Trees of Irreducible Numerical Semigroups

A 2011 paper by Blanco and Rosales describes an algorithm for constructing a directed tree graph of irreducible numerical semigroups of fixed Frobenius numbers. This paper will provide an overview of irreducible numerical semigroups and the directed tree graphs. We will also present new findings and conjectures concerning the structure of these trees

Drug delivery to the lymphatic system: importance in future cancer diagnosis and therapies

This is an Accepted Manuscript of an article published by Taylor & Francis in Expert Opinion on Drug Delivery on 2009-08, available online: http://www.tandfonline.com/10.1517/17425240903085128.Cancer is the second leading cause of death in the US. Currently, protocols for cancer treatment include surgery to remove diseased and suspect tissues, focused radiation, systemic chemotherapy, immunotherapy and their combinations. With conventional chemotherapy, it is almost impossible to deliver anticancer drugs specifically to the tumor cells without damaging healthy organs or tissues. Over the past several decades, efforts have been made to improve drug delivery technologies that target anticancer drugs specifically to tumor cells. It has been known for over four decades that the lymphatics are the first site of metastasis for most solid cancers; however, few efforts have been made to localize chemotherapies to lymphatic tissues. Trials of several systemic targeted drug delivery systems based on nanoparticles containing chemotherapeutic agents (e.g., liposomal doxorubicin) have shown similar antitumor activity but better patient tolerance compared with conventional formulations. Animal studies have demonstrated that nanoparticles made of natural or synthetic polymers and liposomal carriers have higher accumulation in the lymph nodes and surrounding lymphatics compared to conventional intravenous therapies. This combination has the potential to both reduce nonspecific organ toxicities and increase the chemotherapeutic dose to the most likely sites of locoregional cancer metastasis

Impact of Molecular Weight on Lymphatic Drainage of a Biopolymer-Based Imaging Agent

New lymphatic imaging technologies are needed to better assess immune function and cancer progression and treatment. Lymphatic uptake depends mainly on particle size (10–100 nm) and charge. The size of carriers for imaging and drug delivery can be optimized to maximize lymphatic uptake, localize chemotherapy to lymphatic metastases, and enable visualization of treatment deposition. Toward this end, female BALB/c mice were injected subcutaneously in the hind footpad or forearm with a series of six different molecular weight hyaluronan (HA) near-infrared dye (HA-IR820) conjugates (ca. 5–200 nm). Mice were imaged using whole body fluorescent imaging over two weeks. HA-IR820 fluorescence was clearly visualized in the draining lymphatic capillaries, and in the popliteal and iliac or axillary lymph nodes. The 74-kDa HA-IR820 had the largest lymph node area-under-the-curve. In contrast to prior reports, mice bearing limb tumors exhibited three-fold longer retention of 74-kDa HA-IR820 in the popliteal node compared to mice without tumors. HA conjugate kinetics and disposition can be specifically tailored by altering their molecular weight. The specific lymphatic uptake and increased nodal retention of HA conjugates indicate significant potential for development as a natural biopolymer for intralymphatic drug delivery and imaging

Lymphatic trafficking kinetics and near-infrared imaging using star polymer architectures with controlled anionic character

Targeted lymphatic delivery of nanoparticles for drug delivery and imaging is primarily dependent on size and charge. Prior studies have observed increased lymphatic uptake and retentions of over 48 hrs for negatively charged particles compared to neutral and positively charged particles. We have developed new polymeric materials that extend retention over a more pharmaceutically relevant 7-day period. We used whole body fluorescence imaging to observe in mice the lymphatic trafficking of a series of anionic star poly-(6-O-methacryloyl-D-galactose) polymer-NIR dye (IR820) conjugates. The anionic charge of polymers was increased by modifying galactose moieties in the star polymers with succinic anhydride. Increasing anionic nature was associated with enhanced lymphatic uptake up to a zeta potential of ca. -40 mV; further negative charge did not affect lymphatic uptake. Compared to the 20% acid-conjugate, the 40 to 90% acid-star-polymer conjugates exhibited a 2.5- to 3.5-fold increase in lymphatic uptake in both the popliteal and iliac nodes. The polymer conjugates exhibited node half-lives of 2 to 20 hrs in the popliteal nodes and 19 to 114 hrs in the deeper iliac nodes. These polymer conjugates can deliver drugs or imaging agents with rapid lymphatic uptake and prolonged deep-nodal retention; thus they may provide a useful vehicle for sustained intralymphatic drug delivery with low toxicity

Lymphatic trafficking kinetics and near-infrared imaging using star polymer architectures with controlled anionic character

This is the published version. Copyright ElsevierTargeted lymphatic delivery of nanoparticles for drug delivery and imaging is primarily dependent on size and charge. Prior studies have observed increased lymphatic uptake and retentions of over 48 hrs for negatively charged particles compared to neutral and positively charged particles. We have developed new polymeric materials that extend retention over a more pharmaceutically relevant 7-day period. We used whole body fluorescence imaging to observe in mice the lymphatic trafficking of a series of anionic star poly-(6-O-methacryloyl-D-galactose) polymer-NIR dye (IR820) conjugates. The anionic charge of polymers was increased by modifying galactose moieties in the star polymers with succinic anhydride. Increasing anionic nature was associated with enhanced lymphatic uptake up to a zeta potential of ca. -40 mV; further negative charge did not affect lymphatic uptake. Compared to the 20% acid-conjugate, the 40 to 90% acid-star-polymer conjugates exhibited a 2.5- to 3.5-fold increase in lymphatic uptake in both the popliteal and iliac nodes. The polymer conjugates exhibited node half-lives of 2 to 20 hrs in the popliteal nodes and 19 to 114 hrs in the deeper iliac nodes. These polymer conjugates can deliver drugs or imaging agents with rapid lymphatic uptake and prolonged deep-nodal retention; thus they may provide a useful vehicle for sustained intralymphatic drug delivery with low toxicity.This work was supported by awards from the American Cancer Society (RSG-08-133-01-CDD), the Susan G. Komen Foundation (KG090481), a Pfizer Predoctoral Scholarship to TRB, and a PhRMA Foundation Predoctoral Fellowship to TRB. Also, the authors would like to thank Dr. Sarah Kieweg and Thora Whitmore for the use of the Advanced Rheometer 2000. TRB performed imaging studies and SD characterized and synthesized the materials; their contributions and authorship were equal in this study

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Abstract Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries