A Blood Brain Pharmacokinetic Model

A Blood Brain Pharmacokinetic Model Pharmacokinetics, an emerging field in BioPhysics and chemistry is the study of the time variation of drug and metabolite levels in various tissues and fluids of the body. Compartment models are used to interpret data. In our problem, we consider a simple blood-brain compartment model as shown in the figure below: k21 Input d(t) k12 K where, Compartment 1 = Blood Compartment 2 = Brain This model is made such that it can aid to help estimate dosage strengths of an orally administered antidepressant drug. The rate of movement of drug from compartment i to compartment j is denoted by the rate constant kji and the rate at which the drug is removed from the blood is represented by the rate constant K. A pharmaceutical company must deal with many factors like dosage strengths that will aid a physician in determining a patients dosage in order to maintain the right concentration levels and also minimizing irritation and other side effects (Brannan 208). If we assume that the drug is rapidly absorbed into the blood stream after it is introduced into the stomach, a mathematical representation of the dosage will be of a periodic square wave given as follows: Based on our model and the equations we can solve the problems: 1. If we let xj(t) be the amount of drug in milligrams in compartment j, j =1,2. The mass balance law states: (i) Using the mass balance law and the figure, we find: System in Blood compartment: System in Brain compartment: From (i) and the above equations, we can find the following: (ii) The systems above are the rates of drug over time in the compartments. 2. If we let ci(t) denote the concentration of the drug and Vi denote the apparent volume of distribution in compartment i, we can use the relation ci = xi/Vi in the equations of system (ii) to obtain: (iii) Dividing the above systems by V1 and V2 respectively, we get : 3. Assuming x1(0) =0 and x2(0) =0, and the various parameters listed below: k21 k12 K V1 V2 Tb 0.29/h 0.31/h 0.16/h 6L 0.25L 1h and with the numerical simulation program Maple , we can perform simulations of the system with given parameters to recommend two different encapsulated dosage strengths A=RTb. => Guidelines to use for recommendation of drug dosage: 1) Target concentration level in the brain should be kept as close as possible between levels 10 mg/L and 30 mg/L and concentration fluctuation should not exceed 25% of the average of the steady-state response. 2) Lower frequency of administration (once every 24 hours or once every 12 hours is best). Once every 9.5 hours is unacceptable and multiple doses are acceptable (i.e. taking two capsules every 4 hours) Analysis: Drug usage of more than 4 times per day is unacceptable which makes maximum allowable dose to be 3, making 3 doses at 8 hours interval per day the best choice. We can then simulate from Tp = 8 to Tp = 12, 16 and 24. From the numerical simulations obtained from Maple, we obtain the following data: Tp(h) R (mg/h) Steady-state variance Comments 8 4 9.04 mg/L to 12.5 mg/L Below effective therapeutic concentration 8 5 11.7 mg/L to 15.5 mg/L 8 6 14.4 mg/L to 19.2 mg/L 8 8 19.2 mg/L to 25.3 mg/L 8 9 21.1 mg/L to 27.9 mg/L 8 10 23.2 mg/L to 31.2 mg/L Above maximum therapeutic concentration 12 5 10.9 mg/L to 6.5 mg/L Below minimum therapeutic concentration 12 6 8.6 mg/L to 14.1 mg/L Below minimum therapeutic concentration 12 7 8.32 mg/L to 15.1 mg/L Below minimum therapeutic concentration 12 8 10.6 mg/L to 18.3 mg/L 12 10 13.2 mg/L to 22.8 mg/L 12 13 17.9 mg/L to 30 mg/L 16 10 9.11 mg/L to 19.5 mg/L Sharp fluctuations; Below minimum therapeutic concentration 16 12 10.7 mg/L to 23.5 mg/L Sharp fluctuations. 16 13 11.5 mg/L to 25.4 mg/L Sharp fluctuations. 16 14 12.5 mg/L to 27.3 mg/L Sharp fluctuations. 