# A Novel Multi-Model High Spatial Resolution Method for Analysis of DCE MRI Data: Insights from Vestibular Schwannoma Responses to Antiangiogenic Therapy in Type II Neurofibromatosis

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## Abstract

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^{trans}), vascular fraction (v

_{p}), extravascular extracellular fraction (v

_{e}), capillary plasma flow (F

_{p}), and the capillary permeability-surface area product (PS) could be obtained, and their predictive value was examined. Of the five microvascular parameters derived using the new method, baseline PS exhibited the strongest correlation with the baseline tumour volume (p = 0.03). Baseline v

_{e}showed the strongest correlation with the change in tumour volume, particularly the percentage tumour volume change at 90 days after treatment (p < 0.001), and PS demonstrated a larger reduction at 90 days after treatment (p = 0.0001) when compared to K

^{trans}or F

_{p}alone. Both the capillary permeability-surface area product (PS) and the extravascular extracellular fraction (v

_{e}) significantly differentiated the ‘responder’ and ‘non-responder’ tumour groups at 90 days (p < 0.05 and p < 0.001, respectively). These results highlight that this novel DCE-MRI analysis approach can be used to evaluate tumour microvascular changes during treatment and the need for future larger clinical studies investigating its role in predicting antiangiogenic therapy response.

## 1. Introduction

_{p}), transfer constant (K

^{trans}), and the fractional volume of extravascular extracellular space (v

_{e}) is to be achieved [9,10,11,12,13,14]. Usage of DCE-MRI as a clinical tool, however, also requires high spatial resolution and whole-brain coverage, especially when lesions are small, heterogenous, or widespread throughout the brain. A DCE-MRI technique that can provide both high spatiotemporal resolution and whole-brain coverage for quantitative microvascular analysis is therefore highly desirable [15,16,17], and in earlier works, it was demonstrated that a novel dual-temporal resolution (DTR) DCE-MRI-based data construction technique termed the LEGATOS (level and rescale the gadolinium contrast concentration curves of high temporal to high spatial) method could be used to provide this [18,19].

^{trans}, v

_{p}, and v

_{e}[20,21]. A key limitation of the ETM, however, is that the derived parameter K

^{trans}is a hybrid parameter reflecting both capillary plasma flow (F

_{p}) and the capillary permeability-surface area product (PS) [22]. The ETM is also unable to accurately measure low-level permeability within normal-appearing brain tissue, which is of increasing importance in neuro-oncology and may help predict both prognosis and treatment response [23,24,25].

#### 1.1. Multi-Model LEGATOS Analysis Theory

#### 1.1.1. Construction of a 4D High Spatiotemporal Resolution GBCA Concentration-Volume Using the LEGATOS Method

_{aligned}volume. The signal intensity-time curves from this 4D LDHT

_{aligned}and the 4D HS dynamic image volumes are then converted to GBCA concentration-time curves, before combining the HT and HS resolution series to construct a 4D GBCA concentration volume. In the second step, the LDHT

_{aligned}arterial phase of each voxel concentration curve is re-scaled using a derived voxel-wise calibration ratio (ratio

_{calib}) to increase the spatial resolution of the derived kinetic parameter maps. Further details on the LEGATOS reconstruction method and derivation of the calibration ratio are provided in prior publications [20,21].

#### 1.1.2. Use of LEGATOS with the ETM and ET-CBF Model to Derive High Spatial Resolution K^{trans}, v_{p}, v_{e}, and F_{p} Maps

_{t}is the tissue contrast agent concentration and C

_{p}is the GBCA concentration in the vascular plasma space. In the convolution integral, t is considered a constant and τ is the variable. Through use of the LEGATOS technique in combination with the ETM high spatial resolution, estimates of K

^{trans}, v

_{p}, and v

_{e}could be provided.

_{t}(t), is equal to the amount of GBCA delivered to 1 mL of tissue by time t; f is the absolute CBF (mL min

^{−1}mL

^{−1}); and C

_{b}(t’) is the arterial blood concentration at time t′. ETW is the early time window, i.e., the time window that meets the microsphere prerequisite. Using the microsphere model and Equation (2), low spatial resolution early time points absolute cerebral blood flow (CBF

_{ET}) maps can be derived from the arterial concentration-time curve of a low dose high temporal DCE-MRI acquisition.

_{ET}(CBF

_{ET-HS}) maps can also be derived from DTR DCE-MRI data through the use of the microsphere model with LEGATOS. CBF

_{ET-HS}maps can be obtained either directly from the concatenated 4D high spatiotemporal resolution GBCA concentration volume generated using the LEGATOS approach described above or by using the calibration ratio maps generated as part of the LEGATOS procedure to rescale (see Equation (3)) the low spatial resolution CBF

_{ET}(CBF

_{ET-HT}) derived from a 4D LDHT

_{aligned}volume (see Appendix A for details):

#### 1.1.3. Theoretical Derivation of the Capillary Permeability-Surface Area Product (PS) from Derived K^{trans} and CBF_{ET} Values

_{p}is plasma flow. F

_{p}relates to blood flow by the following:

_{ET}is the absolute cerebral blood flow estimated using the early time points method.

