Estimating breast tumor blood flow during neoadjuvant chemotherapy using interleaved high temporal and high spatial resolution MRI

Digital reference object toolkit of breast DCE MRI for quantitative evaluation of image reconstruction and analysis methods

PURPOSE

To develop a digital reference object (DRO) toolkit to generate realistic breast DCE-MRI data for quantitative assessment of image reconstruction and data analysis methods.

METHODS

A simulation framework in a form of DRO toolkit has been developed using the ultrafast and conventional breast DCE-MRI data of 53 women with malignant (n = 25) or benign (n = 28) lesions. We segmented five anatomical regions and performed pharmacokinetic analysis to determine the ranges of pharmacokinetic parameters for each segmented region. A database of the segmentations and their pharmacokinetic parameters is included in the DRO toolkit that can generate a large number of realistic breast DCE-MRI data. We provide two potential examples for our DRO toolkit: assessing the accuracy of an image reconstruction method using undersampled simulated radial k-space data and assessing the impact of theB 1 + $$ {\mathrm{B}}_1^{+} $$ field inhomogeneity on estimated parameters.

RESULTS

The estimated pharmacokinetic parameters for each region showed agreement with previously reported values. For the assessment of the reconstruction method, it was found that the temporal regularization resulted in significant underestimation of estimated parameters by up to 57% and 10% with the weighting factor λ = 0.1 and 0.01, respectively. We also demonstrated that spatial discrepancy ofv p $$ {v}_p $$ andPS $$ \mathrm{PS} $$ increase to about 33% and 51% without correction forB 1 + $$ {\mathrm{B}}_1^{+} $$ field.

CONCLUSION

We have developed a DRO toolkit that includes realistic morphology of tumor lesions along with the expected pharmacokinetic parameter ranges. This simulation framework can generate many images for quantitative assessment of DCE-MRI reconstruction and analysis methods.

The relationship between parameters measured using intravoxel incoherent motion and dynamic contrast-enhanced MRI in patients with breast cancer undergoing neoadjuvant chemotherapy: a longitudinal cohort study

Purpose

The primary aim of this study was to explore whether intravoxel incoherent motion (IVIM) can offer a contrast-agent-free alternative to dynamic contrast-enhanced (DCE)-MRI for measuring breast tumor perfusion. The secondary aim was to investigate the relationship between tissue diffusion measures from DWI and DCE-MRI measures of the tissue interstitial and extracellular volume fractions.

Materials and methods

A total of 108 paired DWI and DCE-MRI scans were acquired at 1.5 T from 40 patients with primary breast cancer (median age: 44.5 years) before and during neoadjuvant chemotherapy (NACT). DWI parameters included apparent diffusion coefficient (ADC), tissue diffusion (Dt), pseudo-diffusion coefficient (Dp), perfused fraction (f), and the product f×Dp (microvascular blood flow). DCE-MRI parameters included blood flow (Fb), blood volume fraction (vb), interstitial volume fraction (ve) and extracellular volume fraction (vd). All were extracted from three tumor regions of interest (whole-tumor, ADC cold-spot, and DCE-MRI hot-spot) at three MRI visits: pre-treatment, after one, and three cycles of NACT. Spearman's rank correlation was used for assessing between-subject correlations (r), while repeated measures correlation was employed to assess within-subject correlations (rrm) across visits between DWI and DCE-MRI parameters in each region.

Results

No statistically significant between-subject or within-subject correlation was found between the perfusion parameters estimated by IVIM and DCE-MRI (f versus vb and f×Dp versus Fb; P=0.07-0.81). Significant moderate positive between-subject and within-subject correlations were observed between ADC and ve (r=0.461, rrm=0.597) and between Dt and ve (r=0.405, rrm=0.514) as well as moderate positive within-subject correlations between ADC and vd and between Dt and vd (rrm=0.619 and 0.564, respectively) in the whole-tumor region.

