATCs of length 3.0 and 2.5 min, respectively, for the K

^{trans}parameter. Analysis of the experimental data found that at least 90% of patients met this CCC cut-off of 0.80 for the ATCs of the aforementioned lengths. Patlak analysis of experimental data found that 80% of patients from the 15 s resolution dataset and 90% of patients from the 7.27 s resolution dataset met the 0.80 CCC cut-off for ATC lengths of 1.25 and 1.09 min, respectively. This study provides evidence for both the feasibility and potential utility of performing a quantitative analysis of abbreviated breast DCE-MRI in conjunction with acquisition of current standard-of-care high resolution scans without significant loss of information in the community setting.

## 1. Introduction

_{1}-weighted images before, during, and after the injection of a gadolinium-based contrast agent. To perform quantitative DCE-MRI analysis, in addition to the time course data just mentioned, a pre-contrast T

_{1}map, an arterial input function (an estimate of the time rate of change of the concentration of the contrast agent in the blood plasma), and a pharmacokinetic model to analyze the resulting data are also required. Typical pharmacokinetic analyses include the Kety–Tofts [19], tissue homogeneity [20], reference region [21], shutter-speed [22], and Patlak models [23]. Quantitative information derived from full-length DCE-MRI acquisitions (approximately 10 min in length) has demonstrated added benefit in distinguishing malignancies [5,13,24]. Specifically, the volume transfer constant, K

^{trans}, has been shown to statistically distinguish malignant from benign lesions, including in the ultra-fast DCE-MRI setting with superior temporal resolution [13,24,25,26]. Still, quantitative DCE-MRI can be challenging to incorporate into the clinical workflow as it requires higher temporal resolution data which comes at the expense of missing spatial resolution in the images required by radiologists. This is a pronounced problem in the ultra-fast regime that lacks high spatial resolution [24] and thus does not provide a viable solution for quantitative imaging in the clinical workflow. Importantly, no studies have been published that seek to characterize the errors introduced into pharmacokinetic modeling that is performed on the shortened time course data acquired from an abbreviated protocol.

^{trans}) and the extravascular/extracellular volume fraction (v

_{e}) when we apply these models to both simulated and experimentally measured DCE-MRI data obtained in two different clinical breast imaging settings: a multi-site, network-based clinical trial and a single site, community-based imaging center. Analysis in multiple settings provides a robust approach for future feasibility and widespread implementation. For each abbreviated time course, we quantify the error in the parameter values as compared to those measured using the original, full-time course data to determine a recommendation on how quantitative analysis of abbreviated DCE-MRI of the breast can be performed in the clinical setting.

## 2. Methodology

#### 2.1. ACRIN 6883 Trial DCE-MRI Acquisition

_{1}maps for the imaged tissue. DCE-MRI data was collected with TR/TE = 100/4–5 ms, a flip angle of α = 90°, and an acquisition matrix of 256 × 128 over a (160–180) × (160 to 180) mm

^{2}field-of-view (FOV) with a slice thickness of 4 mm. Each of the 11-slice sets was collected in 15 s over various scan times ranging from 14 total time points (3.50 min) to 37 total time points (9.25 min). The dynamic scan was initiated simultaneously with the delivery of 0.1 mmol/kg of a gadolinium chelate (Omniscan, GE Healthcare; Prohance, Bracco; or Magnevist, Berlex) administered over 10 s through a catheter placed within an antecubital vein followed by a saline flush. No arterial input function was available for this study; however, dynamic data were collected from reference regions drawn within the chest wall muscle of each patient, thereby enabling a reference region analysis. To determine the tumor regions-of-interest (ROIs), a conservative boundary was drawn around each lesion and refined by selecting voxels with a percent enhancement greater than 50% [6]. Going forward, we will refer to these data as the ACRIN dataset. The acquisition details were sourced from previous studies [6,13].

#### 2.2. Single-Site DCE-MRI Acquisition

_{1}-corrected flip angles to estimate pre-contrast T

_{1}maps for the imaged tissue. The data for the B

_{1}-correction were obtained via the Siemens TurboFLASH sequence with a pre-conditioning radiofrequency pulse [27] with TR/TE = 8680/2 ms, a flip angle of α = 8°, an acquisition matrix of 96 × 96, and a slice thickness of 5 mm. DCE-MRI data was collected with TR/TE = 7.02/4.60 ms, a flip angle of α = 6°, an acquisition matrix of 192 × 192 over a 256 × 256 mm

^{2}FOV, a slice thickness of 5 mm, and a GRAPPA (generalized autocalibrating partial parallel acquisition) acceleration factor of 2. Each of the 10-slice sets was collected in 7.27 s across 66 total time points for 8 min of total DCE-MRI scan time. After collecting one minute of baseline dynamic scans (i.e., the first eight time points), 10 mL of Gadavist (Bayer, Whippany, NJ, USA) was delivered at 2 mL/sec followed by a saline flush through a catheter placed within an antecubital vein. A population averaged arterial input function was established from the present dataset based on previously established methodology [7]. To determine the tumor ROIs, a conservative bounding-box was manually drawn over each focal lesion using the percent enhancement map (increase over 50% compared to baseline signal intensity) obtained from the DCE-MRI data. These ROIs were then refined using a fuzzy c-means clustering algorithm [28]. Going forward, we will refer to these data as the single-site dataset.

#### 2.3. DCE-MRI Data Analysis

^{trans}) characterizes the delivery and retention of contrast agent in both the SKT and Patlak models, while the extravascular extracellular volume fraction (v

_{e}) is exclusive to the SKT models.