^{trans}and F

_{p}using Equation (6). Using Equation (4), K

^{trans}is dominated by the smallest of PS and F

_{p}[38].

^{trans}/PS is the ratio of plasma flow to the sum of F

_{p}and PS or R

_{Fp}, ranging from 0 to 1:

_{p}>> PS, R

_{Fp}≈ 1;

_{p}= PS, R

_{Fp}= 0.5;

_{p}<< PS, R

_{Fp}becomes a small positive value (≈ F

_{p}/PS).

_{Fp}maps can be useful in identifying areas of high perfusion but inadequate permeability (High R

_{Fp}) and high permeability but inadequate perfusion (Low R

_{Fp}), respectively, thereby providing insight into tumour vascular heterogeneity [39]. High spatial resolution PS maps can also be obtained from estimates of K

^{trans}and F

_{p}derived using the LEGATOS

_{ETM}and CBF

_{ET-HS}techniques described above, respectively.

#### 1.1.4. Use of LEGATOS-Patlak for Measuring K^{trans} within Normal-Appearing Brain Regions

_{t}) is given by the following:

_{p}(t), one obtains the Patlak plot (Equation (9)) where the slope represents K

^{trans}and the intercept represents v

_{p}. The abscissa has the units of time, but this is not laboratory time; it is concentration-stretched time and will be referred to hereafter as t

_{stretch}[41].

^{trans}and v

_{p}. A previous study proposed a “hybrid FP-PP” method that combines a first-pass analytical approach [46,47] with the Patlak plot to address these limitations [24]. Both computer simulation and in vivo studies demonstrated improved reliability in v

_{p}and K

^{trans}estimates with the hybrid method [24], and further details on this hybrid FP-PP method can be found in the included reference [24].

_{p}estimates obtained from LEGATOS-ETM (instead of from the FP analysis) can also be used as the known v

_{p}in the modified Patlak plot linear regression analysis [24] to produce the only free-fitting parameter, K

^{trans}.

## 2. Results

#### 2.1. High Spatial Multi-Model Assessment of Perfusion and Permeability Parameters within Both Tumour and Normal-Appearing Brain

_{ET}maps for a patient with NF2-related VS and meningioma are shown in Figure 2 and demonstrate how high spatial resolution absolute CBF

_{ET-HS}maps can be achieved using the early time points model with LEGATOS. Figure 2A shows representative pre-treatment images from an NF2 patient with a small convexity meningioma (white arrow). This meningioma was not clearly defined within the native ET-CBF map (left) due to the low spatial resolution and partial volume effects, but it is much better demonstrated within the reconstructed HS-CBF map and the LEGATOS-ETM derived high spatial resolution v

_{p}map (right column).

_{ET-HS}map offered superior visualization of intratumoural heterogeneity within the left-sided VS compared to the CBF

_{ET-HT}map and closely resembled the LEGATOS-ETM derived high spatial resolution tumour v

_{p}map as expected. Compared to the unreconstructed, low spatial resolution CBF

_{ET}images, the CBF

_{ET-HS}maps offered superior visualization of both the smaller right-sided VS and intratumoural heterogeneity in blood flow. The CBF

_{ET-HS}maps spatially corresponded with the pattern of vascularisation seen in the LEGATOS-ETM-derived high spatial resolution v

_{p}maps.

^{trans}maps provided by the LEGATOS method, using either the FP-PP approach or ETM are shown in Figure 3A. Both maps showed comparably high K

^{trans}values within the pre-treatment meningioma, with median tumour K

^{trans}values of 0.025 and 0.017 min

^{−1}for ETM and FP-PP models, respectively. The Patlak analysis underestimated K

^{trans}of the meningioma because the backflux of GBCA from the extravascular extracellular space to the plasma was too large to ignore in the tumour tissue. Compared to the LEGATOS

_{ETM}method, however, integration of the hybrid FP-PP model with LEGATOS (LEGATOS

_{FP-PP}) permitted high spatial resolution assessment of low-level K

^{trans}in the normal-appearing brain.

^{trans}statistics obtained from NAGM/NAWM in the 12 patients are shown in Table 1. Segmented NAGM displayed non-significantly higher mean (p = 0.30) and significantly higher median (p = 0.03) and max (p = 0.002) K

^{trans}values compared to segmented NAWM (paired t-test). Pearson correlation analysis (Figure 3B) shows that in this NF2 patient cohort, significant positive correlations between tumour volume and NAGM/NAWM K

^{trans}values were observed. Mean K

^{trans}measured from both the NAGM or NAWM segments showed a significant correlation with both average VS volume size (p ≤ 0.02) and total VS volume (p ≤ 0.01). Kendall rank correlation test also shows significant positive monotonic correlations of NAGM K

^{trans}values with both average and total VS volume size (p = 0.04 and p = 0.05, respectively).