Conclusion

No correlations were observed between the perfusion parameters estimated by IVIM and DCE-MRI. This may be attributed to imprecise estimates of fxDp and vb, or an underlying difference in what IVIM and DCE-MRI measure. Care should be taken when interpreting the IVIM parameters (f and f×Dp) as surrogates for those measured using DCE-MRI. However, the moderate positive correlations found between ADC and Dt and the DCE-MRI parameters ve and vd confirms the expectation that as the interstitial and extracellular volume fractions increase, water diffusion increases.

Low-dose GBCA administration for brain tumour dynamic contrast enhanced MRI: a feasibility study

A key limitation of current dynamic contrast enhanced (DCE) MRI techniques is the requirement for full-dose gadolinium-based contrast agent (GBCA) administration. The purpose of this feasibility study was to develop and assess a new low GBCA dose protocol for deriving high-spatial resolution kinetic parameters from brain DCE-MRI. Nineteen patients with intracranial skull base tumours were prospectively imaged at 1.5 T using a single-injection, fixed-volume low GBCA dose, dual temporal resolution interleaved DCE-MRI acquisition. The accuracy of kinetic parameters (ve, Ktrans, vp) derived using this new low GBCA dose technique was evaluated through both Monte-Carlo simulations (mean percent deviation, PD, of measured from true values) and an in vivo study incorporating comparison with a conventional full-dose GBCA protocol and correlation with histopathological data. The mean PD of data from the interleaved high-temporal-high-spatial resolution approach outperformed use of high-spatial, low temporal resolution datasets alone (p < 0.0001, t-test). Kinetic parameters derived using the low-dose interleaved protocol correlated significantly with parameters derived from a full-dose acquisition (p < 0.001) and demonstrated a significant association with tissue markers of microvessel density (p < 0.05). Our results suggest accurate high-spatial resolution kinetic parameter mapping is feasible with significantly reduced GBCA dose.

Dynamic Contrast-Enhanced (DCE) MRI

The non-invasive dynamic contrast-enhanced MRI (DCE-MRI) method provides valuable insights into tissue perfusion and vascularity. Primarily used in oncology, DCE-MRI is typically utilized to assess morphology and contrast agent (CA) kinetics in the tissue of interest. Interpretation of the temporal signatures of DCE-MRI data includes qualitative, semi-quantitative, and quantitative approaches. Recent advances in MRI technology allow simultaneous high spatial and temporal resolutions in DCE-MRI data acquisition on most vendor platforms, enabling the more desirable approach of quantitative data analysis using pharmacokinetic (PK) modeling. Many technical factors, including signal-to-noise ratio, temporal resolution, quantifications of arterial input function and native tissue T1, and PK model selection, need to be carefully considered when performing quantitative DCE-MRI. Standardization in data acquisition and analysis is especially important in multi-center studies.

Analysis of simplicial complexes to determine when to sample for quantitative DCE MRI of the breast

PURPOSE

A method is presented to select the optimal time points at which to measure DCE-MRI signal intensities, leaving time in the MR exam for high-spatial resolution image acquisition.

THEORY

Simplicial complexes are generated from the Kety-Tofts model pharmacokinetic parameters Ktrans and ve . A geometric search selects optimal time points for accurate estimation of perfusion parameters.

METHODS

The DCE-MRI data acquired in women with invasive breast cancer (N = 27) were used to retrospectively compare parameter maps fit to full and subsampled time courses. Simplicial complexes were generated for a fixed range of Kety-Tofts model parameters and for the parameter ranges weighted by estimates from the fully sampled data. The largest-area manifolds determined the optimal three time points for each case. Simulations were performed along with retrospectively subsampled data fits. The agreement was computed between the model parameters fit to three points and those fit to all points.

RESULTS

The optimal three-point sample times were from the data-informed simplicial complex analysis and determined to be 65, 204, and 393 s after arrival of the contrast agent to breast tissue. In the patient data, tumor-median parameter values fit using all points and the three selected time points agreed with concordance correlation coefficients of 0.97 for Ktrans and 0.67 for ve .

