Variance Change Point Detection Under a Smoothly-Changing Mean Trend with Application to Liver Procurement

<p>Literature on change point analysis mostly requires a sudden change in the data distribution, either in a few parameters or the distribution as a whole. We are interested in the scenario, where the variance of data may make a significant jump while the mean changes in a smooth fashion. The motivation is a liver procurement experiment monitoring organ surface temperature. Blindly applying the existing methods to the example can yield erroneous change point estimates since the smoothly changing mean violates the sudden-change assumption. We propose a penalized weighted least-squares approach with an iterative estimation procedure that integrates variance change point detection and smooth mean function estimation. The procedure starts with a consistent initial mean estimate ignoring the variance heterogeneity. Given the variance components the mean function is estimated by smoothing splines as the minimizer of the penalized weighted least squares. Given the mean function, we propose a likelihood ratio test statistic for identifying the variance change point. The null distribution of the test statistic is derived together with the rates of convergence of all the parameter estimates. Simulations show excellent performance of the proposed method. Application analysis offers numerical support to non invasive organ viability assessment by surface temperature monitoring. Supplementary materials for this article are available online.</p

7.0-T Magnetic Resonance Imaging Characterization of Acute Blood-Brain-Barrier Disruption Achieved with Intracranial Irreversible Electroporation

<div><p>The blood-brain-barrier (BBB) presents a significant obstacle to the delivery of systemically administered chemotherapeutics for the treatment of brain cancer. Irreversible electroporation (IRE) is an emerging technology that uses pulsed electric fields for the non-thermal ablation of tumors. We hypothesized that there is a minimal electric field at which BBB disruption occurs surrounding an IRE-induced zone of ablation and that this transient response can be measured using gadolinium (Gd) uptake as a surrogate marker for BBB disruption. The study was performed in a Good Laboratory Practices (GLP) compliant facility and had Institutional Animal Care and Use Committee (IACUC) approval. IRE ablations were performed <em>in vivo</em> in normal rat brain (n = 21) with 1-mm electrodes (0.45 mm diameter) separated by an edge-to-edge distance of 4 mm. We used an ECM830 pulse generator to deliver ninety 50-μs pulse treatments (0, 200, 400, 600, 800, and 1000 V/cm) at 1 Hz. The effects of applied electric fields and timing of Gd administration (−5, +5, +15, and +30 min) was assessed by systematically characterizing IRE-induced regions of cell death and BBB disruption with 7.0-T magnetic resonance imaging (MRI) and histopathologic evaluations. Statistical analysis on the effect of applied electric field and Gd timing was conducted via Fit of Least Squares with α = 0.05 and linear regression analysis. The focal nature of IRE treatment was confirmed with 3D MRI reconstructions with linear correlations between volume of ablation and electric field. Our results also demonstrated that IRE is an ablation technique that kills brain tissue in a focal manner depicted by MRI (n = 16) and transiently disrupts the BBB adjacent to the ablated area in a voltage-dependent manner as seen with Evan's Blue (n = 5) and Gd administration.</p> </div

Morphologic characteristics of IRE-induced BBB disruption on 7.0-T MRI and Evan's Blue brain sections.

<p>The zones of ablation were achieved with ninety 50-μs pulses at a rate of one pulse per second. The Gadolinium (Gd) and Evan's Blue dyes were administered IP 5 minutes before the delivery of the pulses. The positive correlation between the applied voltage-to-distance ratios and the extent of BBB disruption induced by IRE is indicated by the uniformly contrast-enhancing zones of ablation on the T1W+Gd MR images and corresponding Evan's Blue brain slices. IRE-induced zones of ablation are sharply demarcated from the surrounding brain parenchyma. Linear hypointensities in the center of the zones of ablation, corresponding to the electrode insertions, are evident in the MR images from the 600, 800, and 1000 V/cm treatments.</p

Pulse parameters and Evan's Blue/Gd administration schedule used in IRE study.

†<p> <b> =  Evan's Blue (n = 5); *  =  Gadolinium (n = 16) (Magnevist®). A separate animal was used to assess each time point and electric field (n = 21).</b></p

Quantification of IRE-induced BBB disruption from the 3D MRI reconstructions.