#### 2.2. High Spatial Evaluation of Changes in Tumour Microvascular Parameters during Antiangiogenic Therapy

^{trans}, PS, F

_{p}, and R

_{Fp}) are shown in Figure 4A for an NF2 patient with a large VS. Pre-treatment, there was intratumoural heterogeneity in the derived perfusion and permeability metrics with distinct tumour regions showing either high F

_{p}or high K

^{trans}and PS, respectively. Such heterogeneity was also evident in derived R

_{Fp}maps (ratio of plasma flow to the sum of F

_{p}and PS, F

_{p}/(F

_{p}+ PS)), with regions showing high R

_{Fp}(permeability limited) and low R

_{Fp}(perfusion limited), respectively. At 90 days post-bevacizumab therapy, reductions in VS volume are also seen along with substantial reductions in both K

^{trans}and PS. There is also an observed corresponding increase in R

_{Fp,}with an increase in the tumour subregion displaying high perfusion but inadequate permeability.

^{trans}and PS histograms showed a shift towards lower values, with a median decrease of 21% in K

^{trans}and a 33% decrease in PS. R

_{Fp}histograms conversely showed a shift towards higher values, with a median increase of 10%. The overall tumour volume was reduced by 28%, and tumour volume loss was principally seen in voxels with F

_{p}in the range of 0.2–0.8 min

^{−1}(see arrowed red lines on F

_{p}histogram), with 2638 out of 3005 and 1588 out of 2163 tumour voxels being in this range at day 0 and day 90 post-treatment, respectively.

^{trans}(p ≤ 0.001) and PS (p = 0.0002) and significant increases in R

_{Fp}(p = 0.004). Post-treatment decreases in F

_{p}(p = 0.08), v

_{p}(p = 0.07), and v

_{e}(p = 0.56) were also seen but these did not reach statistical significance. Non-responding VS also displayed a significant increase in R

_{Fp}at day 90 (p = 0.04). Decreases in mean K

^{trans}and PS were not significant (p > 0.05); however, in contrast to responding tumours, non-responding VS displayed significant increases in v

_{e}(p = 0.01).

#### 2.3. Differences between Responding and Non-Responding Tumours in Baseline (Pre-Treatment) High Spatial Resolution Microvascular Parameters

_{e}(p < 0.001) values. Responding tumours also displayed higher K

^{trans}than non-responding VS but these differences (p = 0.07) did not reach statistical significance. Of the five parameters, baseline v

_{e}correlated most strongly with percentage volume change at day 90 (p < 0.001).

^{trans}, Fp, PS, v

_{p}, and v

_{e}and tumour volumetric parameters (the baseline tumour volume, tumour volume change, or percentage tumour volume change at day 90) assessed by linear regression analysis. Both PS and K

^{trans}(a hybrid flow-permeability parameter) showed a significant correlation with baseline tumour volume (p = 0.03 and p = 0.05, respectively) and a non-significant trend of correlation with tumour volume change at day 90 (p = 0.06 and p = 0.12, respectively). On the other hand, v

_{e}, an oedema-associated parameter [48], showed a significant correlation with tumour volume change and percentage tumour volume change at day 90 (p = 0.04 and p = 0.0002, respectively) and a non-significant trend of correlation with baseline tumour volume (p = 0.08). F

_{p}and v

_{p}did not show correlations with any of the three tumour volumetric parameters.

_{e}estimates (AUC = 0.896, p = 0.02, Table 4) showed the greatest ability in the prediction of 90-day response in NF2-related vestibular schwannoma. v

_{p}was the only variable with a p value greater than 0.50. In multivariate analysis, the backward selection procedure starts with the five potential predictors and eliminates the least significant variable at each step. The model with three variables (v

_{e}, PS, and F

_{p}) demonstrated a higher AUC, sensitivity, and specificity than the models with fewer variables.

## 3. Discussion

^{trans}estimates had the potential ability to predict later VS volume response to anti-VEGF therapy [4]. As a parameter, however, K

^{trans}reflects regional capillary blood flow, capillary endothelial permeability, and the surface area of the capillary endothelial membrane [22], and the extent to which changes in each of these physiological variables changed during treatment was unknown. From earlier in vivo studies, the primary action of VEGF inhibitors, such as bevacizumab, was thought to be the rapid reduction in capillary endothelial membrane permeability [49,50], and it was hypothesized that the reduction in K

^{trans}observed following treatment might be indicative of this mechanism. However, an alternative interpretation was that changes in tumour blood flow could also affect measured K

^{trans}, and to address this question, our study utilized a high spatial resolution multi-kinetic model analysis technique that permits simultaneous estimation of both F

_{p}and PS within the tumour microvasculature.