CONCLUSION

It is possible to accurately estimate pharmacokinetic parameters from three properly selected time points inserted into a clinical DCE-MRI breast exam. This technique can provide guidance on when to capture images for quantitative data between high-spatial-resolution DCE-MRI images.

Multitasking dynamic contrast enhanced magnetic resonance imaging can accurately differentiate chronic pancreatitis from pancreatic ductal adenocarcinoma

Background and aims

Accurate differentiation of chronic pancreatitis (CP) and pancreatic ductal adenocarcinoma (PDAC) is an area of unmet clinical need. In this study, a novel Multitasking dynamic contrast enhanced (DCE) magnetic resonance imaging (MRI) technique was used to quantitatively evaluate the microcirculation properties of pancreas in CP and PDAC and differentiate between them.

Methods

The Multitasking DCE technique was able to acquire one 3D image per second during the passage of MRI contrast agent, allowing the quantitative estimation of microcirculation properties of tissue, including blood flow F_p, plasma volume fraction v_p, transfer constant K^trans, and extravascular extracellular volume fraction v_e. Receiver operating characteristic (ROC) analysis was performed to differentiate the CP pancreas, PDAC pancreas, normal control pancreas, PDAC tumor, PDAC upstream, and PDAC downstream. ROCs from quantitative analysis and conventional analysis were compared.

Results

Fourteen PDAC patients, 8 CP patients and 20 healthy subjects were prospectively recruited. The combination of F_p, v_p, K^trans, and v_e can differentiate CP versus PDAC pancreas with good AUC (AUC [95% CI] = 0.821 [0.654 - 0.988]), CP versus normal pancreas with excellent AUC (1.000 [1.000 - 1.000]), PDAC pancreas versus normal pancreas with excellent AUC (1.000 [1.000 - 1.000]), CP versus PDAC tumor with excellent AUC (1.000 [1.000 - 1.000]), CP versus PDAC downstream with excellent AUC (0.917 [0.795 - 1.000]), and CP versus PDAC upstream with fair AUC (0.722 [0.465 - 0.980]). This quantitative analysis outperformed conventional analysis in differentiation of each pair.

Conclusion

Multitasking DCE MRI is a promising clinical tool that is capable of unbiased quantitative differentiation between CP from PDAC.

Predicting pathological complete response after neoadjuvant chemotherapy: A nomogram combining clinical features and ultrasound semantics in patients with invasive breast cancer

Background

Early identification of response to neoadjuvant chemotherapy (NAC) is instrumental in predicting patients prognosis. However, since a fixed criterion with high accuracy cannot be generalized to molecular subtypes, our study first aimed to redefine grades of clinical response to NAC in invasive breast cancer patients (IBC). And then developed a prognostic model based on clinical features and ultrasound semantics.

Methods

A total of 480 IBC patients were enrolled who underwent anthracycline and taxane-based NAC between 2018 and 2020. The decrease rate of the largest diameter was calculated by ultrasound after NAC and their cut-off points were determined among subtypes. Thereafter, a nomogram was constructed based on clinicopathological and ultrasound-related data, and validated using the calibration curve, receiver operating characteristic (ROC) curve, decision curve analysis (DCA), and clinical impact curve (CIC).

Results

The optimal cut-off points for predicting pCR were 53.23%, 51.56%, 41.89%, and 53.52% in luminal B-like (HER2 negative), luminal B-like (HER2 positive), HER2 positive, and triple-negative, respectively. In addition, time interval, tumor size, molecular subtypes, largest diameter decrease rate, and change of blood perfusion were significantly associated with pCR (all p < 0.05). The prediction model based on the above variables has great predictive power and clinical value.

Conclusion

Taken together, our data demonstrated that calculated cut-off points of tumor reduction rates could be reliable in predicting pathological response to NAC and developed nomogram predicting prognosis would help tailor systematic regimens with high precision.