_{n}”. For application of the SKT model to the ACRIN dataset, n was selected as the inclusive set of integers from 7 to 18, incrementing by one (an increment of 0.25 min); for the single-site dataset, n was chosen to be the inclusive set ranging from 13 through 53, incrementing by eight (an increment of 1.0 min) to span the entirety of the eight-minute FTC. For the Patlak analysis of the ACRIN dataset, n was chosen as the inclusive set of integers from 2 to 7, incrementing by one (an increment of 0.25 min); and, for the single-site dataset, n was chosen as the inclusive set of integers from 5 to 14, incrementing by one (an increment of 0.12 min). Because the Patlak model assumes no washout occurs in the early part of perfusion, the range of n for the Patlak analysis of both datasets was chosen to include the enhancement phase across varying ATCs with an effort to exclude the washout phase entirely. The SKT and Patlak models were fit to the FTCs, as well as the ATCs, to estimate K

^{trans}(SKT and Patlak) and v

_{e}(SKT only) using the “lsqnonlin” function implemented in MATLAB (Mathworks, Natick, MA). Voxels for which the estimated parameters fell outside of the physiological range (the range being 0.001 < K

^{trans}< 5.0 and 0.001 < v

_{e}< 1.0) were eliminated from further analysis. The FTC parameter estimates were considered to be the gold standard to which all ATC

_{n}parameter estimates were compared on a voxel-wise basis.

#### 2.4. DCE-MRI Simulated Data Analysis

^{trans}and v

_{e}FTC parameter values from each voxel within each patient’s acquisition to construct a set of zero-noise DCE-MRI time courses via the SKT model. Next, the signal-to-noise ratio (SNR) from each patient’s DCE-MRI study was calculated using the first seven pre-contrast time points from the adipose for the single-site dataset and the first seven time points from the adipose tissue for the ACRIN dataset. Finally, the voxel-wise SNR was averaged over the tumor ROI for the entire cohort such that each patient dataset is characterized by a single SNR value (Table 1). The ATC

_{n}of the simulated data were generated in the same fashion as in the experimental data through truncation of the simulated FTC data. The SKT and Patlak models were then fit to the both the noiseless and noisy versions of each simulated DCE-MRI time course to arrive at K

^{trans}and v

_{e}values for each voxel in the simulated tumor ROI. Again, the FTC parameter estimates were treated as the gold standard to which all ATC

_{n}parameters were compared.

#### 2.5. Statistical Analysis

^{trans}(from both the SKT and Patlak models) and v

_{e}(SKT model only) estimated from fitting the FTCs and ATCs were averaged over the ROI to produce mean values and 95% confidence intervals (CIs) for each patient. Additionally, the absolute average percent error between the ATC

_{n}and FTC parameter values were computed and averaged over the tumor ROI along with their 95% CIs over the ACRIN and single-site patient datasets, respectively. To determine the similarity between the ATC

_{n}and FTC (gold-standard) parameter values for each voxel within the tumor ROIs, the concordance correlation coefficient (CCC, ranging from 0 to 1) was used to assess the level of agreement between each FTC–ATC

_{n}pair from each patient dataset. The Pearson’s linear correlation coefficient (r, ranging from −1 to 1) was used as a measure of goodness of fit for all models to all FTC and ATC

_{n}data.

## 3. Results

_{n}s, yielding 13 sets of mean K

^{trans}and v

_{e}parameter values and the corresponding 95% CIs. Similarly, the Patlak analysis of these same patients, one FTC and six ATC

_{n}s, were analyzed to yield seven mean K

^{trans}parameter values and the corresponding 95% CIs. An analogous set of results was computed from the 15 sets of simulated data based on patient-specific signal-to-noise (SNR) values and imaging parameters of the ACRIN acquisition protocol.

#### 3.1. Pharmacokinetic Assessment of ACRIN-Based Simulated Data

_{n}simulated from each patient, a pair of ROI-averaged K

^{trans}(Figure 1A) and v

_{e}(Figure S1A) values were compared to the corresponding FTC average parameter values obtained from the SKT model. In all simulated patients, the mean estimates of K

^{trans}and v

_{e}tended to be greater than their FTC “gold-standard” counterparts (p > 0.05 for all ATCs except ATC

_{7}, ATC

_{8}, and ATC

_{9}for v

_{e}only, where p < 0.05), revealing a systematic overestimation of both parameters as the time series were increasingly truncated. A direct relationship was observed in the CCC values of both parameters (Figures S1B and S2A), which asymptotically approached a value of 1.0 as the ATCs were lengthened. Choosing a CCC cut-off value of 0.90 for K

^{trans}, we observed that 14 patients met this cut-off for ATC

_{15}(i.e., 3.8 min of scan time), with the mean and standard deviation of the CCCs being 0.94 ± 0.07. Choosing a less conservative CCC value of 0.80 as the cut-off, then the shortest ATC for which all patients met this cut-off increased to ATC

_{17}(i.e., 4.25 min of scan time) with mean and standard deviation of 0.97 ± 0.05. The average percent error between the ATC

_{n}s and FTC K

^{trans}values monotonically decreased with longer ATCs (e.g., 11.30% error for ATC

_{18}compared to 77.25% error for ATC

_{7}) (Figure 1B), though the percent error was significantly higher (p < 0.05) in v

_{e}than in K

^{trans}(44.60% error for ATC

_{18}compared to 106.68% error for ATC

_{7}) (Supplemental Figure S1C) over all ATC

_{n}lengths.