^{trans}, with responding tumours showing both significantly higher baseline PS and significant reductions in PS at 90 days post-treatment compared to non-responding VS. On the other hand, our findings revealed that F

_{p}alone was not predictive of tumour volume response to bevacizumab treatment. There was no difference in pre-treatment F

_{p}between responding and non-responding tumour groups, and in neither group was there a significant change in F

_{p}during treatment observed. Instead, across all VS studied, there was an increase in the relative scale of perfusion to permeability (higher R

_{Fp}) during treatment. Overall, these imaging observations suggest that the changes observed in K

^{trans}following bevacizumab treatment are primarily driven by a reduction in capillary endothelial membrane permeability, rather than hypothesized changes in tumour blood flow. Such a finding is in line with previous in vivo murine models evaluating anti-VEGF therapy response [4,51,52], which have shown early (< 24 h) vascular normalization with reductions in both vascular permeability and the surface area of vessels; this is to our knowledge the first time that microvascular flow and permeability changes following anti-VEGF therapy in NF2-related VS have been differentiated through an in vivo human imaging analysis.

^{trans}, PS, F

_{p}, v

_{p}, and v

_{e}), baseline v

_{e}showed the most significant association with tumour volume response to bevacizumab treatment. These findings are supported by previous studies on the predictive value of an apparent diffusional coefficient (ADC) and a native longitudinal relaxation rate (R1

_{N}) in relation to tumour volume response to the VEGF inhibition [4,35,53]. High values of ADC and low values of R1

_{N}are in keeping with a larger extravascular extracellular space, increased levels of interstitial free fluid, and likely higher capillary permeability. Within our study, we found that baseline v

_{e}had a strong correlation with percent volume reduction at day 90, which is consistent with Plotkin et al., who found that high baseline ADC values were associated with tumour volume reduction at 3 months [35]. Although high baseline v

_{e}was a strong correlate of tumour shrinkage, tumour median values of v

_{e}showed only a non-significant percentage decrease (−3.1% ± 21.4%, p = 0.56) in the ‘responder’ group and a significant percentage increase (19.3% ± 17.0%, p = 0.01) in the ‘non-responder’ group at day 90. A multivariate model combining pre-treatment v

_{e}, PS, and F

_{p}demonstrated high sensitivity and specificity for the prediction of volumetric response at 90 days, and these results, whilst preliminary, suggest that initial volumetric response to anti-VEGF therapy appears more likely in VSs that show both high levels of permeability and intratumoural oedema [4,54]. Future larger studies are, however, required to better understand the role of v

_{e}and PS in anti-VEGF therapy prediction.

^{trans}estimates within NAGM compared to NAWM. In this NF2 patient cohort, a significant positive correlation between total VS disease burden and K

^{trans}values in NAGM/NAWM was observed. In patients with VS, there is emerging evidence that there can be effects on the brain remote to the tumour, with previous diffusion and functional MRI studies demonstrating widespread changes in activity networks, grey matter volume, and white matter fibre integrity in auditory and non-auditory regions in patients with these tumours [57,58,59,60,61]. To date, however, changes in DCE-MRI parameters within the normal-appearing brain of patients with NF2 have not been evaluated and further large, detailed studies are required to better understand the pathophysiology of the observed K

^{trans}changes and their relationship to the tumour burden in these patients.

## 4. Materials and Methods

#### 4.1. Patients

^{3}and/or a relative volume decrease exceeding 5%. Further details on how volume response was defined are provided in the included reference [4].

#### 4.2. MRI Data Acquisition

^{3}) resolution DCE-MRI series (N

_{Frame}= 300) with a low-dose fixed-volume (3 mL) of GBCA was performed for a total scan duration of 5.1 min. Subsequently, a high spatial (voxel size = 1 × 1 × 2 mm

^{3}) but low temporal (Δt = 10.7 s) resolution DCE-MRI series with a full dose (0.2 mL/kg·weight—3 mL dose of pre-bolus) of GBCA was performed for a total scan duration of 10.6 min (N

_{Frame}= 60). Variable flip angle (a = 2°, 8°, 15°, and 20°) acquisitions were performed prior to the LDHT and FDHS DCE series for baseline longitudinal relaxation rate estimation.

#### 4.3. Image Processing

^{trans}, v

_{p}, v

_{e}, CBF

_{ET}, F

_{p}, R

_{Fp}, and PS, and to detect low-level permeability (K

^{trans}) in normal-appearing brain regions.

_{ET}maps were derived from the arterial phase of the 4D LDHT

_{aligned}volume (which is the arterial phase of the concatenated 4D DTR GBCA concentration volume generated in key step I of the LEGATOS approach). High spatial resolution CBF

_{ET}maps were obtained by rescaling the low spatial resolution CBF

_{ET}with the calibration ratio maps generated as part of the LEGATOS procedure. CBF

_{ET-HS}and CBF

_{ET-HT}maps could therefore be compared as part of this study.

