Pharmacokinetic Consideration to Formulate Sustained Release Drugs: Understanding the Controlled Drug Diffusion through the Body Compartment of the Systemic Circulation and Tissue Medium-A Caputo Model

الهدف من هذه الدراسة هو تقديم لمحة عامة عن النماذج المختلفة لدراسة انتشار الدواء لفترة طويلة في جسم الإنسان وداخله. تم التأكيد على نماذج المقصورة الرياضية باستخدام نهج المشتقة الجزئية (نموذج كابوتو) للتحقيق في التغير في تركيز الدواء المستدام في أجزاء مختلفة من نظام جسم الإنسان من خلال الطريق الفموي أو الطريق الوريدي. و تم استخدام قانون العمل الجماعي ، وحركية الدرجة الأولى ، ومبدأ الإرواء لفيك لتطوير نماذج المقصورة الرياضية التي تمثل انتشارا مستداما للأدوية في جميع أنحاء جسم الإنسان. للتنبؤ بشكل كافٍ بانتشار الدواء المستمر في أجزاء مختلفة من جسم الإنسان، وضعنا في الاعتبار(نموذج كابوتو (للتحقيق في معدل تغير التركيز اعتمادًا على التغيير في ترتيب التمايز الجزئي في جميع الأجزاء الممكنة من الجسم، أي الدوران الجهازي وحجرات الأنسجة. أيضا ، تم تعيين قيمة معلمة عددية لمعدل تدفق الدواء في مقصورات مختلفة لتقدير تركيز الدواء. تم حساب النتائج وتصوير الأرقام باستخدام برنامج MATLAB (الإصدار R2020a). التأثيرات الرسومية الموضحة للتغير في معدل التركيز بافتراض قيم وسيطة مختلفة وفقا للمشتقة الكسرية (نموذج كابوتو ). التأثيرات الرسومية الموضحة للتغير في معدل التركيز بافتراض قيم وسيطة مختلفة وفقا للمشتقة الكسرية (نموذج كابوتو). يخلص التمثيل البياني الناتج إلى أنه بالنظر إلى ترتيب قيم المعادلات التفاضلية ، يختلف تركيز الدواء اعتمادا على معدل الثوابت في المقصورات المتعلقة بالوقت.   النظر في الحالة الأولية للتقدير التقريبي حيث يشير الجسم كحجرة كاملة، بعد تقسيم الجسم إلى مقصورتين نموذجيتين. في حين أن النموذج الأول يمثل المعدة والكبد والدم الجهازي ؛ والنموذج الثاني يأخذ في الاعتبار الدم الشرياني وأنسجة الكبد والدم الوريدي.The aim of this study is to provide an overview of various models to study drug diffusion for a sustained period into and within the human body. Emphasized the mathematical compartment models using fractional derivative (Caputo model) approach to investigate the change in sustained drug concentration in different compartments of the human body system through the oral route or the intravenous route. Law of mass action, first-order kinetics, and Fick's perfusion principle were used to develop mathematical compartment models representing sustained drug diffusion throughout the human body. To adequately predict the sustained drug diffusion into various compartments of the human body, consider fractional derivative (Caputo model) to investigate the rate of concentration changing depending upon the change in the order of fractional differentiation in all the possible compartments of the body, i.e., systemic circulation and tissue compartments. Also, assigned a numerical parameter value to the rate of drug flow in different compartments to estimate the drug concentration. Results were calculated and figures were depicted by using MATLAB software (version R2020a). Illustrated graphical effects of change in concentration rate by assuming various intermediate values according to the fractional derivative (Caputo model). The resultant graphical representation concludes that considering the order of the differential equation values, the drug concentration varies depending upon its rate of constants in compartments concerning time. Considering the initial case for rough estimation where the body is indicated as a whole compartment, following division of the body into two model compartments. Whereas, the model I represents stomach, liver, and systemic blood, and model II consider arterial blood, liver tissue, and venous blood

Construction of Linear Codes from the Unit Graph G(Zn)G(\mathbb{Z}_{n})