16 16 14.3mg/L 31.4mg/L Sharp fluctuations; Above maximum therapeutic concentration 24 15 6.19mg/L 24mg/L Sharp fluctuations; Below minimum therapeutic concentration 24 20 8.52mg/L 32mg/L Sharp fluctuations; Above maximum therapeutic concentration Obtained corresponding Graphs from Maple and their respective Tp and R values are listed below: Tp = 8, R = 4 Tp = 8, R = 5 Tp = 8, R = 6 Tp = 8, R = 8 Tp = 8, R = 9 Tp = 8, R = 10 Tp = 12, R = 6 Tp = 12, R = 8 Tp = 12, R = 10 Tp = 12, R = 12 Tp = 12, R = 13 Tp=16, R=10 Tp=16, R=12 Tp=16, R=13 Tp=16, R=14 Tp=16, R=16 Tp=24, R=15 Tp=24, R=20 Some Comments: When Tp= 8 and R = 4, the recommended dosage is below minimum therapeutic concentration range. When Tp= 8 and R = 10 , the recommended dosage is above maximum therapeutic concentration range. When Tp= 8 and R = 5 to 7, the recommended dosage is below effective therapeutic concentration range. When Tp= 8 and R = 4, the recommended dosage is below therapeutic concentration range. When Tp= 12 and R = 5 to 7, the recommended dosage is below minimum therapeutic concentration range. When Tp= 16 and R = 12 to 14, sharp fluctuation is seen. When Tp= 24 and R = 20, sharp fluctuation is seen and the recommended dosage is below therapeutic concentration range. =>Calculation and Analysis of dosage strength A Now we can calculate the dosage frequency for the remaining dosage frequency intervals of 8 hours and 12 hours: (8 hour interval) (R being from 5 mg/h to 9 mg/h) A = RTb = 5 mg/h x 1h= 5 mg A = RTb = 9 mg/h x 1h= 9 mg (12 hour interval) (R being from 8 mg/h to 13 mg/h) A = RTb = 8 mg/h x 1h = 8 mg A = RTb = 13 mg/h x 1h= 13 mg 4. From the simulation, we can know that it is best to skip the dose than to try to catch up and double the dose and ultimately overdose from the figures illustrated. If we assume the patient is at a 12 hour interval dose frequency, and R being 10mg/h, the following scenarios can be simulated:   Scenario: missed a dosage and skipped     Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Scenario: missing a dosage catching up Analysis: From the scenarios simulations above, we can have a clear picture of what will go through the patients drug level. In the 1st scenario, where the patient missed a dosage and skipped, the concentration level in the brain of the patient stays within the recommended level. In the 2nd scenario, where the patient tries to catch up, the drug level will cross the recommended level and that also by a lot. Thus, skipping the dose is better than to catch up overdosing the drug level resulting in fatality.   5. Supposing the drug can be packaged in a timed-release form so that Tb = 8 hours and R also adjusted likewise, we get the following data from the Maple: Tp(h) R(mg/h) Steady-state variance Reasons 12 0.75 10.4mg/L 13mg/L 12 1 13.9mg/L 17mg/L 12 1.5 21mg/L 25.5mg/L 12 1.75 24.5mg/L 29.8mg/L 12 2 28.1mg/L 34mg/L Above maximum therapeutic concentration 16 1 9mg/L 14.3mg/L Below minimum therapeutic concentration 16 1.25 11.2mg/L 17.7mg/L 16 1.5 13.6mg/L 21.3mg/L 16 2 18.3mg/L 28.4mg/L 16 2.25 20.5mg/L 31.8mg/L Above maximum therapeutic concentration 16 2.5 22.8mg/L 35.4mg/L Above maximum therapeutic concentration 24 2 8.7mg/L 23.3mg/L Sharp fluctuation 24 2.25 9.86mg/L 25.9mg/L Sharp fluctuation 24 2.5 10.9mg/L 29mg/L Sharp fluctuation T=12, R=0.75 T=12, R=1 T=12, R=1.5 T=12, R=1.75 T=12, R=2 T=16, R=1 T=16, R=1.25 T=16, R=1.5 T=16, R=2 T=16, R=2.25 T=16, R=2.5 T=24, R=2 T=24, R=2.5 Analysis: If the drug can be packaged in a timed release form so that Tb = 8 and R is also adjusted likewise, we perform the simulations for the dosage of interval of a 12 hour frequency. We observe zero sharp fluctuations. Every graph seems to produce the concentration level within the recommended range of 10mg/L to 30mg/L when R is between 0.75 mg/h and 1.75 mg/h. =>Calculation and Analysis of new dosage strength A We can calculate the new strength level of the drugs as: (12 hour frequency interval): A=RTb = 0.75 mg/h * 8h = 6mg   A=RTb = 1.75 mg/h * 8h = 14mg Same analysis can be performed for 16 hour frequency interval. We observe zero sharp fluctuations and every graph produce the concentration level within the recommended range of 10mg/L to 30mg/L; R being in between 1.25mg/h and 2mg/h.   =>Calculation and Analysis of new dosage strength A We can calculate the new strength level of the drugs as:   (16 hour frequency interval): A = RTb=1.25 mg/h * 8h = 10mg    A = RTb=2.00 mg/h * 8h = 16mg Thus, this changes our recommendation. Simulation Program Maple: We used the following code and simulated varying R and P values. g :=t> piecewise(0 DEplot({diff(x(t), t) = (1/6)*g(t)+(1/6)*(.31*.25)*y(t)-x(t)*(.29+.16), diff(y(t), t) = (.29*6)*x(t)/(.25)-.31*y(t)}, [x(t), y(t)], t = 0 .. 40, x = 0 .. .50, y = 0 .. 80, scene = [t, y], [[x(0) = 0, y(0) = 0]], stepsize = .1, color = blue)