^{trans}(Figure 1C) from all ATC

_{n}s were closer in value to their FTC “gold-standard” counterparts as the time series were increasingly truncated. The CCCs (Supplemental Figure S2B) did not monotonically increase toward a value of 1.0 for all patients, instead more often peaking at a specific ATC

_{n}before decreasing again; and two patients exhibited monotonically decreasing CCCs. Choosing a CCC cut-off value of 0.90 for K

^{trans}yielded a maximum of two patients that meet this cut-off for ATC

_{3}(i.e., 0.75 min of scan time), with the mean and standard deviation of the CCCs being 0.75 ± 0.13. For a less conservative CCC value of 0.80 as the cut-off, a maximum of seven patients met this cut-off at ATC

_{4}(i.e., 1.0 min of scan time) with a mean and standard deviation of 0.76 ± 0.14. The average percent error between the ATC

_{n}and FTC K

^{trans}values monotonically decreased until a minimum was reached at ATC

_{6}(32.66% error) before increasing again with ATC

_{7}(34.18% error) (Figure 1D).

#### 3.2. Pharmacokinetic Assessment of ACRIN Clinical Data

^{trans}(Figure 1E) and v

_{e}(Figure S1D) from all ATC

_{n}s were not significantly different from their FTC “gold-standard” counterparts (p > 0.05 for all ATCs except ATC

_{7}, ATC

_{8}, and ATC

_{7}for v

_{e}only, where p < 0.05), revealing a systematic underestimation in K

^{trans}and overestimation in v

_{e}as the time series were increasingly truncated (Figure 2A–C and Figure 3A–C, Figures S5A–C and S6A–C). A direct relationship was observed in the CCC values of both parameters (Figures S1E and S2C), which asymptotically approached a value of 1.0 as the lengths of the ATC

_{n}s were increased. Choosing a CCC cut-off value of 0.90 for K

^{trans}, we observed that at most 11 patients met this cut-off for ATC

_{14}(i.e., 3.5 min of scan time) with CCCs of 0.88 ± 0.16. If we choose a less conservative CCC value of 0.80 as the cut-off, then the shortest ATC

_{n}for which a maximum of 12 patients met this cut-off is again ATC

_{14}(i.e., 3.5 min of scan time). The average percent error between the ATC

_{n}s and FTC K

^{trans}values monotonically decreased with longer ATC

_{n}s (9.77% error for ATC

_{18}compared to 30.60% error for ATC

_{7}) (Figure 1F), though the percent error was higher (p = 0.08) in v

_{e}than in K

^{trans}over nearly all ATC

_{n}lengths except ATC

_{18}(9.16% error for ATC

_{18}compared to 106.61% error for ATC

_{7}) (Supplemental Figure S1F).

^{trans}(Figure 1G) from all ATC

_{n}s approached their FTC “gold-standard” counterparts for intermediary abbreviations rather than the shortest or longest ones (Figure 2G–I and Figure 3G–I). The CCCs (Figure S2D) did not monotonically increase toward a value of 1.0 for all patients, instead more often peaking at a specific ATC

_{n}before fluctuating in value thereafter. Choosing a CCC cut-off value of 0.90, a maximum of four patients met this cut-off for ATC

_{4}(i.e., 1.0 min of scan time) with mean and standard deviation of the CCCs being of 0.74 ± 0.21. For a CCC cut-off value of 0.80, the shortest ATC for which a maximum number of patients, namely eight, met this CCC cut-off was ATC

_{5}(i.e., 1.25 min of scan time) with a mean and standard deviation of 0.77 ± 0.18. The average percent error between the ATC and FTC K

^{trans}values monotonically decreased until a minimum was reached at ATC

_{5}(30.51% error) before increasing again with ATC

_{6}(30.79% error) (Figure 1H).

_{n}s, yielding seven sets of mean K

^{trans}and v

_{e}parameter values and the corresponding 95% CIs. Similarly, for analysis with the Patlak model of these same patients, one FTC and ten ATC

_{n}s were analyzed, yielding eleven mean K

^{trans}parameter values and the corresponding 95% CIs. An analogous set of results was computed from the 15 sets of simulated data based on patient-specific SNR values and the imaging parameters of the single-site acquisition protocol.

#### 3.3. Pharmacokinetic Assessment of Single-Site-Based Simulated Data

^{trans}(Figure 4A) and v

_{e}(Figure S3A) from all ATC

_{n}s tented to be greater than their FTC “gold-standard” counterparts (p > 0.05). A direct relationship was observed in the CCC values of both parameters (Figures S3B and S4A), which asymptotically approached a value of 1.0 as the ATCs were lengthened. Choosing a CCC cut-off value of 0.90 for K

^{trans}, we observed that all ten patients met this cut-off for ATC

_{37}(i.e., 4.5 min of scan time) with the mean and standard deviation of the CCCs being 0.99 ± 0.02. If we choose a less conservative CCC value of 0.80 as the cut-off, then the shortest ATC for which all patients meet this cut-off is ATC

_{29}(i.e., 3.5 min of scan time) with a mean and standard deviation of 0.98 ± 0.02. The average percent error between the ATC

_{n}s and FTC K

^{trans}values monotonically decreased with longer ATCs (1.93% error for ATC

_{53}compared to 28.51% error for ATC

_{13}) (Figure 4B). This percent error was systematically higher (p = 0.07), in v

_{e}(4.23% error for ATC

_{53}compared to 135.13% error for ATC

_{13}) (Figure S3C) than in K

^{trans}over the course of all ATC

_{n}lengths.

^{trans}(Figure 4C) from all ATCs were closer in value to their FTC “gold-standard” counterparts as the time series were increasingly abbreviated. The CCCs (Figure S4B) did not monotonically increase toward a value of 1.0 for all patients, instead more often peaking at a specific ATC

_{n}before fluctuating in value thereafter. Choosing a CCC cut-off value of 0.90 for K

^{trans}, we observe that a maximum of nine patients met this cut-off for ATC

_{9}(i.e., 1.09 min of scan time) with CCCs of 0.88 ± 0.10. If we choose a less conservative CCC value of 0.80 as the cut-off, then the shortest ATC

_{n}for which a maximum of 13 patients met this CCC cut-off was ATC

_{6}(i.e., 0.73 min of scan time). The average percent error between the ATC

_{n}s and FTC K

^{trans}values monotonically decreased until a minimum was reached at ATC

_{12}(17.34% error) before increasing again with ATC

_{13}(17.40% error) (Figure 4D).

