A Maximum-Likelihood Approach for ADC Estimation of Lesions in Visceral Organs

Improving hyperpolarized 129 Xe ADC mapping in pediatric and adult lungs with uncertainty propagation

RATIONALE

Hyperpolarized (HP) ¹²⁹ Xe-MRI provides non-invasive methods to quantify lung function and structure, with the ¹²⁹ Xe apparent diffusion coefficient (ADC) being a well validated measure of alveolar airspace size. However, the experimental factors that impact the precision and accuracy of HP ¹²⁹ Xe ADC measurements have not been rigorously investigated. Here, we introduce an analytical model to predict the experimental uncertainty of ¹²⁹ Xe ADC estimates. Additionally, we report ADC dependence on age in healthy pediatric volunteers.

METHODS

An analytical expression for ADC uncertainty was derived from the Stejskal-Tanner equation and simplified Bloch equations appropriate for HP media. Parameters in the model were maximum b-value (b_max ), number of b-values (N_b ), number of phase encoding lines (N_ph ), flip angle and the ADC itself. This model was validated by simulations and phantom experiments, and five fitting methods for calculating ADC were investigated. To examine the lower range for ¹²⁹ Xe ADC, 32 healthy subjects (age 6-40 years) underwent diffusion-weighted ¹²⁹ Xe MRI.

RESULTS

The analytical model provides a lower bound on ADC uncertainty and predicts that decreased signal-to-noise ratio yields increases in relative uncertainty (ϵADC) . As such, experimental parameters that impact non-equilibrium ¹²⁹ Xe magnetization necessarily impact the resulting ϵADC . The values of diffusion encoding parameters (N_b and b_max ) that minimize ϵADC strongly depend on the underlying ADC value, resulting in a global minimum for ϵADC . Bayesian fitting outperformed other methods (error < 5%) for estimating ADC. The whole-lung mean ¹²⁹ Xe ADC of healthy subjects increased with age at a rate of 1.75 × 10^-4  cm² /s/yr (p = 0.001).

CONCLUSIONS

HP ¹²⁹ Xe diffusion MRI can be improved by minimizing the uncertainty of ADC measurements via uncertainty propagation. Doing so will improve experimental accuracy when measuring lung microstructure in vivo and should allow improved monitoring of regional disease progression and assessment of therapy response in a range of lung diseases.

Diffusion MRI with Semi-Automated Segmentation Can Serve as a Restricted Predictive Biomarker of the Therapeutic Response of Liver Metastasis

PURPOSE

To assess the value of semi-automated segmentation applied to diffusion MRI for predicting the therapeutic response of liver metastasis.

METHODS

Conventional diffusion weighted magnetic resonance imaging (MRI) was performed using b-values of 0, 150, 300 and 450s/mm(2) at baseline and days 4, 11 and 39 following initiation of a new chemotherapy regimen in a pilot study with 18 women with 37 liver metastases from primary breast cancer. A semi-automated segmentation approach was used to identify liver metastases. Linear regression analysis was used to assess the relationship between baseline values of the apparent diffusion coefficient (ADC) and change in tumor size by day 39.

RESULTS

A semi-automated segmentation scheme was critical for obtaining the most reliable ADC measurements. A statistically significant relationship between baseline ADC values and change in tumor size at day 39 was observed for minimally treated patients with metastatic liver lesions measuring 2-5cm in size (p=0.002), but not for heavily treated patients with the same tumor size range (p=0.29), or for tumors of smaller or larger sizes. ROC analysis identified a baseline threshold ADC value of 1.33μm(2)/ms as 75% sensitive and 83% specific for identifying non-responding metastases in minimally treated patients with 2-5cm liver lesions.

CONCLUSION

Quantitative imaging can substantially benefit from a semi-automated segmentation scheme. Quantitative diffusion MRI results can be predictive of therapeutic outcome in selected patients with liver metastases, but not for all liver metastases, and therefore should be considered to be a restricted biomarker.

Task-based evaluation of segmentation algorithms for diffusion-weighted MRI without using a gold standard

In many studies, the estimation of the apparent diffusion coefficient (ADC) of lesions in visceral organs in diffusion-weighted (DW) magnetic resonance images requires an accurate lesion-segmentation algorithm. To evaluate these lesion-segmentation algorithms, region-overlap measures are used currently. However, the end task from the DW images is accurate ADC estimation, and the region-overlap measures do not evaluate the segmentation algorithms on this task. Moreover, these measures rely on the existence of gold-standard segmentation of the lesion, which is typically unavailable. In this paper, we study the problem of task-based evaluation of segmentation algorithms in DW imaging in the absence of a gold standard. We first show that using manual segmentations instead of gold-standard segmentations for this task-based evaluation is unreliable. We then propose a method to compare the segmentation algorithms that does not require gold-standard or manual segmentation results. The no-gold-standard method estimates the bias and the variance of the error between the true ADC values and the ADC values estimated using the automated segmentation algorithm. The method can be used to rank the segmentation algorithms on the basis of both the ensemble mean square error and precision. We also propose consistency checks for this evaluation technique.