Why Is Assessment Important

4 Why is assessment for learning important? Adopting strategies that support Assessment for Learning can transform learning and teaching and take away the stigma that haunts assessment. In fact, research has shown that Assessment for Learning can have a significant effect on how well pupils achieve in terms of their attainment, behaviour, motivation, engagement and their ability to work independently. a) It Improves Performance -Black and William’s 1998 literature review examined 250 research articles from 160 journals published over a nine-year period.From this, they documented significant, and often substantial, quantifiable learning gains due to Assessment for Learning practices. Their review of over 20 studies on classroom assessment showed increases in primary and post-primary performance ranging from 15 to 30% compared to control groups. In post-primary, differential effects were measured at approximately half a level at Key Stage 3, over half a grade at GCSE, and two fu ll grades at GCSE after two to three years. They concluded that no other single improvement initiative improved performance levels to the extent that formative assessment did.Subsequent research in UK schools has substantiated these figures. For instance, research conducted in primary schools through the Gillingham Partnership’s Formative Assessment Project 2002 indicated improved standardised test scores in reading and numeracy as well as improvements in writing levels. Learning b) It Increases Learning Independence – Pupils who understand their own goals and their role in learning are more independent in managing their learning; they know what to do, how they have to work and take more responsibility for their own learning and assessment.Assessment for Learning helps cultivate these valuable skills by giving pupils a role in determining these components of the learning as well as experience in providing feedback and assessing themselves and their peers. The learning is no longer something they receive; it becomes something they pursue and have a hand in shaping. This can help learners later in life as well as in the classroom. c) It Improves Morale, Motivation and Risk-Taking – Knowing the goals and success indicators may help pupils to gain learning independence, but they are not the only influencing factors.Morale and motivation are also pivotal components, and here, too, Assessment for Learning plays an important role. Black and William found that many assessment approaches used in classrooms compare pupils with one another – particularly those that focus on marks and grades. Evidence shows that pupils interpret the prime purpose of these assessments to be competition rather than personal improvement. As a result, feedback from these types of assessment actually reduces pupil morale. It teaches them, particularly low-attaining pupils, that they lack ability, leading them to believe they are unable to learn. ) It Enhances Relati onships and Reflection – Assessment for Learning also helps foster a more positive classroom environment. It strengthens teacher-pupil relationships by increasing two-way communication. These interactions can make them more motivated to learn and more aware of their learning. Assessment for Learning can also improve planning and delivery of learning. This is because these practices lead you to analyse and make learning specific to pupils. It creates an opportunity to quality assure and amend activities to ensure they meet the learning needs. Why Is Assessment Important 4 Why is assessment for learning important? Adopting strategies that support Assessment for Learning can transform learning and teaching and take away the stigma that haunts assessment. In fact, research has shown that Assessment for Learning can have a significant effect on how well pupils achieve in terms of their attainment, behaviour, motivation, engagement and their ability to work independently. a) It Improves Performance -Black and William’s 1998 literature review examined 250 research articles from 160 journals published over a nine-year period.From this, they documented significant, and often substantial, quantifiable learning gains due to Assessment for Learning practices. Their review of over 20 studies on classroom assessment showed increases in primary and post-primary performance ranging from 15 to 30% compared to control groups. In post-primary, differential effects were measured at approximately half a level at Key Stage 3, over half a grade at GCSE, and two fu ll grades at GCSE after two to three years. They concluded that no other single improvement initiative improved performance levels to the extent that formative assessment did.Subsequent research in UK schools has substantiated these figures. For instance, research conducted in primary schools through the Gillingham Partnership’s Formative Assessment Project 2002 indicated improved standardised test scores in reading and numeracy as well as improvements in writing levels. Learning b) It Increases Learning Independence – Pupils who understand their own goals and their role in learning are more independent in managing their learning; they know what to do, how they have to work and take more responsibility for their own learning and assessment.Assessment for Learning helps cultivate these valuable skills by giving pupils a role in determining these components of the learning as well as experience in providing feedback and assessing themselves and their peers. The learning is no longer something they receive; it becomes something they pursue and have a hand in shaping. This can help learners later in life as well as in the classroom. c) It Improves Morale, Motivation and Risk-Taking – Knowing the goals and success indicators may help pupils to gain learning independence, but they are not the only influencing factors.Morale and motivation are also pivotal components, and here, too, Assessment for Learning plays an important role. Black and William found that many assessment approaches used in classrooms compare pupils with one another – particularly those that focus on marks and grades. Evidence shows that pupils interpret the prime purpose of these assessments to be competition rather than personal improvement. As a result, feedback from these types of assessment actually reduces pupil morale. It teaches them, particularly low-attaining pupils, that they lack ability, leading them to believe they are unable to learn. ) It Enhances Relati onships and Reflection – Assessment for Learning also helps foster a more positive classroom environment. It strengthens teacher-pupil relationships by increasing two-way communication. These interactions can make them more motivated to learn and more aware of their learning. Assessment for Learning can also improve planning and delivery of learning. This is because these practices lead you to analyse and make learning specific to pupils. It creates an opportunity to quality assure and amend activities to ensure they meet the learning needs.