#### 3.4. Pharmacokinetic Assessment of Single-Site Clinical Data

^{trans}(Figure 4E) and v

_{e}(Figure S3D) from all ATC

_{n}s were, respectively, greater than and less than (p > 0.05) their FTC “gold-standard” counterparts (except for significance in ATC

_{13}for K

^{trans}where p < 0.05). This reveals a systematic overestimation in K

^{trans}and underestimation in v

_{e}as the time series were increasingly truncated (Figure 2D–F and Figure 3D–F, Figures S5D–F and S6D–F). A direct relationship was observed in the CCC values of both parameters (Figures S3E and S4C), which asymptotically approached a value of 1.0 as the lengths of the ATC

_{n}s were lengthened. Choosing a CCC cut-off value of 0.90 for K

^{trans}, all ten patients met this cut-off for ATC

_{37}(i.e., 4.5 min of scan time) with the mean and standard deviation of the CCCs being 0.99 ± 0.02. If we choose a less conservative CCC value of 0.80 as the cut-off, then the shortest ATC for which 14 out of 15 patients met this CCC cut-off was ATC

_{29}(i.e., 3.5 min of scan time) with a mean and standard deviation of 0.94 ± 0.04. The average percent error between the ATC

_{n}and FTC K

^{trans}values decreased monotonically with longer ATC

_{n}s (0.63% error for ATC

_{53}compared to 117.34% error for ATC

_{13}) (Figure 4F), though the percent error was higher (p = 0.59) in v

_{e}than in K

^{trans}over the course of nearly all ATC lengths except ATC

_{13}(2.19% error for ATC

_{53}compared to 74.27% error for ATC

_{13}) (Figure S3F).

^{trans}(Figure 4G) from all ATCs deviated from their FTC “gold-standard” counterparts in nearly all simulated patients as the time series were increasingly abbreviated, with significant differences observed in ATC

_{5}(p = 0.005) (Figure 2J-L and Figure 3J–L). The CCCs (Figure S4D) were again observed to not monotonically increase toward a value of 1.0 for all patients, instead more often peaking at a specific ATC before fluctuating in value thereafter. Choosing a CCC cut-off value of 0.90, we observed that at most 12 patients meet this cut-off for ATC

_{10}(i.e., 1.20 min of scan time) from the set of CCCs with a mean and standard deviation of 0.91 ± 0.09. If we choose a less conservative CCC value of 0.80 as the cut-off, then the shortest ATC

_{n}for which a maximum of 12 patients meets this CCC cut-off is ATC

_{10}again. The average percent error between the ATC and FTC K

^{trans}values decreased monotonically until a minimum was reached at ATC

_{12}(7.67% error) before increasing again with ATC

_{13}(7.95% error) (Figure 4H).

## 4. Discussion

^{trans}exhibits substantially low error and high CCC values across ATCs for both the SKT and Patlak analyses. This strongly suggests that the length of a DCE-MRI measurement can be substantially shortened without a substantial reduction in the ability to quantify the pharmacokinetics. Our results indicate it is feasible for 80% of patients from the single-site cohort analyzed by the Patlak model to exceed a CCC for K

^{trans}of 0.80 for an abbreviated time course as short as 1.20 min. Similarly, it is feasible for 60% of patients from the ACRIN cohort (with a substantially poorer temporal resolution) analyzed by the Patlak model to exceed a CCC for K

^{trans}of 0.80 for an abbreviated time course as short as 1.25 min. This implies that abbreviated—but still quantitative—DCE-MRI can be performed for screening high-risk patients. This reduction in total scan time can then be “spent” on making additional measurements of interest (e.g., diffusion-weighted MRI [29,30]), or simply be used to shorten the entire examination. In particular, K

^{trans}may add specificity in distinguishing malignant lesions in DCE-MRI screening scans for high-risk women [13]. Conversely, as v

_{e}has not yet been shown to statistically separate malignant from benign tissue, collecting the full extent of the washout phase may not be necessary. It is important to recall that this study also made use of data acquired in two very different settings: a multi-site, clinical trial run at academic research-oriented medical centers, and a single-site, community-based care setting. Thus, the results have the potential to be generalizable across clinical imaging environments.

_{e}from the SKT model was consistently higher than the absolute error in K

^{trans}across most ATC

_{n}s when compared to the FTC. K

^{trans}and v

_{e}are largely determined by the enhancement and washout phases, respectively; thus, as the data truncation did not exclude the enhancement phase, a smaller absolute error is expected in K

^{trans}than in v

_{e}. In terms of CCCs from the SKT analysis, we found that a similar number of patients met the higher CCC cut-off for K

^{trans}of 0.90 in the single-site cohort (93% in the experimental data analysis for a 3.5 min abbreviation, 100% in the simulation data analysis for a 3.5 min abbreviation) and the ACRIN cohort (80% in the experimental data analysis for a 4.25 min abbreviation, 100% in the simulation data analysis for a 3.5 min abbreviation). The Patlak analysis of the single-site cohort achieved smaller absolute error in both the simulated (17.34% error for a 1.5 min abbreviation) and experimental (7.67% error for a 1.5 min abbreviation) datasets compared to the Patlak analysis of the ACRIN cohort in both the simulated (32.66% error for a 1.25 min abbreviation) and experimental (30.51% error for a 1.5 min abbreviation) datasets. This difference is most likely due to the superior temporal resolution of the single-site study compared to the ACRIN study (7.27 versus 15 s). In terms of CCCs from the Patlak analysis, we found that more patients met the higher CCC cut-off of 0.90 in the single-site cohort (80% in the experimental data analysis for a 1.2 min abbreviation, 60% in the simulation data analysis for 1.2 and 1.09 min abbreviations, respectively) than the ACRIN cohort did (27% in the experimental data analysis for a 1.0 min abbreviation, 13% in the simulation data analysis for a 0.75 min abbreviation). The Patlak model will improve in accuracy as long as the amount of data from the enhancement phase of the DCE-MRI time course is being increased; but once the data begins to include the plateauing and washout phases of the time course, the Patlak model is no longer an appropriate model, and its accuracy in parameter estimation begins to decrease. Overall, these findings indicate that an abbreviated DCE-MRI breast scan with sufficient temporal resolution can be feasibly analyzed with the Patlak model as well as the SKT model to produce K

^{trans}values that closely match those from analyzing a full-length scan with the SKT model.