_{p}(t), from the LDHT series with the later parenchymal phase of the dose-calibrated GBCA concentration-time curve from the FDHS-DCE series [4,6]. The amplitude of the C

_{p}(t) from the FDHS series is scaled down to match the LDHT-derived C

_{p}(t) using the dose calibration ratio prior to concatenation. Further details on the derivation of the VIF for this analysis can be found in the included reference [20].

^{trans}within normal-appearing brain regions.

#### 4.4. Statistical Analysis

^{trans}, PS, F

_{p}, R

_{Fp}, v

_{e}, and v

_{p}were calculated for each visit for the 20 VSs across the 12 NF2 patients. The group mean and standard deviation of these tumour median values were compared across the two visits using a paired t-test, with responding (N = 12) and non-responding (N = 8) VSs analysed separately. Histograms of the fitted voxelwise microvascular parameters (K

^{trans}, PS, F

_{p}, R

_{Fp}, v

_{e}, and v

_{p}) before and 90 days after treatment were also compared.

^{trans}within NAGM and NAWM across the twelve patients were compared using descriptive statistics and paired t-tests. Estimates of mean K

^{trans}measured from the NAGM/NAWM segmentations were also compared with VS volume using scatterplot analysis and reported as Pearson’s and Kendall’s correlation coefficients (r, r

_{s}, and τ, respectively). The tumour volume used in the correlation analysis was defined as either (1) the average size across both VSs (or the size of the single VS in patients previously having undergone a VS resection) or (2) the cumulative tumour volume across both/single VSs.

^{trans}, PS, F

_{p}, v

_{p}, and v

_{e}do not differ between responding and non-responding VS was tested using the unpaired Student’s t-test. Binary logistic regression (S-Plus, version 6.1; Insightful, Seattle, WA, USA) was also performed to assess the ability of these imaging biomarkers to predict tumour response at day 90. The predictive performance of the model was assessed by receiver operator characteristics (ROC) analysis and calculation of the area under the curve (AUC). Univariate and multivariate analyses were performed. A backward elimination variable selection method was used in the multivariate analysis to obtain the best model.

## 5. Conclusions

^{trans}) changes within the normal-appearing brain and that, within the tumour microenvironment, this new approach allowed for concomitant evaluation of blood flow and permeability changes, with the tumoural capillary permeability-surface area product demonstrating the most pronounced reduction at 90 days. In a preliminary study of volumetric response predictors, baseline v

_{e}showed the strongest correlation with the change in tumour volume during treatment, and a multivariate model combining v

_{e}, PS, and F

_{p}demonstrated high sensitivity and specificity for the prediction of volume reduction at 90 days. These results highlight the utility of this novel DCE-MRI analysis approach in evaluating tumour microvascular changes during treatment and the need for future larger studies investigating its role in predicting antiangiogenic therapy response.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{ET}has been previously described and is based on averaging the concentration of early time points during the first pass of a low-dose compact bolus [26]. For dual-injection, dual-temporal resolution DCE-MRI, high spatial resolution CBF

_{ET}(CBF

_{ET-HS}) maps can also be derived through rescaling the low spatial resolution CBF

_{ET}(CBF

_{ET-HT}) derived from the 4D LDHT

_{aligned}volume with the calibration ratio maps generated as part of the LEGATOS procedure. Assuming that the GBCA concentration curve in each HS pixel has a similar first pass shape as its concatenated LDHT

_{aligned}arterial phase, the ratio of the HS arterial phase, C

_{t-HS}(t), over the LDHT

_{aligned}arterial phase, C

_{t-HT}(t), can be used to convert the CBF estimate derived from the LDHT

_{aligned}arterial phase (CBF

_{ET-HT}) to the CBF of the concatenated HS pixel, CBF

_{ET-HS}, that is,

_{calib}, can be defined as follows:

_{adj}is the ending time point of the arterial phase. In the proposed LEGATOS method, C

_{t-HS}(t

_{adj}) was calculated as the mean concentration of the five HS frames following the HT arterial phase and C

_{t-HT}(t

_{adj}) as the mean concentration of several ending frames of the HT arterial phase series.

_{aligned}arterial phase to high spatial resolution:

## Appendix B

Symbol | Definition | Units |

CBF | Cerebral blood flow | mL min^{−1} mL^{−1} |

CBF_{ET} | Absolute cerebral blood flow generated using early time points method | mL min^{−1} mL^{−1} |

CBF_{ET-HS} | High spatial resolution estimates of CBF_{ET} | mL min^{−1} mL^{−1} |

CBF_{ET-HT} | Low spatial resolution estimates of CBF_{ET} | mL min^{−1} mL^{−1} |

C_{b}(t) | Concentration of contrast medium in arterial blood at time t | mmol |

C_{p} | Concentration of contrast medium in arterial blood plasma at time t | mmol |