Vascularity and Dynamic Contrast-Enhanced Breast Magnetic Resonance Imaging

Angiogenesis is a key step in the initiation and progression of an invasive breast cancer. High microvessel density by morphological characterization predicts metastasis and poor survival in women with invasive breast cancers. However, morphologic characterization is subject to variability and only can evaluate a limited portion of an invasive breast cancer. Consequently, breast Magnetic Resonance Imaging (MRI) is currently being evaluated to assess vascularity. Recently, through the new field of radiomics, dynamic contrast enhanced (DCE)-MRI is being used to evaluate vascular density, vascular morphology, and detection of aggressive breast cancer biology. While DCE-MRI is a highly sensitive tool, there are specific features that limit computational evaluation of blood vessels. These include (1) DCE-MRI evaluates gadolinium contrast and does not directly evaluate biology, (2) the resolution of DCE-MRI is insufficient for imaging small blood vessels, and (3) DCE-MRI images are very difficult to co-register. Here we review computational approaches for detection and analysis of blood vessels in DCE-MRI images and present some of the strategies we have developed for co-registry of DCE-MRI images and early detection of vascularization.

Assessing the reproducibility of high temporal and spatial resolution dynamic contrast-enhanced magnetic resonance imaging in patients with gliomas

Temporal and spatial resolution of dynamic contrast-enhanced MR imaging (DCE-MRI) is critical to reproducibility, and the reproducibility of high-resolution (HR) DCE-MRI was evaluated. Thirty consecutive patients suspected to have brain tumors were prospectively enrolled with written informed consent. All patients underwent both HR-DCE (voxel size, 1.1 × 1.1 × 1.1 mm³; scan interval, 1.6 s) and conventional DCE (C-DCE; voxel size, 1.25 × 1.25 × 3.0 mm³; scan interval, 4.0 s) MRI. Regions of interests (ROIs) for enhancing lesions were segmented twice in each patient with glioblastoma (n = 7) to calculate DCE parameters (K^trans, V_p, and V_e). Intraclass correlation coefficients (ICCs) of DCE parameters were obtained. In patients with gliomas (n = 25), arterial input functions (AIFs) and DCE parameters derived from T2 hyperintense lesions were obtained, and DCE parameters were compared according to WHO grades. ICCs of HR-DCE parameters were good to excellent (0.84–0.95), and ICCs of C-DCE parameters were moderate to excellent (0.66–0.96). Maximal signal intensity and wash-in slope of AIFs from HR-DCE MRI were significantly greater than those from C-DCE MRI (31.85 vs. 7.09 and 2.14 vs. 0.63; p < 0.001). Both 95^th percentile K^trans and V_e from HR-DCE and C-DCE MRI could differentiate grade 4 from grade 2 and 3 gliomas (p < 0.05). In conclusion, HR-DCE parameters generally showed better reproducibility than C-DCE parameters, and HR-DCE MRI provided better quality of AIFs.

Assessment of quantitative dynamic contrast-enhanced MRI in distinguishing different histologic grades of breast phyllode tumor

OBJECTIVES

To investigate whether quantitative DCE-MRI (qDCE-MRI) could help distinguish breast phyllodes tumor (PT) grades.

MATERIALS AND METHODS

This retrospective study included 67 breast PTs (26 benign lesions, 25 borderline lesions, and 16 malignant lesions) from April 2016 to July 2020. MRI was performed with a 1.5-T MR system. Perfusion parameters (K^trans, k_ep, v_e, iAUC60) derived from qDCE-MRI, tumor size, and the mean ADC value were correlated with histologic grades using Spearman's rank correlation coefficient. K^trans, k_ep, v_e, and iAUC60 of three histologic grades were also calculated and compared.

