Direction Modulated Brachytherapy for the Treatment of Cervical Cancer

Purpose: To evaluate and compare the performance of 9 experimental DMBT tandem models of varying physical dimensions in relation to 24 previously planned HDR cervical cancer treatment plans from multiple institutions that used conventional tandem and rings or ovoid applicators. Methods and Materials: The DMBT tandem is designed to be used concurrently with IGABT and is made from an MRI-compatible tungsten-alloy rod with 6 channels grooved out of its periphery. 9 experimental DMBT tandem prototypes were provided. Each of the models was of equal lengths but varied in thickness, channel diameter size, and circle channel diameter size. Replanning was performed using our research TPS (BrachyVisionÒ v.16.1, Varian, Palo Alto, CA). Inverse optimization using Acuros was performed for 12 patient cases (24 plans) belonging to three institutions: Virginia Commonwealth University, University of Michigan, and University of California San Diego. Original plans used conventional tandem and ovoids or ring applicators. Each of the 9 DMBT tandem models replaced the location of the original tandem such that the new dwell positions were at the level of the original plan. The dwell positions of the ovoids or rings remained unchanged. Results: The average relative reduction in D2cc using the thinnest DMBT tandem (model 1) were: -9.65% (∆EQD2 D2ccBladder = -3.6 Gy), -19.91% (∆EQD2 D2ccRectum = -3.87 Gy), and -14.55% (∆EQD2 D2ccSigmoid = -3.55 Gy), for the bladder, rectum, and sigmoid respectively. The average relative reduction in D2cc using the thickest DMBT tandem (model 9) were: -12.82% (∆EQD2 D2ccBladder = -4.05 Gy), -24.69% (∆EQD2 D2ccRectum = -4.05 Gy), and -18.42% (∆EQD2 D2ccSigmoid = -3.63 Gy), for the bladder, rectum, and sigmoid respectively. Conclusions: Significant reductions in OAR dose while maintaining identical target coverage (D90) can be achieved by the use of any of the 9 DMBT tandem models. As DMBT tandem thickness increases, OAR dose decreases; however, there is no significant differences in performance between models. Unless necessary to remain within an OAR’s total dose (EQD2) limit, we advise the use of a moderately thick DMBT tandem (model 5) for clinical use as its physical dimensions resemble that of already used clinically conventional tandems while offering enhanced modulating capabilities

How Much String to String a Cardioid?

A residue design is an artistic geometric construction in which we have $n$ equally-spaced points on a circle numbered 0 through $n-1$ and we join with a line segment each point $k$ to $ak$ modulo $n$ for some fixed $a\ge 2.$ The envelopes of these lines are epicycloids, like cardioids. In this note, we prove that when $a-1$ and $n$ are relatively prime, the sum of the lengths of these line segments has the surprising closed form of $2\cot(\tfrac{\pi}{2n})$ times the radius of the circle.Comment: 5 pages, 3 figure

Elementary Students\u27 Analysis of Diverse History-Based Sources

This study analyzed students\u27 use of diverse sources for a history-based writing assignment on Abraham Lincoln. Participants includes 41 students in a fifth grade self-contained classroom in rural Illinois. The study was conducted during students\u27 30-minute writing period, every day for six weeks. During this time period, students close-read trade books and primary sources to collect research on Lincoln. Students also gathered additional information during their field trip to the Abraham Lincoln Presidential Library and Museum. Students synthesized their information from the various sources and organized the notes to write an informational, history-based writing piece on Lincoln. Students were required to cite their various sources and corroborate information between sources. Finally, student selected one of three finishing option to share their information with others. The results of the study suggested that students seemed genuinely motivated and intrigued by the assignment, they used close reading to analyze diverse texts effectively but not perfectly, and they engaged in complex forms of writing using non-fiction, history-based curricula. Overall, students were successful in using, citing, and corroborating diverse sources for this complex, history-based writing unit