<p>Volumes (<b>A</b>) and mean concentrations (<b>B</b>) of Gd enhancement are provided as a function of the applied voltage-to-distance ratio and timing of Gd administration. Although N is low, the finding of increasing volume of affected tissue with increasing voltage applied (for the electrode configuration and pulse parameters used) suggests that volume is directly related to voltage. Similarly, the finding of a trend toward decreased volumes with increasing delays after Gd administration suggests a possible transient quality to the permeabilization surrounding the regions of ablation. The linear fit used to correlate the electric field and zone of ablation was found appropriate using previously published data <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050482#pone.0050482-Garcia3" target="_blank">[25]</a>. The mean concentrations of Gd within the reconstructed IRE-induced regions of BBB disruption are also positively correlated with the applied electric field. This is a critical observation since it provides evidence that with increasing electric field strengths even more electroporation is achieved and transport of Gd or other exogenous agents is enhanced.</p

Resulting IRE-induced BBB disruption mean concentrations, volumes, and cross-sectional areas calculated using the Gd enhancement in MRI, H&E, and Evan's Blue.

<p> <b>Note: The cross-sectional areas were determined from the regions intersecting the rostral electrode tip.</b></p

Qualitative representations of IRE-induced BBB disruption using 7.0-T MRI.

<p>2D IRE lesion tracing on the coronal (<b>A, B</b>), dorsal (<b>C, D</b>), and sagittal (<b>E, F</b>) planes with the corresponding non-contiguous (<b>G</b>) and contiguous (<b>H</b>) 3D reconstruction zones of ablation representative of 400 V/cm and 1000 V/cm IRE treatments, respectively. These reconstructions illustrate the shapes of the IRE zones of ablation, which are consistent with the electric field distributions that would be generated with the electrode configuration and pulse parameters used in this study. By optimizing treatment protocols and electrode configurations, it is possible to disrupt the BBB to target different size and shapes of tissue.</p

Histopathologic evaluation of IRE-induced effects determined with Hematoxylin and Eosin stain.

<p>Histopathologic sections of cerebral cortex from untreated control rat (<b>A</b>), sham treated rat with physical displacement of the neuropil in the trajectory of the electrode (<b>B</b>), and cortical ablation zone resulting from 800 V/cm IRE treatment (<b>C</b>). Histopathologic lesion area determination in presence of IRE induced cavitary cerebral defect (<b>D</b>). The IRE lesion area (mm²)  =  untreated cerebral area (X) – IRE lesioned cerebral area (Y). Bar  = 500 µm in panels A–C.</p

Original inoculation tumor volume curves.

<p>(A) Imputed median primary tumor volumes (mm³) for each group, showing significantly smaller median tumor size in the treated immunocompetent (IC) BALB/c mice. (B–E) Individual trial tumor comparisons between (B,D) immunodeficient (ID) nude and (C,E) immunocompetent mouse strains for (B,C) sham and (D,E) pulsed treatment groups, showing a clear improvement in progressive disease free survival for the treated IC mice (E) relative to both controls and treated ID mice (B–D). Treated ID mice show an initial pause in tumor volume for the first 12 days from the treatment, followed by progressive growth, a result of selecting a sub-optimal IRE pulsing protocol for this study. All endpoints in data are a result of euthanasia due to tumor reaching 18 mm in any dimension.</p

CD3⁺ Immunohistochemsistry of primary (T1) tumors.

<p>CD3⁺ staining, indicative for T-cell presence, performed for (A,C) untreated and (B,D) treated initial T1 tumors between (A,B) ID nude and (C,D) IC BALB/c mice. There is no notable difference observed in CD3⁺ infiltration for ID nude mice between (A) untreated and (B) treated tumors. For the IC BALB/c mice, a robust increase in CD3⁺ (T-cell) infiltration is observed in some treated tumors (D) relative to untreated T1 controls (C). Increased T-cell presence in treated T1 IC mice was also more robust than for both groups for nude mice (A,B). All scale bars 200 µm. Panels (A,C,D) 200x, panel (B) 400x magnification.</p