RESULTS

The Spearman correlation coefficient with histologic grade of the tumor size was 0.578 (p < 0.001); the ADC value was not correlated with histologic grades of breast PT (p = 0.059). The K^trans, k_ep, v_e, and iAUC60 of benign breast PTs were significantly lower than those of borderline breast PTs (p < 0.001) and lower than those of malignant breast PTs (p < 0.001). In comparison, the K^trans, v_e, and iAUC60 of borderline breast PTs were significantly lower than those of malignant breast PTs (p < 0.001, p < 0.001, p = 0.007, respectively). For ROC analysis, AUCs of K^trans, v_e, and iAUC60 were higher than tumor size and ADC value for differentiating three PT grades.

CONCLUSION

Quantitative and semi-quantitative perfusion parameters (K^trans, v_e, and iAUC60, especially K^trans) derived from qDCE-MRI showed better diagnosis efficiency than tumor size and ADC for grading breast PTs. Therefore, qDCE-MRI may be helpful for preoperative differentiating breast PT grades.

KEY POINTS

• Quantitative dynamic contrast-enhanced MRI can be used as a complementary noninvasive method to improve the differential diagnosis of breast PT. • K^trans, v_e, and iAUC60 derived from qDCE-MRI showed better diagnosis efficiency than tumor size and ADC for grading breast PTs.

Breast tumour volume and blood flow measured by MRI after one cycle of epirubicin and cyclophosphamide-based neoadjuvant chemotherapy as predictors of pathological response

OBJECTIVES

Better markers of early response to neoadjuvant chemotherapy (NACT) in patients with breast cancer are required to enable the timely identification of non-responders and reduce unnecessary treatment side-effects. Early functional imaging may better predict response to treatment than conventional measures of tumour size. The purpose of this study was to test the hypothesis that the change in tumour blood flow after one cycle of NACT would predict pathological response.

METHODS

In this prospective cohort study, dynamic contrast-enhanced MRI was performed in 35 females with breast cancer before and after one cycle of epirubicin and cyclophosphamide-based NACT (EC90). Estimates of tumour blood flow and tumour volume were compared with pathological response obtained at surgery following completion of NACT.

RESULTS

Tumour blood flow at baseline (mean ± SD; 0.32 ± 0.17 ml/min/ml) reduced slightly after one cycle of NACT (0.28 ± 0.18 ml/min/ml). Following treatment 15 patients were identified as pathological responders and 20 as non-responders. There were no relationships found between tumour blood flow and pathological response. Conversely, tumour volume was found to be a good predictor of pathological response (smaller tumours did better) at both baseline (area under the receiver operating characteristic curve 0.80) and after one cycle of NACT (area under the receiver operating characteristic curve 0.81).

CONCLUSION & ADVANCES IN KNOWLEDGE

The change in breast tumour blood flow following one cycle of EC90 did not predict pathological response. Tumour volume may be a better early marker of response with such agents.

Comparison of data-driven and general temporal constraints on compressed sensing for breast DCE MRI

PURPOSE

Current breast DCE-MRI strategies provide high sensitivity for cancer detection but are known to be insufficient in fully capturing rapidly changing contrast kinetics at high spatial resolution across both breasts. Advanced acquisition and reconstruction strategies aim to improve spatial and temporal resolution and increase specificity for disease characterization. In this work, we evaluate the spatial and temporal fidelity of a modified data-driven low-rank-based model (known as MOCCO, model consistency condition) compressed-sensing (CS) reconstruction compared to CS with temporal total variation with radial acquisition for high spatial-temporal breast DCE MRI.

METHODS

Reconstruction performance was characterized using numerical simulations of a golden-angle stack-of-stars breast DCE-MRI acquisition at 5-second temporal resolution. Specifically, MOCCO was compared with CS total variation and conventional SENSE reconstructions. The temporal model for MOCCO was prelearned over the source data, whereas CS total variation was performed using a first-order temporal gradient sparsity transform.

RESULTS

The MOCCO reconstruction was able to capture rapid lesion kinetics while providing high image quality across a range of optimal regularization values. It also recovered kinetics in small lesions (1.5 mm) in line-profile analysis and error images, whereas g-factor maps showed relatively low and constant values with no significant artifacts. The CS-TV method demonstrated either recovery of high spatial resolution with reduced temporal accuracy using large regularization values, or recovery of rapid lesion kinetics with reduced image quality using low regularization values.