C_{t}(t) | Concentration of contrast medium in the voxel at time t | mmol |

DCE-MRI | Dynamic contrast-enhanced MRI | |

DTR | Dual-temporal resolution | |

ETM | The extended Tofts model | |

ET-CBF | The ‘early time points’ method for absolute cerebral blood flow quantification | |

FP-PP | The hybrid first-pass Patlak plot method | |

ETW | The early time window, i.e., the time window that meets the microsphere prerequisite. | |

FDHS | Full-dose high spatial resolution | |

F_{p} | Plasma flow | mL min^{−1} mL^{−1} |

HS | High spatial (HS) resolution | |

HT | High temporal (HT) resolution | |

K^{trans} | Volume transfer constant between blood plasma and extravascular extracellular space | min^{−1} |

LDHT | Low-dose high temporal resolution | |

LDHT_{aligned} | 4D LDHT DCE images co-registered to subsequent HS DCE series in dual-injection DTR DCE-MRI | |

LEGATOS | A DTR DCE-MRI data construction technique: the level and rescale the gadolinium contrast concentration curves of high temporal to high spatial | |

R_{Fp} | The ratio of F_{p} to the sum of F_{p} and PS | None |

PS | Capillary permeability–surface area product per unit mass of tissue | mL min^{−1} mL^{−1} |

v_{e} | Volume of the extravascular extracellular space per unit volume of tissue | none |

v_{p} | Fractional blood plasma volume | none |

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**Figure 1.**Flowchart showing the key steps in the multi-model LEGATOS integrated kinetic analysis. Blue highlights the key steps of the dual-injection, dual-temporal resolution DCE-MRI acquisition; red highlights the key steps of the LEGATOS data reconstruction to generate a high spatiotemporal resolution GBCA concentration volume; lilac highlights the key kinetic models used; and black highlights the derived microvascular parameters. ET-CBF = ‘early time points’ method for absolute cerebral blood flow quantification; HS = high spatial resolution; FDHS = full-dose high spatial resolution DCE-MRI data; K

^{trans}= volume transfer constant between blood plasma and extravascular extracellular space; LDHT

_{aligned}= low-dose high temporal resolution DCE-MRI data co-registered to the FDHS DCE series; F

_{p}= plasma flow, where F

_{p}= CBF

_{ET}·(1 − Hct); FP-PP = the hybrid first-pass Patlak plot model; GBCA= gadolinium-based contrast agent; LEGATOS = level and rescale the gadolinium contrast concentration curves of high temporal to high spatial DCE-MRI; PS = permeability-surface area product; v

_{e}= volume of the extravascular extracellular space per unit volume of tissue; v

_{p}= fractional blood plasma volume.

**Figure 2.**Use of the LEGATOS technique with the ‘early time points’ absolute cerebral blood flow (ET-CBF) method to generate high spatial resolution CBF

_{ET}estimates. (

**A**) Representative pre-treatment images from an NF2 patient with multiple meningiomas including a right parasagittal convexity meningioma (white arrow). (

**B**) Representative images from a patient with bilateral NF2-related VS. Note the imaging artifact from the left-sided bone-anchored hearing aid within the post-contrast T1-weighted image. The low spatial resolution CBF

_{ET}map (CBF

_{ET-HT}) derived from the low dose high temporal resolution DCE data is rescaled by the LEGATOS calibration ratio map to generate the high spatial resolution CBF

_{EHS}map. T1W + C = T1-weighted image post-contrast.

**Figure 3.**(

**A**) Representative post-contrast T1W image and high spatial resolution K

^{trans}maps in an NF2 patient with multiple meningioma. Data were fitted using either the hybrid FP-PP approach (LEGATOS

_{FP-PP}, middle) or ETM (LEGATOS

_{ETM}, right). Note the comparatively high K

^{trans}values seen within the right-frontal and left-parasagittal meningioma on both maps. Compared to LEGATOS

_{ETM}the LEGTOS

_{FP-PP}permits high spatial resolution assessment of low-level vascular permeability within the normal-appearing brain. (

**B**) Correlation between mean NAGM/NAWM K

^{trans}and VS volume. Top row: correlation between average VS volume and mean NAGM (left)/NAWM (right) K

^{trans}values; bottom row: correlation between cumulative VS volume and mean NAGM (left)/NAWM (right) K

^{trans}values. NAGM = normal-appearing grey matter; NAWM = normal-appearing white matter. T1W + C = T1-weighted image post-contrast.