_{e}; this can be remedied by employing a larger flip angle. Conversely, the 90° flip angle employed in the ACRIN study will limit the image contrast and reduce the overall SNR (being far away from the Ernst angle). In addition, the presence and location of breast clips post-biopsy and how they affected the signal intensity curves in the surrounding tissue were not available and thus not considered in the perfusion model analyses [32]. Lastly, while strides have been made toward reproducible quantitative DCE-MRI of the breast across multiple sites [33,34], the results of the present study could be strengthened by being repeated in prospectively abbreviated quantitative scans with uniform imaging parameters across multiple sites.

^{trans}in the abbreviated setting has shown promise with 100% of patients meeting a stringent CCC cut-off of 0.90 for K

^{trans}from the SKT analysis in the single-site cohort for a 4.5 min abbreviation and at least 73% of patients from the ACRIN cohort for a 3.5 min abbreviation). At least 80% of patients met a stringent CCC cut-off of 0.90 from the Patlak analysis for the single-site cohort. These robust results indicate the potential for employing abbreviated quantitative DCE-MRI scans for screening high-risk patients in the routine clinical setting.

## Supplementary Materials

_{e}from fitting the SKT model to ACRIN-based simulated data and ACRIN clinical data, Figure S2: CCCs from SKT and Patlak model analysis of ACRIN-based simulated data and ACRIN clinical data, Figure S3: Analysis of v

_{e}from fitting the SKT model to single-site-based simulated data and single-site clinical data, Figure S4: CCCs from SKT and Patlak model analysis of single-site-based simulated data and single-site clinical data., Figure S5: Comparing SKT ve error for a long ATC for a representative patient from each dataset, and Figure S6: Comparing SKT v

_{e}error for a short ATC for a representative patient from each dataset.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