CONCLUSION

Simulations demonstrated that MOCCO with radial acquisition provides a robust imaging technique for improving temporal fidelity, while maintaining high spatial resolution and image quality in the setting of bilateral breast DCE MRI.

Five-dimensional quantitative low-dose Multitasking dynamic contrast- enhanced MRI: Preliminary study on breast cancer

PURPOSE

To develop a low-dose Multitasking DCE technique (LD-MT-DCE) for breast imaging, enabling dynamic T₁ mapping-based quantitative characterization of tumor blood flow and vascular properties with whole-breast coverage, a spatial resolution of 0.9 × 0.9 × 1.1 mm³ , and a temporal resolution of 1.4 seconds using a 20% gadolinium dose (0.02 mmol/kg).

METHODS

Magnetic resonance Multitasking was used to reconstruct 5D images with three spatial dimensions, one T₁ recovery dimension for dynamic T₁ quantification, and one DCE dimension for contrast kinetics. Kinetic parameters F p , v p , K trans , and v e were estimated from dynamic T₁ maps using the two-compartment exchange model. The LD-MT-DCE repeatability and agreement against standard-dose MT-DCE were evaluated in 20 healthy subjects. In 7 patients with triple-negative breast cancer, LD-MT-DCE image quality and diagnostic results were compared with that of standard-dose clinical DCE in the same imaging session. One-way unbalanced analysis of variance with Tukey test was performed to evaluate the statistical significance of the kinetic parameters between control and patient groups.

RESULTS

The LD-MT-DCE technique was repeatable, agreed with standard-dose MT-DCE, and showed excellent image quality. The diagnosis using LD-MT-DCE matched well with clinical results. The values of F p , v p , and K trans were significantly different between malignant tumors and normal breast tissue (P < .001, < .001, and < .001, respectively), and between malignant and benign tumors (P = .020, .003, and < .001, respectively).

CONCLUSION

The LD-MT-DCE technique was repeatable and showed excellent image quality and equivalent diagnosis compared with standard-dose clinical DCE. The estimated kinetic parameters were capable of differentiating between normal breast tissue and benign and malignant tumors.

Quantitative analysis of vascular properties derived from ultrafast DCE-MRI to discriminate malignant and benign breast tumors

PURPOSE

We propose a novel methodology to integrate morphological and functional information of tumor-associated vessels to assist in the diagnosis of suspicious breast lesions.

THEORY AND METHODS

Ultrafast, fast, and high spatial resolution DCE-MRI data were acquired on 15 patients with suspicious breast lesions. Segmentation of the vasculature from the surrounding tissue was performed by applying a Hessian filter to the enhanced image to generate a map of the probability for each voxel to belong to a vessel. Summary measures were generated for vascular morphology, as well as the inputs and outputs of vessels physically connected to the tumor. The ultrafast DCE-MRI data was analyzed by a modified Tofts model to estimate the bolus arrival time, K^trans (volume transfer coefficient), and v_p (plasma volume fraction). The measures were compared between malignant and benign lesions via the Wilcoxon test, and then incorporated into a logistic ridge regression model to assess their combined diagnostic ability.

RESULTS

A total of 24 lesions were included in the study (13 malignant and 11 benign). The vessel count, K^trans , and v_p showed significant difference between malignant and benign lesions (P = 0.009, 0.034, and 0.010, area under curve [AUC] = 0.76, 0.63, and 0.70, respectively). The best multivariate logistic regression model for differentiation included the vessel count and bolus arrival time (AUC = 0.91).

CONCLUSION

This study provides preliminary evidence that combining quantitative characterization of morphological and functional features of breast vasculature may provide an accurate means to diagnose breast cancer.

