# Ordinary differential equation approximation of gamma distributed delay model

AbstractIn many models of pharmacodynamic systems with delays, a delay of an input is introduced by means of the convolution with the gamma distribution. An approximation of the convolution integral of bound functions based on a system of ordinary differential equations that utilizes properties of the binomial series has been introduced. The approximation converges uniformly on every compact time interval and an estimate of the approximation error has been found$$O\left( {\frac{1}{{N^{\nu } }}} \right)$$ where$$N$$ is the number of differential equations and$$\nu$$ is the shape parameter of the gamma distribution. The accuracy of approximation has been tested on a set of input functions for which the convolution is known explicitly. For tested functions,$$N \ge 20$$ has resulted in an  accurate approximation, if$$\nu \ge 1$$. However, if$$\nu 100$$ might be necessary to achieve acceptable accuracy. Finally, the approximation was applied to estimate parameters for the distributed delay model of chemotherapy-induced myelosuppression from previously published WBC count data in rats treated with 5-fluorouracil.
Source: Journal of Pharmacokinetics and Pharmacodynamics - Category: Drugs & Pharmacology Source Type: research

os AC Abstract PURPOSE: To examine the effects of Arrabidaa chica (Bignoniacea) extract, a native plant of the Amazon known as crajiru, on a 7,12-dimethyl-1,2-benzanthracene (DMBA)-induced breast cancer model in Wistar rats. METHODS: We compared the response of breast cancer to the oral administration of A. chica extract (ACE) for 16 weeks, associated or not with vincristine. Groups: normal control; DMBA (50mg/kg v.o,) without treatment; DMBA+ACE (300 mg/kg); DMBA+vincristine. 500μg/kg injected i.p; DMBA+ACE+Vincristine 250μg/kg i.p. Imaging by microPET and fluorescence, biochemistry, oxidative stress, ...
Source: Acta Cirurgica Brasileira - Category: Surgery Authors: Tags: Acta Cir Bras Source Type: research
Triple-negative breast cancer is difficult to treat. A new study indicates that a common chemotherapy drug improves overall survival in this tumor type -- big news in cancer treatment.Medscape Medical News
Source: Medscape General Surgery Headlines - Category: Surgery Tags: Hematology-Oncology News Source Type: news
This study is registered with Clinicaltrials.gov, number NCT02560025, and has completed enrolment.FindingsBetween Dec 31, 2015, and Aug 1, 2017, we enrolled a total of 39 eligible patients. 19 (49%) of 39 patients had secondary acute myeloid leukaemia and three (8%) had therapy-related acute myeloid leukaemia. At mid-induction, 33 (85%) of 39 patients showed marrow aplasia, six (15%) received re-induction. The median follow-up was 13·7 months (IQR 12·7–14·4). Composite remission was 64% (two-stage 95% CI 48–79), with 20 (51%) of 39 patients achieving complete remission and five (13%) achiev...
Source: The Lancet Haematology - Category: Hematology Source Type: research
CONCLUSIONS: Early supplemental parenteral nutrition after chemotherapy-induced severe granulocytopenia could reduce the risk of infection, improve the likelihood of chemotherapy completion, and shorten hospital stays and leukocyte recovery times. PMID: 31826367 [PubMed - in process]
Source: Asia Pacific Journal of Clinical Nutrition - Category: Nutrition Authors: Tags: Asia Pac J Clin Nutr Source Type: research
Abstract BACKGROUND AND OBJECTIVES: To systematically assess the safety and effectiveness of probiotics in preventing and treating chemotherapy-induced diarrhea (CID), so as to provide the evidence-based evidence for clinical practice. METHODS AND STUDY DESIGN: Electronic databases, including EMbase, Cochrane Library, pubMed, CNKI, VIP, CBM, and Wanfang databases, were retrieved to search for the randomized controlled trials (RCTs) of CIDs among patients with malignant tumors treated with probiotics as of March 2019. Later, the Rev Man 5.3 statistical software was employed to extract data and assess the quali...
Source: Asia Pacific Journal of Clinical Nutrition - Category: Nutrition Authors: Tags: Asia Pac J Clin Nutr Source Type: research
Conditions:   Myeloid Neoplasm;   Recurrent Acute Myeloid Leukemia;   Refractory Acute Myeloid Leukemia Interventions:   Drug: Cladribine;   Drug: Cytarabine;   Biological: Granulocyte Colony-Stimulating Factor;   Drug: Mitoxantrone Sponsors:   University of Washington;   National Cancer Institute (NCI) Not yet recruiting
Source: ClinicalTrials.gov - Category: Research Source Type: clinical trials