DCE-MRI | dynamic contrast-enhanced MRI |

FTC | full time course |

ATC | abbreviated time course |

GRAPPA | generalized autocalibrating partial parallel acquisition |

BI-RADS | breast imaging reporting and data system |

IBMC | International Breast MR Consortium |

ACRIN | American College of Radiology Imaging Network |

ROI | region of interest |

SPGR | spoiled gradient echo |

## References

- Sardanelli, F.; Podo, F.; Santoro, F.; Manoukian, S.; Bergonzi, S.; Trecate, G.; Vergnaghi, D.; Federico, M.; Cortesi, L.; Corcione, S.; et al. Multicenter surveillance of women at high genetic breast cancer risk using mammography, ultrasonography, and contrast-enhanced magnetic resonance imaging (the high breast cancer risk italian 1 study): Final results. Investig. Radiol.
**2011**, 46, 94–105. [Google Scholar] [CrossRef] - Moy, L.; Elias, K.; Patel, V.; Lee, J.; Babb, J.S.; Toth, H.K.; Mercado, C.L. Is breast MRI helpful in the evaluation of inconclusive mammographic findings? Am. J. Roentgenol.
**2009**, 193, 986–993. [Google Scholar] [CrossRef] [PubMed] - Kuhl, C.K.; Schrading, S.; Leutner, C.C.; Morakkabati-Spitz, N.; Wardelmann, E.; Fimmers, R.; Kuhn, W.; Schild, H.H. Mammography, breast ultrasound, and magnetic resonance imaging for surveillance of women at high familial risk for breast cancer. J. Clin. Oncol.
**2005**, 23, 8469–8476. [Google Scholar] [CrossRef] [PubMed] - Leach, M.O.; Boggis, C.R.; Dixon, A.K.; Easton, D.F.; Eeles, R.A.; Evans, D.G.R.; Gilbert, F.J.; Griebsch, I.; Hoff, R.J.C.; Kessar, P.; et al. Screening with magnetic resonance imaging and mammography of a UK population at high familial risk of breast cancer: A prospective multicentre cohort study (MARIBS). Lancet
**2005**, 365, 1769–1778. [Google Scholar] - Li, K.; Machireddy, A.; Tudorica, A.; Moloney, B.; Oh, K.Y.; Jafarian, N.; Partridge, S.C.; Li, X.; Huang, W. Discrimination of Malignant and Benign Breast Lesions Using Quantitative Multiparametric MRI: A Preliminary Study. Tomography
**2019**, 6, 148–159. [Google Scholar] [CrossRef] - Schnall, M.D.; Blume, J.; Bluemke, D.A.; Deangelis, G.A.; Debruhl, N.; Harms, S.; Heywang-Köbrunner, S.H.; Hyltono, N.; Kuhl, C.K.; Pisanoo, E.D.; et al. MRI detection of distinct incidental cancer in women with primary breast cancer studied in IBMC 6883. J. Surg. Oncol.
**2005**, 92, 32–38. [Google Scholar] [CrossRef] [PubMed] - Sippo, D.A.; Burk, K.S.; Mercaldo, S.F.; Rutledge, G.M.; Edmonds, C.; Guan, Z.; Hughes, K.S.; Lehman, C.D. Performance of Screening Breast MRI across Women with Different Elevated Breast Cancer Risk Indications. Radiology
**2019**, 292, 51–59. [Google Scholar] [CrossRef] - Kuhl, C.K.; Weigel, S.; Schrading, S.; Arand, B.; Bieling, H.; König, R.; Tombach, B.; Leutner, C.; Rieber-Brambs, A.; Nordhoff, D.; et al. Prospective multicenter cohort study to refine management recommendations for women at elevated familial risk of breast cancer: The EVA trial. J. Clin. Oncol.
**2010**, 28, 1450–1457. [Google Scholar] [CrossRef][Green Version] - Heller, S.L.; Moy, L. MRI breast screening revisited. J. Magn. Reson. Imaging
**2019**, 49, 1212–1221. [Google Scholar] [CrossRef] - Kuhl, C.K.; Schrading, S.; Strobel, K.; Schild, H.H.; Hilgers, R.D.; Bieling, H.B. Abbreviated Breast Magnetic Resonance Imaging (MRI): First Postcontrast Subtracted Images and Maximum-Intensity Projection—A Novel Approach to Breast Cancer Screening With MRI. J. Clin. Oncol.
**2014**, 32, 2304–2310. [Google Scholar] [CrossRef] - Greenwood, H.I. Abbreviated protocol breast MRI: The past, present, and future. Clin. Imaging
**2019**, 53, 169–173. [Google Scholar] [CrossRef] [PubMed] - Chen, S.Q.; Huang, M.; Shen, Y.Y.; Liu, C.L.; Xu, C.X. Abbreviated MRI protocols for detecting breast cancer in women with dense breasts. Korean J. Radiol.
**2017**, 18, 470–475. [Google Scholar] [CrossRef] [PubMed][Green Version] - Sorace, A.G.; Partridge, S.C.; Li, X.; Virostko, J.; Barnes, S.L.; Hippe, D.S.; Huang, W.; Yankeeloov, T.E. Distinguishing benign and malignant breast tumors: Preliminary comparison of kinetic modeling approaches using multi-institutional dynamic contrast-enhanced MRI data from the International Breast MR Consortium 6883 trial. J. Med. Imaging
**2018**, 5, 011019. [Google Scholar] - Wu, C.; Pineda, F.; Hormuth, D.A.; Karczmar, G.S.; Yankeelov, T.E. Quantitative analysis of vascular properties derived from ultrafast DCE-MRI to discriminate malignant and benign breast tumors. Magn. Reson. Med.
**2019**, 81, 2147–2160. [Google Scholar] [CrossRef] [PubMed] - Grimm, L.J.; Soo, M.S.; Yoon, S.; Kim, C.; Ghate, S.V.; Johnson, K.S. Abbreviated Screening Protocol for Breast MRI. A Feasibility Study. Acad. Radiol.
**2015**, 22, 1157–1162. [Google Scholar] [CrossRef] [PubMed] - Leithner, D.; Moy, L.; A Morris, E.; A Marino, M.; Helbich, T.H.; Pinker, K. Abbreviated MRI of the Breast: Does It Provide Value? J. Magn. Reson. Imaging
**2019**, 49, e85–e100. [Google Scholar] [CrossRef] [PubMed] - Li, H.-N.; Chen, C.-H. Ultrasound-Guided Core Needle Biopsies of Breast Invasive Carcinoma: When One Core is Sufficient for Pathologic Diagnosis and Assessment of Hormone Receptor and HER2 Status. Diagnostics
**2019**, 9, 54. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hormuth, D.A.; Sorace, A.G.; Virostko, J.; Abramson, R.G.; Bhujwalla, Z.M.; Enriquez-Navas, P.; Gillies, R.; Hazle, J.D.; Mason, R.P.; Quarles, C.C.; et al. Translating preclinical MRI methods to clinical oncology. J. Magn. Reson. Imaging
**2019**, 50, 1377–1392. [Google Scholar] [CrossRef] [PubMed] - Tofts, P.; Kermode, A.G. Measurement of the blood-brain barrier permeability and leakage space using dynamic MR imaging. 1. Fundamental concepts. Magn. Reson. Med.
**1991**, 17, 357–367. [Google Scholar] [CrossRef] - Lawrence, K.S.; Lee, T.Y. An adiabatic approximation to the tissue homogeneity model for water exchange in the brain: I. Theoretical derivation. J. Cereb. Flow Metab.
**1998**, 18, 1365–1377. [Google Scholar] [CrossRef] - Planey, C.R.; Welch, E.B.; Xu, L.; Chakravarthy, A.B.; Gatenby, J.C.; Freehardt, D.; Mayer, I.; Meszeoly, I.; Kelley, M.; Means-Powell, J.; et al. Temporal sampling requirements for reference region modeling of DCE-MRI data in human breast cancer. J. Magn. Reson. Imaging JMRI
**2009**, 30, 121–134. [Google Scholar] [CrossRef] [PubMed][Green Version] - Jajamovich, G.H.; Huang, W.; Besa, C.; Li, X.; Afzal, A.; Dyvorne, H.A.; Taouli, B. DCE-MRI of hepatocellular carcinoma: Perfusion quantification with Tofts model versus shutter-speed model—Initial experience. Magma Magn. Reson. Mater. Phys. Biol. Med.
**2015**, 29, 49–58. [Google Scholar] [CrossRef][Green Version] - Karakatsanis, N.A.; Zhou, Y.; Lodge, M.A.; Casey, M.E.; Wahl, R.L.; Zaidi, H.; Rahmim, A. Generalized whole-body Patlak parametric imaging for enhanced quantification in clinical PET. Phys. Med. Biol.
**2015**, 60, 8643–8673. [Google Scholar] [CrossRef] [PubMed][Green Version] - Pineda, F.D.; Medved, M.; Wang, S.; Fan, X.; Schacht, D.; Sennett, C.; Aytekin, O.; Newstead, G.M.; Hiroyuki, A.; Karczmar, G.S. Ultrafast bilateral DCE-MRI of the breast with conventional Fourier sampling: Preliminary evaluation of semi-quantitative analysis. Acad. Radiol.
**2016**, 23, 1137–1144. [Google Scholar] [CrossRef] [PubMed][Green Version] - Li, X.; Welch, E.B.; Chakravarthy, A.B.; Xu, L.; Arlinghaus, L.R.; Farley, J.; Mayer, I.A.; Kelley, M.C.; Meszoely, I.M.; Means-Powell, J.; et al. Statistical comparison of dynamic contrast-enhanced MRI pharmacokinetic models in human breast cancer. Magn. Reson. Med.
**2012**, 68, 261–271. [Google Scholar] [CrossRef][Green Version] - Amarnath, J.; Sangeeta, T.; Mehta, S.B. Role of quantitative pharmacokinetic parameter (transfer constant: K(trans)) in the characterization of breast lesions on MRI. Indian J. Radiol. Imaging
**2013**, 23, 19–25. [Google Scholar] - Chung, S.; Kim, D.; Breton, E.; Axel, L. Rapid B1+ mapping using a preconditioning RF pulse with TurboFLASH readout. Magn. Reson. Med.
**2010**, 64, 439–446. [Google Scholar] [CrossRef][Green Version] - Chen, W.; Giger, M.L.; Bick, U. A fuzzy c-means (FCM)-based approach for computerized segmentation of breast lesions in dynamic contrast-enhanced MR images. Acad. Radiol.
**2006**, 13, 63–72. [Google Scholar] [CrossRef] - Partridge, S.C.; Nissan, N.; Rahbar, H.; Kitsch, A.E.; Sigmund, E.E. Diffusion-weighted breast MRI: Clinical applications and emerging techniques. J. Magn. Reson. Imaging
**2017**, 45, 337–355. [Google Scholar] [CrossRef] - Shin, H.J.; Chae, E.Y.; Choi, W.J.; Ha, S.M.; Park, J.Y.; Shin, K.C.; Cha, J.H.; Kim, H.H. Diagnostic performance of fused diffusion-weighted imaging using unenhanced or postcontrast T1-weighted MR imaging in patients with breast cancer. Medicine
**2016**, 95, e3502. [Google Scholar] [CrossRef] - Barnes, S.L.; Quarles, C.C.; Yankeelov, T.E. Modeling the effect of intra-voxel diffusion of contrast agent on the quantitative analysis of dynamic contrast enhanced magnetic resonance imaging. PLoS ONE
**2014**, 9, e108726. [Google Scholar] [CrossRef] [PubMed] - Cronenweth, C.M.; Shellock, F.G. Assessment of MRI Issues at 3 Tesla for a New Metallic Tissue Marker. Int. J. Breast Cancer
**2015**, 2015, 823759. [Google Scholar] [CrossRef] - Huang, W.; Li, X.; Chen, Y.; Li, X.; Chang, M.C.; Oborski, M.J.; Malyarenko, D.I.; Muzi, M.; Jajamovich, G.H.; Fedorov, A.; et al. Variations of dynamic contrast-enhanced magnetic resonance imaging in evaluation of breast cancer therapy response: A multicenter data analysis challenge. Transl. Oncol.
**2014**, 7, 153–166. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kim, H. Variability in Quantitative DCE-MRI: Sources and Solutions. South Pac. J. Nat. Appl. Sci.
**2018**, 4, 1–16. [Google Scholar]