A functional form for a representative individual arterial input function measured from a population using high temporal resolution DCE MRI

PURPOSE

To measure the arterial input function (AIF), an essential component of tracer kinetic analysis, in a population of patients using an optimized dynamic contrast-enhanced (DCE) imaging sequence and to estimate inter- and intrapatient variability. From these data, a representative AIF that may be used for realistic simulation studies can be extracted.

METHODS

Thirty-nine female patients were imaged on multiple visits before and during a course of neoadjuvant chemotherapy for breast cancer. A total of 97 T₁ -weighted DCE studies were analyzed including bookend estimates of T₁ and model-fitting to each individual AIF. Area under the curve and cardiac output were estimated from each first pass peak, and these data were used to assess inter- and intrapatient variability of the AIF.

RESULTS

Interpatient variability exceeded intrapatient variability of the AIF. There was no change in cardiac output as a function of MR visit (mean value 5.6 ± 1.1 L/min) but baseline blood T₁ increased significantly following the start of chemotherapy (which was accompanied by a decrease in hematocrit).

CONCLUSION

The AIF in an individual patient can be measured reproducibly but the variability of AIFs between patients suggests that use of a population AIF will decrease the precision of tracer kinetic analysis performed in cross-patient comparison studies. A representative AIF is presented that is typical of the population but retains the characteristics of an individually measured AIF.

Shutter-speed dynamic contrast-enhanced MRI: Is it fit for purpose?

PURPOSE

To test the ability of shutter-speed dynamic contrast-enhanced (DCE) MRI to estimate water exchange (WX) using simulations and assess its performance in clinical case studies of malignant and benign breast tumors.

METHODS

Data were simulated using a 1-compartment tracer kinetic (TK) model combined with a 2-pool WX model (2PX) and with a 2-compartment TK model. Typical DCE-MRI acquisition parameters were used with both WX-sensitive (8°) and -insensitive (25°) flip angles. Clinical data were obtained from patients with malignant and benign breast tumors. Data were fitted using a 2-compartment TK model and a 1-compartment TK model combined with 4 WX models: fast exchange limit (FXL), no exchange, 2PX, and shutter-speed.

RESULTS

Fits to the 1-compartment simulated data were excellent, but estimates of WX obtained using the 2PX and shutter-speed models were poor. One-compartment TK model fits to the clinical malignant tumor data were bad, except for the shutter-speed model. However, that overestimated TK parameters compared to the best-fit 2-compartment TK model, which predicted a significant blood volume and leaky capillaries (1 tracer compartment is insufficient, 2 are necessary). All models produced excellent fits to the clinical benign tumor data with little variation between parameter estimates (1 tracer compartment is sufficient).

CONCLUSION

The 2PX and shutter-speed models were unable to estimate WX from the DCE-MRI data. A good fit to malignant tumor data using the shutter-speed model was not explained by WX, but the choice of an inappropriate TK model leading to distorted parameter estimates.

Quantifying the efficacy of first aid treatments for burn injuries using mathematical modelling and in vivo porcine experiments

First aid treatment of burns reduces scarring and improves healing. We quantify the efficacy of first aid treatments using a mathematical model to describe data from a series of in vivo porcine experiments. We study burn injuries that are subject to various first aid treatments. The treatments vary in the temperature and duration. Calibrating the mathematical model to the experimental data provides estimates of the thermal diffusivity, the rate at which thermal energy is lost to the blood, and the heat transfer coefficient controlling the loss of thermal energy at the interface of the fat and muscle. A limitation of working with in vivo experiments is the difficulty of measuring variations in temperature across the tissue layers. This limitation motivates us to use a simple, single layer mathematical model. Using the solution of the calibrated mathematical model we visualise the temperature distribution across the thickness of the tissue. With this information we propose a novel measure of the potential for tissue damage. This measure quantifies two important factors: (i) the volume of tissue that rises above the threshold temperature associated with the accumulation of tissue damage; and (ii) the duration of time that the tissue remains above this threshold temperature.