In this paper, we consider the unit graph $G(\mathbb{Z}_{n})$, where $n=p_{1}^{n_{1}} \text{ or } p_{1}^{n_{1}}p_{2}^{n_{2}} \text{ or } p_{1}^{n_{1}}p_{2}^{n_{2}}p_{3}^{n_{3}}$ and $p_{1}, p_{2}, p_{3}$ are distinct primes. For any prime $q$, we construct $q$-ary linear codes from the incidence matrix of the unit graph $G(\mathbb{Z}_{n})$ with their parameters. We also prove that the dual of the constructed codes have minimum distance either 3 or 4. Lastly, we stated two conjectures on diameter of unit graph $G(\mathbb{Z}_{n})$ and linear codes constructed from the incidence matrix of the unit graph $G(\mathbb{Z}_{n})$ for any integer $n$

Effect of angiotensin-converting enzyme inhibitor and angiotensin receptor blocker initiation on organ support-free days in patients hospitalized with COVID-19

IMPORTANCE Overactivation of the renin-angiotensin system (RAS) may contribute to poor clinical outcomes in patients with COVID-19. Objective To determine whether angiotensin-converting enzyme (ACE) inhibitor or angiotensin receptor blocker (ARB) initiation improves outcomes in patients hospitalized for COVID-19. DESIGN, SETTING, AND PARTICIPANTS In an ongoing, adaptive platform randomized clinical trial, 721 critically ill and 58 non–critically ill hospitalized adults were randomized to receive an RAS inhibitor or control between March 16, 2021, and February 25, 2022, at 69 sites in 7 countries (final follow-up on June 1, 2022). INTERVENTIONS Patients were randomized to receive open-label initiation of an ACE inhibitor (n = 257), ARB (n = 248), ARB in combination with DMX-200 (a chemokine receptor-2 inhibitor; n = 10), or no RAS inhibitor (control; n = 264) for up to 10 days. MAIN OUTCOMES AND MEASURES The primary outcome was organ support–free days, a composite of hospital survival and days alive without cardiovascular or respiratory organ support through 21 days. The primary analysis was a bayesian cumulative logistic model. Odds ratios (ORs) greater than 1 represent improved outcomes. RESULTS On February 25, 2022, enrollment was discontinued due to safety concerns. Among 679 critically ill patients with available primary outcome data, the median age was 56 years and 239 participants (35.2%) were women. Median (IQR) organ support–free days among critically ill patients was 10 (–1 to 16) in the ACE inhibitor group (n = 231), 8 (–1 to 17) in the ARB group (n = 217), and 12 (0 to 17) in the control group (n = 231) (median adjusted odds ratios of 0.77 [95% bayesian credible interval, 0.58-1.06] for improvement for ACE inhibitor and 0.76 [95% credible interval, 0.56-1.05] for ARB compared with control). The posterior probabilities that ACE inhibitors and ARBs worsened organ support–free days compared with control were 94.9% and 95.4%, respectively. Hospital survival occurred in 166 of 231 critically ill participants (71.9%) in the ACE inhibitor group, 152 of 217 (70.0%) in the ARB group, and 182 of 231 (78.8%) in the control group (posterior probabilities that ACE inhibitor and ARB worsened hospital survival compared with control were 95.3% and 98.1%, respectively). CONCLUSIONS AND RELEVANCE In this trial, among critically ill adults with COVID-19, initiation of an ACE inhibitor or ARB did not improve, and likely worsened, clinical outcomes. TRIAL REGISTRATION ClinicalTrials.gov Identifier: NCT0273570

On Existence of Solutions of Impulsive Nonlinear Functional Neutral Integro-Differential Equations With Nonlocal Condition

In the present paper, we investigate the existence, uniqueness and continuous dependence of mild solutions of an impulsive neutral integro-differential equations with nonlocal condition in Banach spaces. We use Banach contraction principle and the theory of fractional power of operators to obtain our results

On Some Qualitative Properties of Mild Solutions of Nonlocal Semilinear Functional Differential Equations

In the present paper, we investigate the qualitative properties such as existence, uniqueness and continuous dependence on initial data of mild solutions of first and second order nonlocal semilinear functional differential equations with delay in Banach spaces. Our analysis is based on semigroup theory and modified version of Banach contraction theorem