**Figure 4.**(

**A**) High spatial resolution tumour K

^{trans}, PS, F

_{p}, and R

_{Fp}(= F

_{p}/(F

_{p}+ PS)) maps imaged at day 0 (baseline) and day 90 in an NF2 patient with left-sided VS. (

**B**) Histograms of tumour voxel values for K

^{trans}, F

_{p}, v

_{p}, PS, R

_{Fp}, and v

_{e}at baseline (the solid line) and 90 days post-bevacizumab treatment (dashed line), calculated in the same tumour as in panel A. Tumour volume size was 6.01 cm

^{3}(3005 voxels) at day 0 and 4.33 cm

^{3}(2163 voxels) at day 90. The overall tumour volume was reduced by 28%, and tumour volume loss was principally seen in voxels with F

_{p}in the range of 0.2 to 0.8 min

^{−1}(red arrow lines) and v

_{p}in the range of 0.02 to 0.10 in the histogram. Tumour mean ± SD (median) for each of the 6 parameters measured at day 0 and day 90 are shown in the panel corresponding to that parameter, respectively. T1W + C = T1-weighted image post-contrast. The x-axis of each histogram represents the range of parameter values divided into bins, and the y-axis represents frequency (how many voxels fall within each bin).

**Figure 5.**Predictive value of pre-treatment tumour median values of microvascular parameters. (

**A**–

**E**) Comparison of the pre-treatment (day 0) microvascular parameters (K

^{trans}, PS, Fp, v

_{p}, and v

_{e}) between the responder (res) and non-responder (non) VS groups. Boxplots show mean (dot on the box plot), median (bar within the box), upper and lower quartiles (box limits), and extreme values (whiskers). The p values are calculated using a two-sided Student t-test. (

**F**) Correlation between pre-treatment tumour median v

_{e}and percentage change in tumour volume at day 90; volume

_{d0}= baseline tumour volume; volume

_{d90}= tumour volume at day 90.

**Table 1.**K

^{trans}statistics estimated from segmented normal-appearing grey matter (NAGM) and white matter (NAWM) in twelve patients with NF2.

K^{trans} Statistics of NAGM/NAWM Segments | NAGM Segment Statistics Mean ± SD | NAWM Segment Statistics Mean ± SD | p Value Paired t-Test |
---|---|---|---|

Mean (min^{−1}) | 0.00089 ± 0.0011 | 0.00062 ± 0.00030 | 0.30 |

Median (min^{−1}) | 0.00047 ± 0.00037 | 0.00028 ± 0.00034 | 0.03 |

SD (min^{−1}) | 0.0030 ± 0.0026 | 0.0012 ± 0.00021 | 0.04 |

Max (min^{−1}) | 0.050 ± 0.034 | 0.014 ± 0.0058 | 0.002 |

Min (min^{−1}) | −0.023 ± 0.0074 | −0.015 ± 0.0040 | 0.002 |

**Table 2.**Mean and standard deviation of the tumour median K

^{trans}, F

_{p}, PS, R

_{Fp}, v

_{p}, and v

_{e}estimated at day 0 and day 90 from 20 VSs in 12 NF2 patients.

Microvascular Parameter | Day 0 Mean ± SD (Median) | Day 90 Mean ± SD (Median) | p Value Paired t-Test |
---|---|---|---|

K^{trans} (min^{−1}) | |||

Res (N = 12) | 0.121 ± 0.023 (0.121) | 0.083 ± 0.031 (0.082) | 0.001 |

Non (N = 8) | 0.095 ± 0.037 (0.100) | 0.086 ± 0.025 (0.096) | 0.18 |

All (N = 20) | 0.111 ± 0.059 (0.123) | 0.085 ± 0.028 (0.093) | 0.0008 |

PS (mL min^{−1} mL^{−1}) | |||

Res (N = 12) | 0.169 ± 0.039 (0.174) | 0.109 ± 0.043 (0.106) | 0.0002 |

Non (N = 8) | 0.125 ± 0.053 (0.128) | 0.107 ± 0.032 (0.118) | 0.10 |

All (N = 20) | 0.151 ± 0.087 (0.162) | 0.108 ± 0.038 (0.117) | 0.0001 |

F_{p} (mL min^{−1} mL^{−1}) | |||

Res (N = 12) | 0.514 ± 0.114 (0.496) | 0.414 ± 0.103 (0.423) | 0.08 |

Non (N = 8) | 0.485 ± 0.175 (0.470) | 0.541 ± 0.139 (0.579) | 0.36 |

All (N = 20) | 0.502 ± 0.270 (0.477) | 0.465 ± 0.132 (0.452) | 0.37 |

R_{Fp} (%) | |||

Res (N = 12) | 0.752 ± 0.065 (0.744) | 0.792 ± 0.048 (0.788) | 0.004 |

Non (N = 8) | 0.784 ± 0.063 (0.790) | 0.826 ± 0.045 (0.820) | 0.04 |

All (N = 20) | 0.765 ± 0.114 (0.761) | 0.806 ±0.049 (0.799) | 0.0003 |

v_{p} (%) | |||

Res (N = 12) | 0.047 ± 0.012 (0.043) | 0.038 ± 0.009 (0.040) | 0.07 |

Non (N = 8) | 0.045 ± 0.019 (0.040) | 0.045 ± 0.010 (0.047) | 0.94 |

All (N = 20) | 0.046 ± 0.025 (0.042) | 0.040 ± 0.010 (0.041) | 0.13 |

v_{e} (%) | |||

Res (N = 12) | 0.519 ± 0.047 (0.523) | 0.498 ± 0.103 (0.457) | 0.56 |

Non (N = 8) | 0.431 ± 0.042 (0.423) | 0.511 ± 0.063 (0.500) | 0.01 |

All (N = 20) | 0.484 ± 0.259 (0.500) | 0.504 ± 0.196 (0.488) | 0.43 |

**Table 3.**Correlations between tumour median K

^{trans}, Fp, PS, v

_{p}, and v

_{e}estimated at day 0 and tumour volumetric parameters.