**Figure 1.**SKT and Patlak analysis of ACRIN-based simulated data and ACRIN clinical data. (

**A**) Mean and 95% confidence intervals (CI) for simulated K

^{trans}values from the SKT model with the ATC length (denoted in legend) increasing from left to right in the bar plots for each patient (only a subset of all ATCs are displayed for simplicity in viewing). (

**B**) Average percent error in K

^{trans}as a function of ATC length with 95% CIs. (

**C**,

**D**) present the analogous data for the Patlak analysis of the simulated data. The absolute error in (

**B**,

**D**) decreases as the ATCs are increased, but only up to a certain ATC in panel D at ATC

_{6}. (

**E**) Mean and 95% confidence intervals (CI) for K

^{trans}values from analyzing the clinical data with the SKT model (only a subset of all ATCs are displayed for clarity). (

**F**) Average percent error in K

^{trans}as a function of ATC length with 95% CIs. (

**G**,

**H**) present the analogous data for the Patlak analysis of the clinical data and, similar to (

**D**), (

**H**) shows the absolute error in K

^{trans}decreasing up to ATC

_{5}before increasing again.

**Figure 2.**Comparing SKT and Patlak K

^{trans}error for a long ATC for a representative patient from each dataset. (

**A**) Map of percent error in K

^{trans}over the tumor ROI for an ACRIN patient dataset analyzed with the SKT model for ATC

_{14}(3.5 min). (

**B**) Plot of longitudinal relaxation rate curves, R

_{1}(t), for a representative voxel as indicated by the arrow in (

**A**) with curves labeled in the legend. (

**C**) Scatter plot of K

^{trans}ATC

_{14}and K

^{trans}FTC values in the ROI, where the line of unity is in red. (

**D**) Map of percent error in K

^{trans}over the tumor ROI for a single-site patient dataset analyzed with the SKT model for ATC

_{45}(5.45 min). (

**E**) Plot of signal intensity curves, SI(t), for a representative voxel indicated by the arrow in (

**D**) with curves labeled in the legend. (

**F**) Scatter plot of K

^{trans}ATC

_{45}and K

^{trans}FTC values in the ROI, where line of unity is in red. (

**G**–

**L**) present the analogous data for the Patlak analysis for ATC

_{5}(1.25 min) and ATC

_{9}(1.09 min) from the ACRIN and single-site datasets, respectively. We observe generally close fits in (

