Inverse Function: Pre-Service Teachers’ Techniques and Meanings

Researchers have argued teachers and students are not developing connected meanings for function inverse, thus calling for a closer examination of teachers’ and students’ inverse function meanings. Responding to this call, we characterize 25 pre-service teachers’ inverse function meanings as inferred from our analysis of clinical interviews. After summarizing relevant research, we describe the methodology and theoretical framework we used to interpret the pre-service teachers’ activities. We then present data highlighting the techniques the pre-service teachers used when responding to tasks that involved analytical and graphical representations of functions and inverse functions in both decontextualized and contextualized situations and discuss our inferences of their meanings based on their activities. We conclude with implications for the teaching and learning of inverse function and areas for future research

Dosimetric Performance and Planning/Delivery Efficiency of a Dual-Layer Stacked and Staggered MLC on Treating Multiple Small Targets: A Planning Study Based on Single-Isocenter Multi-Target Stereotactic Radiosurgery (SRS) to Brain Metastases.

Purpose: To evaluate the dosimetric performance and planning/delivery efficiency of a dual-layer MLC system for treating multiple brain metastases with a single isocenter. Materials and Methods: 10 patients each with 6-10 targets with volumes from 0.11 to 8.57 cc, and prescription doses from 15 to 24 Gy, were retrospectively studied. Halcyon has only coplanar delivery mode. Halcyon V1 MLC modulates only with the lower layer at 1 cm resolution, whereas V2 MLC modulates with both layers at an effective resolution of 0.5 cm. For each patient five plans were compared varying MLC and beam arrangements: the clinical plan using multi-aperture dynamic conformal arc (DCA) and non-coplanar arcs, Halcyon-V1 using coplanar-VMAT, Halcyon-V2 using coplanar-VMAT, HDMLC-0.25 cm using coplanar-VMAT, and HDMLC-0.25 cm using non-coplanar-VMAT. All same-case plans were generated following the same planning protocol and normalization. Conformity index (CI), gradient index (GI), V12Gy, V6Gy, V3Gy, and brain mean dose were compared. Results: All VMAT plans met clinical constraints for critical structures. For targets with diameter \u3c 1 cm, Halcyon plans showed inferior CI among all techniques. For targets with diameter \u3e1 cm, Halcyon VMAT plans had CI similar to non-coplanar VMAT plans, and better than non-coplanar clinical DCA plans. For GI, Halcyon MLC plans performed similarly to coplanar HDMLC plans and inferiorly compared to non-coplanar HDMLC plans. All coplanar VMAT plans (Halcyon MLC and HDMLC) and clinical DCA plans had similar V12Gy, but were inferior compared to non-coplanar VMAT plans. Halcyon plans had slightly reduced V3Gy and mean brain dose compared to HDMLC plans. The difference between Halcyon V1 and V2 is only significant in CI of tumors less than 1cm in diameter. Halcyon plans required longer optimization than Truebeam VMAT plans, but had similar delivery efficiency. Conclusion: For targets with diameter \u3e1 cm, Halcyon\u27s dual-layer stacked and staggered MLC is capable of producing similar dose conformity compared to HDMLC while reducing low dose spill to normal brain tissue. GI and V12Gy of Halcyon MLC plans were, in general, inferior to non-coplanar DCA or VMAT plans using HDMLC, likely due to coplanar geometry and wider MLC leaves. HDMLC maintained its advantage in CI for smaller targets with diameter \u3c1 cm. © 2019 Li, Irmen, Liu, Shi, Alonso-Basanta, Zou, Teo, Metz and Dong

ACE-inhibitors and Angiotensin-2 Receptor Blockers are not associated with severe SARS-COVID19 infection in a multi-site UK acute Hospital Trust

Aims: The SARS‐CoV‐2 virus binds to the angiotensin‐converting enzyme 2 (ACE2) receptor for cell entry. It has been suggested that angiotensin‐converting enzyme inhibitors (ACEi) and angiotensin II receptor blockers (ARB), which are commonly used in patients with hypertension or diabetes and may raise tissue ACE2 levels, could increase the risk of severe COVID‐19 infection. Methods and results: We evaluated this hypothesis in a consecutive cohort of 1200 acute inpatients with COVID‐19 at two hospitals with a multi‐ethnic catchment population in London (UK). The mean age was 68 ± 17 years (57% male) and 74% of patients had at least one comorbidity. Overall, 415 patients (34.6%) reached the primary endpoint of death or transfer to a critical care unit for organ support within 21 days of symptom onset. A total of 399 patients (33.3%) were taking ACEi or ARB. Patients on ACEi/ARB were significantly older and had more comorbidities. The odds ratio for the primary endpoint in patients on ACEi and ARB, after adjustment for age, sex and co‐morbidities, was 0.63 (95% confidence interval 0.47–0.84, P < 0.01). Conclusions: There was no evidence for increased severity of COVID‐19 in hospitalised patients on chronic treatment with ACEi or ARB. A trend towards a beneficial effect of ACEi/ARB requires further evaluation in larger meta‐analyses and randomised clinical trials

