Spectral analysis on infinite Sierpinski fractafolds

A fractafold, a space that is locally modeled on a specified fractal, is the fractal equivalent of a manifold. For compact fractafolds based on the Sierpinski gasket, it was shown by the first author how to compute the discrete spectrum of the Laplacian in terms of the spectrum of a finite graph Laplacian. A similar problem was solved by the second author for the case of infinite blowups of a Sierpinski gasket, where spectrum is pure point of infinite multiplicity. Both works used the method of spectral decimations to obtain explicit description of the eigenvalues and eigenfunctions. In this paper we combine the ideas from these earlier works to obtain a description of the spectral resolution of the Laplacian for noncompact fractafolds. Our main abstract results enable us to obtain a completely explicit description of the spectral resolution of the fractafold Laplacian. For some specific examples we turn the spectral resolution into a "Plancherel formula". We also present such a formula for the graph Laplacian on the 3-regular tree, which appears to be a new result of independent interest. In the end we discuss periodic fractafolds and fractal fields

Microwave Assisted Synthesis of Py-Im Polyamides

Microwave synthesis was utilized to rapidly build Py-Im polyamides in high yields and purity using Boc-protection chemistry on Kaiser oxime resin. A representative polyamide targeting the 5′-WGWWCW-3′ (W = A or T) subset of the consensus Androgen and Glucocorticoid Response Elements was synthesized in 56% yield after 20 linear steps and HPLC purification. It was confirmed by Mosher amide derivatization of the polyamide that a chiral α-amino acid does not racemize after several additional coupling steps

Dynamic Surface Activity by Folding and Unfolding an Amphiphilic α-Helix

We describe a rationally designed peptide with tunable surface activity, where the dynamics of surface activity are an outcome of helical folding. Our rationally designed model peptide is surface-active only as an α-helix. We apply circular dichroism to show that the folded population can be controlled with changes in electrolyte concentration, and we apply pendant bubble tensiometry to explore dynamic surfactant activity. This study shows a peptide that responds to environmental stimuli with dynamic folding and surface activity. Extending this concept to selective binding peptides will lead to new tools, where dynamic surface activity is coupled to targeted binding

Dual-Phase PET-CT to Differentiate [F-18]Fluoromethylcholine Uptake in Reactive and Malignant Lymph Nodes in Patients with Prostate Cancer

PURPOSE: To investigate whether time-trends of enhanced [(18)F]Fluoromethylcholine ([(18)F]FCH) in lymph nodes (LN) of prostate cancer (PCa) patients can help to discriminate reactive from malignant ones, and whether single time point standardized uptake value (SUV) measurements also suffice. PROCEDURES: 25 PCa patients with inguinal (presumed benign) and enlarged pelvic LN (presumed malignant) showing enhanced [(18)F]FCH uptake at dual-phase PET-CT were analyzed. Associations between LN status (benign versus malignant) and SUV(max) and SUV(meanA50), determined at 2 min (early) and 30 min (late) post injection, were assessed. We considered two time-trends of [(18)F]FCH uptake: type A (SUV early > SUV late) and type B (SUV late ≥ SUV early). Histopathology and/or follow-up were used to confirm the assumption that LN with type A pattern are benign, and LN with type B pattern malignant. RESULTS: Analysis of 54 nodes showed that LN status, time-trends, and 'late' (30 min p.i.) SUV(max) and SUV(meanA50) parameters were strongly associated (P<0.0001). SUV(max) relative difference was the best LN status predictor. All but one inguinal LN showed a decreasing [(18)F]FCH uptake over time (pattern A), while 95% of the pelvic nodes presented a stable or increasing uptake (pattern B) type. CONCLUSIONS: Time-trends of enhanced [(18)F]FCH uptake can help to characterize lymph nodes in prostate cancer patients. Single time-point SUV measurements, 30 min p.i., may be a reasonable alternative for predicting benign versus malignant status of lymph nodes, but this remains to be validated in non-enlarged pelvic lymph nodes

Gastrin-releasing peptide receptor-based targeting using bombesin analogues is superior to metabolism-based targeting using choline for in vivo imaging of human prostate cancer xenografts

Purpose: Prostate cancer (PC) is a major health problem. Overexpression of the gastrin-releasing peptide receptor (GRPR) in PC, but not in the hyperplastic prostate, provides a promising target for staging and monitoring of PC. Based on the assumption that cancer cells have increased metabolic activity, metabolism-based tracers are also being used for PC imaging. We compared GRPR-based targeting using the68Ga-labelled bombesin analogue AMBA with metabolism-based tar