**B**,

**E**) as well as high agreement (CCCs > 0.80) in the FTC and ATC parameters in (

**C**,

**F**) as well as in the analogous Patlak fits in (

**H**,

**K**) and the Patlak parameters in (

**I**,

**L**).

**Figure 3.**Comparing SKT and Patlak K

^{trans}error for a short ATC for a representative patient from each dataset. Map of percent error in K

^{trans}over the tumor ROI for an ACRIN patient analyzed with the SKT model for ATC

_{7}(1.75 min). (

**B**) Plot of longitudinal relaxation rate curves, R

_{1}(t), for a representative voxel indicated by the arrow in (

**A**) with curves labeled in the legend. (

**C**) Scatter plot of K

^{trans}ATC

_{7}and K

^{trans}FTC values in the ROI, where the line of unity is in red. (

**D**) Map of percent error in K

^{trans}over the tumor ROI for a single-site patient analyzed with the SKT model for ATC

_{13}(1.60 min). (

**E**) Plot of signal intensity curves, SI(t), for a representative voxel indicated by the arrow in (

**D**) with curves labeled in the legend. (

**F**) Scatter plot of K

^{trans}ATC

_{13}and K

^{trans}FTC values in the ROI, where line of unity is in red. (

**G**–

**L**) present the analogous data for the Patlak analysis for ATC

_{3}(0.75 min) and ATC

_{5}(0.61 min) from the ACRIN and single-site datasets, respectively. We observe generally poorer fits in (

**B**,

**E**) as well as less agreement (CCC < 0.80) in the FTC and ATC parameters in (

**C**,

**F**) as well as in the analogous Patlak fits in (

**H**,

**K**) and the Patlak parameters in (

**I**,

**L**).

**Figure 4.**SKT and Patlak analysis of single-site-based simulated data and single-site clinical data. (

**A**) Mean and 95% confidence intervals (CI) for simulated K

^{trans}values from the SKT model with the ATC length (denoted in legend) increasing from left to right in the bar plots for each patient (only a subset of all ATCs are displayed for clarity). (

**B**) Average percent error in K

^{trans}as a function of ATC length with 95% CIs. (

**C**,

**D**) present the analogous data for the Patlak analysis of the simulated data. The absolute error in (

**B**,

**D**) decreases as the ATCs are increased, but only up to a certain ATC in panel D at ATC

_{12}. (

**E**) Mean and 95% confidence intervals (CI) for K

^{trans}values from analyzing the clinical data with the SKT model (only a subset of all ATCs are displayed for simplicity in viewing) (

**F**) Average percent error in K

^{trans}as a function of ATC length with 95% CIs. (

**G**,

**H**) present the analogous data for the Patlak analysis of the clinical data and, similar to (

**D**), (

**H**) shows the absolute error in K

^{trans}decreasing up to ATC

_{12}before increasing again.

Patient | Site | Length | SNR | Diagnosis (benign = 0/malig = 1) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

15 | 1 | 19 | 14 | 0 | |||||||||||

22 | 1 | 24 | 22 | 0 | |||||||||||

183 | 1 | 24 | 26 | 1 | |||||||||||

276 | 1 | 27 | 26 | 0 | |||||||||||

310 | 1 | 27 | 24 | 1 | |||||||||||

718 | 1 | 27 | 25 | 0 | |||||||||||

724 | 3 | 25 | 16 | 1 | |||||||||||

770 | 1 | 31 | 30 | 1 | |||||||||||

867 | 2 | 22 | 18 | 1 | |||||||||||

882 | 2 | 22 | 22 | 1 | |||||||||||

439 | 3 | 25 | 22 | 0 | |||||||||||

84 | 1 | 20 | 13 | 1 | |||||||||||

27 | 1 | 21 | 28 | 0 | |||||||||||

143 | 1 | 24 | 33 | 1 | |||||||||||

725 | 1 | 29 | 6 | 0 | |||||||||||

Patient | 3 | 6 | 7 | 8 | 9 | 11 | 13 | 15 | 17 | 18 | 19 | 22 | 23 | 26 | 28 |

SNR | 19 | 19 | 26 | 19 | 14 | 27 | 24 | 21 | 26 | 19 | 8 | 21 | 25 | 22 | 27 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Slavkova, K.P.; DiCarlo, J.C.; Kazerouni, A.S.; Virostko, J.; Sorace, A.G.; Patt, D.; Goodgame, B.; Yankeelov, T.E. Characterizing Errors in Pharmacokinetic Parameters from Analyzing Quantitative Abbreviated DCE-MRI Data in Breast Cancer. *Tomography* **2021**, *7*, 253-267.
https://doi.org/10.3390/tomography7030023

**AMA Style**

Slavkova KP, DiCarlo JC, Kazerouni AS, Virostko J, Sorace AG, Patt D, Goodgame B, Yankeelov TE. Characterizing Errors in Pharmacokinetic Parameters from Analyzing Quantitative Abbreviated DCE-MRI Data in Breast Cancer. *Tomography*. 2021; 7(3):253-267.
https://doi.org/10.3390/tomography7030023

**Chicago/Turabian Style**

Slavkova, Kalina P., Julie C. DiCarlo, Anum S. Kazerouni, John Virostko, Anna G. Sorace, Debra Patt, Boone Goodgame, and Thomas E. Yankeelov. 2021. "Characterizing Errors in Pharmacokinetic Parameters from Analyzing Quantitative Abbreviated DCE-MRI Data in Breast Cancer" *Tomography* 7, no. 3: 253-267.
https://doi.org/10.3390/tomography7030023