A review of clinical and surgical outcomes of endoscopic endonasal skull base surgery in a Tertiary Center in Sarawak

Background: Endoscopic endonasal approach (EEA) for skull base tumor has been extensively developed in recent years. Objectives: To review the demographic data, indications, clinical presentations and surgical outcomes of endoscopic endonasal skull base surgeries performed. Methods: A retrospective analysis on all patients who had undergone endoscopic endonasal skull base surgery at the Skull Base Unit (ENT & Neurosurgery) from December 2013 to December 2015. Results: A total 34 cases were operated on during the study period. Female patients account for 44% of patients while 56% were male patients, with ages ranging from 8 to 77 years, with the mean age of 51.88 years. Majority of the cases were pituitary tumors (41%), followed by sinonasal tumors (15%), meningioma (12%), clival tumor (8%), cerebrospinal fluid (CSF) leak repair (8%) and frontal mucocoele (6%). Transsellar approach was the commonest approach (41%) followed by the transclival, transplanum, transfrontal approaches. In about 80% of cases, CSF leak was encountered intraoperatively and was successfully repaired endoscopically with the Hadad-Bassagasteguy flap and with the insertion of a lumbar drain. Only one case (3%) of CSF leak was noted postoperatively which was then successful repaired endoscopically with a nasoseptal flap. Systemic complications and intracranial infections were seen in 3 cases (8%) and were managed accordingly. No cases of epitaxis requiring surgical intervention were noted post operatively

Early Cardiac Effects of Contemporary Radiation Therapy in Patients With Breast Cancer

Purpose To characterize the early changes in echocardiographically derived measures of cardiac function with contemporary radiation therapy (RT) in breast cancer and to determine the associations with radiation dose-volume metrics, including mean heart dose (MHD). Methods and Materials In a prospective longitudinal cohort study of 86 patients with breast cancer treated with photon or proton thoracic RT, clinical and echocardiographic data were assessed at 3 time points: within 4 weeks before RT initiation (T0), within 3 days before 6 weeks after the end of RT (T1), and 5 to 9 months after RT completion (T2). Associations between MHD and echocardiographically derived measures of cardiac function were assessed using generalized estimating equations to define the acute (T0 to T1) and subacute (T0 to T2) changes in cardiac function. Results The median estimates of MHD were 139 cGy (interquartile range, 99-249 cGy). In evaluating the acute changes in left ventricular ejection fraction (LVEF) from T0 to T1, and accounting for the time from RT, age, race, preexisting cardiovascular disease, and an interaction term with anthracycline or trastuzumab exposure and MHD, there was a modest decrease in LVEF of borderline significance (0.22%; 95% confidence interval [CI], –0.44% to 0.01%; P = .06) per 30-day interval for every 100 cGy increase of MHD. Similarly, there was a modest worsening in longitudinal strain (0.19%; 95% CI, –0.01% to 0.39%; P = .06) per 30-day interval for each 100 cGy increase in MHD. We did not find significant associations between MHD and changes in circumferential strain or diastolic function. Conclusions With modern radiation planning techniques, there are modest subclinical changes in measures of cardiac function in the short-term. Longer-term follow-up studies are needed to determine whether these early changes are associated with the development of overt cardiac disease

A multi-stage genome-wide association study of bladder cancer identifies multiple susceptibility loci.

We conducted a multi-stage, genome-wide association study of bladder cancer with a primary scan of 591,637 SNPs in 3,532 affected individuals (cases) and 5,120 controls of European descent from five studies followed by a replication strategy, which included 8,382 cases and 48,275 controls from 16 studies. In a combined analysis, we identified three new regions associated with bladder cancer on chromosomes 22q13.1, 19q12 and 2q37.1: rs1014971, (P = 8 × 10⁻¹²) maps to a non-genic region of chromosome 22q13.1, rs8102137 (P = 2 × 10⁻¹¹) on 19q12 maps to CCNE1 and rs11892031 (P = 1 × 10⁻⁷) maps to the UGT1A cluster on 2q37.1. We confirmed four previously identified genome-wide associations on chromosomes 3q28, 4p16.3, 8q24.21 and 8q24.3, validated previous candidate associations for the GSTM1 deletion (P = 4 × 10⁻¹¹) and a tag SNP for NAT2 acetylation status (P = 4 × 10⁻¹¹), and found interactions with smoking in both regions. Our findings on common variants associated with bladder cancer risk should provide new insights into the mechanisms of carcinogenesis