Novel iodinated tracers, MIBG and BMIPP, for nuclear cardiology

With the rapid growth of molecular biology, in vivo imaging of such molecular process (i.e., molecular imaging) has been well developed. The molecular imaging has been focused on justifying advanced treatments and for assessing the treatment effects. Most of molecular imaging has been developed using PET camera and suitable PET radiopharmaceuticals. However, this technique cannot be widely available and we need alternative approach. 123I-labeled compounds have been also suitable for molecular imaging using single-photon computed tomography (SPECT) 123I-labeled meta-iodobenzylguanidine (MIBG) has been used for assessing severity of heart failure and prognosis. In addition, it has a potential role to predict fatal arrhythmia, particularly for those who had and are planned to receive implantable cardioverter-defibrillator treatment. 123I-beta-methyl-iodophenylpentadecanoic acid (BMIPP) plays an important role for identifying ischemia at rest, based on the unique capability to represent persistent metabolic alteration after recovery of ischemia, so called ischemic memory. Since BMIPP abnormalities may represent severe ischemia or jeopardized myocardium, it may permit risk analysis in CAD patients, particularly for those with chronic kidney disease and/or hemodialysis patients. This review will discuss about recent development of these important iodinated compounds

Clinical performance and radiation dosimetry of no-carrier-added vs carrier-added 123I-metaiodobenzylguanidine (MIBG) for the assessment of cardiac sympathetic nerve activity

Purpose We hypothesized that assessment of myocardial sympathetic activity with no-carrier-added (nca) I-123-metaiodobenzylguanidine (MIBG) compared to carrier-added (ca) I-123-MIBG would lead to an improvement of clinical performance without major differences in radiation dosimetry. Methods In nine healthy volunteers, 15 min and 4 h planar thoracic scintigrams and conjugate whole-body scans were performed up to 48 h following intravenous injection of 185 MBq I-123-MIBG. The subjects were given both nca and ca I-123-MIBG. Early heart/mediastinal ratios (H/M), late H/M ratios and myocardial washout were calculated. The fraction of administered activity in ten source organs was quantified from the attenuation-corrected geometric mean counts in conjugate views. Radiation-absorbed doses were estimated with OLINDA/EXM software. Results Both early and late H/M were higher for nca I-123-MIBG (ca I-123-MIBG early H/M 2.46 +/- 0.15 vs nca I-123-MIBG 2.84 +/- 0.15, p = 0.001 and ca I-123-MIBG late H/M 2.69 +/- 0.14 vs nca I-123-MIBG 3.34 +/- 0.18, p = 0.002). Myocardial washout showed a longer retention time for nca I-123-MIBG (p <0.001). The effective dose equivalent (adult male model) for nca I-123-MIBG was similar to that for ca I-123-MIBG (0.025 +/- 0.002 mSv/MBq vs 0.026 +/- 0.002 mSv/MBq, p = 0.055, respectively). Conclusion No-carrier-added I-123-MIBG yields a higher relative myocardial uptake and is associated with a higher myocardial retention. This difference between nca I-123-MIBG and ca I-123-MIBG in myocardial uptake did not result in major differences in estimated absorbed doses. Therefore, nca I-123-MIBG is to be preferred over ca I-123-MIBG for the assessment of cardiac sympathetic activit

Biokinetics and dosimetry of commonly used radiopharmaceuticals in diagnostic nuclear medicine – a review

Purpose The impact on patients’ health of radiopharmaceuticals in nuclear medicine diagnostics has not until now been evaluated systematically in a European context. Therefore, as part of the EU-funded Project PEDDOSE. NET (www.peddose.net), we review and summarize the current knowledge on biokinetics and dosimetry of commonly used diagnostic radiopharmaceuticals. Methods A detailed literature search on published biokinetic and dosimetric data was performed mostly via PubMed (www.ncbi.nlm.nih.gov/pubmed). In principle the criteria for inclusion of data followed the EANM Dosimetry Committee guidance document on good clinical reporting. Results Data on dosimetry and biokinetics can be difficult to find, are scattered in various journals and, especially in paediatric nuclear medicine, are very scarce. The data collection and calculation methods vary with respect to the time-points, bladder voiding, dose assessment after the last data point and the way the effective dose was calculated. In many studies the number of subjects included for obtaining biokinetic and dosimetry data was fewer than ten, and some of the biokinetic data were acquired more than 20 years ago. Conclusion It would be of interest to generate new data on biokinetics and dosimetry in diagnostic nuclear medicine using state-of-the-art equipment and more uniform dosimetry protocols. For easier public access to dosimetry data for diagnostic radiopharmaceuticals, a database containing these data should be created and maintained

Track A Basic Science

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138319/1/jia218438.pd