Characteristics of Anthroponyms Essay

Theses of the scientific paper â€Å"Semantic, social pragmatic and functional characteristics of anthroponyms (based on the novel John Updike â€Å"The Centaur†)†; Viktoriya Melnychuk; Khmelnyts’kyi regional MAN department; Shepetivka educational complex #1; form 11; Tarnavska Olena Myhaylivna, the candidate of philological sciences, associate professor of department of English philology of the Volynskiy national university named after Lesia Ukrainka. The purpose  of this paper  is to analyze anthroponyms, their semantic, social pragmatic and functional characteristics of  anthroponyms (based on the novel  John Updike  Ã¢â‚¬Å"The Centaur†). The full communication, that is correct perception, evaluation and interpretation of information, is impossible without knowing the specific set of anthroponyms and their functions in language and text. The names of famous personalities, literature characters make up a significant part of knowledge, necessary for understanding and assessment of the culture different people. Therefore, our research is relevant. The subject of the research is semantic, social pragmatic and functional characteristics of  anthroponyms (based on the novel  John Updike  Ã¢â‚¬Å"The Centaur†). Anthroponomastics  , a branch of  onomastics, is the study of  anthroponyms  , the names of  human beings. Anthroponyms often preserve lexical elements that have dropped out of the standard  lexicon  of a  language. The subdivisions of anthroponymy include: given names, surnames, clan names, matronyms, patronyms, teknonyms, nicknames, ethnonyms. Allusion is the main feature of the anthroponyms. Allusion is a brief reference to some to some literary or historical event commonly known. Allusion is a subtype of metaphor. Metaphor denotes expressing remaining on the basis of similarity of two objects: the real object of speech and the one whose name is actually used. But there is only affinity, no real connection between the two. Most of anthroponyms in the novel John Updike â€Å"The Centaur† are the individual, which expressed their own names, surnames, status names and perform the nominative function.

George C. Wallace and His Depiction of Freedom vs The...

Wallace v. The Enlightenment George C. Wallace was the governor of Alabama in 1963, the time period when the fight for Civil Rights was at its height. On inauguration day, January 14, 1963, in Montgomery, Alabama, Wallace gave a speech that proves to everyone exactly what kind of man he was and strived to be. Wallace was against the common and moral rights of humanity and he contradicted the philosophies of the Enlightenment thinkers. The Enlightenment was a time period that lasted from the mid seventeenth century through the eighteenth and changed the way people viewed the world. Some of the most famous philosophers from the time period include John Locke, Voltaire, and Montesquieu (www.csudh.edu). George Wallace does not follow either the beliefs or the actions one would expect from an enlightened thinker. He disregards the ideas of freedom, individuality, and natural rights. One of the most famous philosophies of John Locke is his belief in freedom. He is quoted saying, To understand political power right, and derive it from its original, we must consider what state all men are naturally in, and that is, a state of perfect freedom to order their actions, and dispose of their possessions, and persons as they think fit, within the bounds of the law of nature, without asking leave, or depending on the will of any other man.† This quote describes how Locke feels a man’s right to freedom should be. (www.discoverjohnlocke.com) In comparison to the Inaugural Address givenShow MoreRelatedContemporary Issues in Management Accounting211377 Words   |  846 PagesFOREWORD ‘ Michael Bromwich is an exemplar of all that is good about the British tradition of academic accounting. Serious in intent, he has striven both to illuminate practice and to provide ways of improving it. Although always appealing to his economic understandings, he has been open to a wide variety of other ideas, recognizing their intellectual strengths and capabilities rather than making artificial distinctions between what is acceptable and what is not. He also has contributed widely