Linear Regression Analysis (N = 20) | Tumour Volume (cm ^{3}; Day 0) | Tumour Volume Change (cm ^{3}; Day 90) | Percentage Tumour Volume Change (%; Day 90) |
---|---|---|---|

K^{trans} (min^{−1}) | R^{2} = 0.19p = 0.05 | R^{2} = 0.13p = 0.12 | R^{2} = 0.08p = 0.23 |

PS (mL min^{−1} mL^{−1}) | R^{2} = 0.24p = 0.03 | R^{2} = 0.18p = 0.06 | R^{2} = 0.10p = 0.18 |

Fp (mL min^{−1} mL^{−1}) | R^{2} = 0.01p = 0.71 | R^{2} = 0.01p = 0.67 | R^{2} = 0.01p = 0.66 |

v_{p} (%) | R^{2} = 0.02p = 0.55 | R^{2} = 0.03p = 0.48 | R^{2} = 0.00p = 0.90 |

v_{e} (%) | R^{2} = 0.16p = 0.08 | R^{2} = 0.21p = 0.04 | R^{2} = 0.56p < 0.001 |

**Table 4.**Area under the receiver operator curve, sensitivity, and specificity of the binomial regression model for the prediction of tumour response using univariate (

**A**) and multivariate analysis (

**B**).

Prediction of Response | AUC-ROC (p Value) | Sensitivity | Specificity | Overall Classification |
---|---|---|---|---|

A. Univariate analysis | ||||

v_{e} (%) | 0.896 (0.024) | 0.830 | 0.875 | 0.850 |

PS (mL min^{−1} mL^{−1}) | 0.708 (0.10) | 0.920 | 0.500 | 0.750 |

K^{trans} (min^{−1}) | 0.688 (0.11) | 0.92 | 0.375 | 0.700 |

F_{p} (mL min^{−1} mL^{−1}) | 0.667 (0.50) | 1.00 | 0.125 | 0.650 |

v_{p} (%) | 0.615 (0.61) | - | - | - |

B. Multivariate analysis with backward selection | ||||

Step 1 v _{e} + PS + K^{trans} + F_{p} + v_{p} | 0.948 (0.031; 0.92; 0.93; 0.69; 0.83) | 0.830 | 0.875 | 0.850 |

Step 2 v _{e} + PS + F_{p} + v_{p} | 0.948 (0.030; 0.31; 0.70; 0.78) | 0.830 | 0.875 | 0.850 |

Step 3 v _{e} + PS + F_{p} | 0.948 (0.032; 0.35; 0.70) | 0.830 | 0.875 | 0.850 |

Step 4 v _{e} + PS | 0.938 (0.036; 0.37) | 0.830 | 0.750 | 0.800 |

Step 5 v _{e} | 0.896 (0.024) | 0.830 | 0.875 | 0.850 |

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## Share and Cite

**MDPI and ACS Style**

Li, K.-L.; Lewis, D.; Zhu, X.; Coope, D.J.; Djoukhadar, I.; King, A.T.; Cootes, T.; Jackson, A.
A Novel Multi-Model High Spatial Resolution Method for Analysis of DCE MRI Data: Insights from Vestibular Schwannoma Responses to Antiangiogenic Therapy in Type II Neurofibromatosis. *Pharmaceuticals* **2023**, *16*, 1282.
https://doi.org/10.3390/ph16091282

**AMA Style**

Li K-L, Lewis D, Zhu X, Coope DJ, Djoukhadar I, King AT, Cootes T, Jackson A.
A Novel Multi-Model High Spatial Resolution Method for Analysis of DCE MRI Data: Insights from Vestibular Schwannoma Responses to Antiangiogenic Therapy in Type II Neurofibromatosis. *Pharmaceuticals*. 2023; 16(9):1282.
https://doi.org/10.3390/ph16091282

**Chicago/Turabian Style**

Li, Ka-Loh, Daniel Lewis, Xiaoping Zhu, David J. Coope, Ibrahim Djoukhadar, Andrew T. King, Timothy Cootes, and Alan Jackson.
2023. "A Novel Multi-Model High Spatial Resolution Method for Analysis of DCE MRI Data: Insights from Vestibular Schwannoma Responses to Antiangiogenic Therapy in Type II Neurofibromatosis" *Pharmaceuticals* 16, no. 9: 1282.
https://doi.org/10.3390/ph16091282