The document provides an overview of requirements for an Investigational New Drug (IND) application to the FDA. It discusses key components of the IND including chemistry, manufacturing and controls (CMC), preclinical toxicology studies, and clinical trial protocols. The main points are:
1) An IND application is required to begin clinical testing of new drugs, drugs at new dosages, or drug combinations not previously approved.
2) Key sections of the IND include CMC data on drug manufacturing and quality controls, results of preclinical toxicology studies in animals, and protocols for proposed clinical trials.
3) Preclinical studies aim to identify safe starting doses for clinical trials and target organs of toxicity.
Conjugate Gradient for Normal Equations and PreconditioningFahad B. Mostafa
Between many ideas of solving linear systems, each technique has its own merits and demerits. To handle large linear system, it is particularly important to use a convenient method for reducing convergence time and obtaining better outputs. In this project we will use Steepest Decent (SD) method and Conjugate Gradient (CG) method for solving linear system with high dimensions. There are many other techniques to solve such systems, for example, simple Gaussian elimination or Cholesky Factorization, however these methods are unsuitable to handle large systems. On the other hand, SD and CG methods are quite familiar to solve sparse system of linear equations. Moreover, from many existed technique, normal equation is one of the convenient ways to solve big non-invertible system. However, this technique is more ill conditioned, but it plays a good role for some specific methods. We introduce preconditioning of the system so that condition number is close to one. For optimizing convex quadratic functions, CG can be used for optimal results with fast convergence. Then, we apply preconditioned Conjugate Gradient method with normal equation on the modified system. In this study, we compared three different methods (LS with SD, GMRES with Arnoldi’s iteration and PCGNE). PCGNE is the main aim to show in this project. We basically use many plots and tables to show the better method. Finally, we use a block preconditioning technique known as Block Conjugate Gradient algorithms for least squares for some better and faster convergence.
This document discusses the non-clinical drug development process. It begins with an introduction explaining that developing new drugs requires expertise from many disciplines and takes 10-12 years and over $800 million on average. It then discusses the Investigational New Drug (IND) application process, which allows clinical trials in humans after pre-clinical studies in animals. It describes the types of INDs and provides charts outlining the IND and New Drug Application (NDA) processes. Finally, it briefly discusses the Abbreviated New Drug Application (ANDA) process for generic drugs.
Retrometabolic drug design approaches aim to develop safer drugs by designing drugs (soft drugs or chemical delivery systems) that selectively target tissues and undergo deactivation through predictable metabolism. Soft drugs are active but designed to metabolize into inactive species, while chemical delivery systems are inactive prodrugs activated by sequential metabolism. Examples include soft corticosteroids designed to metabolize quickly into inactive compounds to reduce side effects, and brain-targeting prodrugs designed to cross the blood-brain barrier then metabolize to release the active drug sustained in the brain. These approaches rely on metabolism to control drug distribution and action while increasing safety.
The document discusses gradient and divergence. Gradient is a vector quantity that points in the direction of maximum rate of increase of a scalar function. Divergence is a scalar quantity that measures the spread of a vector field from a point. It gives examples of gradient on a hillside and divergence for a faucet and whirlpool. It also provides mathematical expressions and geometric interpretations for gradient and divergence, and examples of problems calculating them.
The document provides an overview of requirements for an Investigational New Drug (IND) application to the FDA. It discusses key components of the IND including chemistry, manufacturing and controls (CMC), preclinical toxicology studies, and clinical trial protocols. The main points are:
1) An IND application is required to begin clinical testing of new drugs, drugs at new dosages, or drug combinations not previously approved.
2) Key sections of the IND include CMC data on drug manufacturing and quality controls, results of preclinical toxicology studies in animals, and protocols for proposed clinical trials.
3) Preclinical studies aim to identify safe starting doses for clinical trials and target organs of toxicity.
Conjugate Gradient for Normal Equations and PreconditioningFahad B. Mostafa
Between many ideas of solving linear systems, each technique has its own merits and demerits. To handle large linear system, it is particularly important to use a convenient method for reducing convergence time and obtaining better outputs. In this project we will use Steepest Decent (SD) method and Conjugate Gradient (CG) method for solving linear system with high dimensions. There are many other techniques to solve such systems, for example, simple Gaussian elimination or Cholesky Factorization, however these methods are unsuitable to handle large systems. On the other hand, SD and CG methods are quite familiar to solve sparse system of linear equations. Moreover, from many existed technique, normal equation is one of the convenient ways to solve big non-invertible system. However, this technique is more ill conditioned, but it plays a good role for some specific methods. We introduce preconditioning of the system so that condition number is close to one. For optimizing convex quadratic functions, CG can be used for optimal results with fast convergence. Then, we apply preconditioned Conjugate Gradient method with normal equation on the modified system. In this study, we compared three different methods (LS with SD, GMRES with Arnoldi’s iteration and PCGNE). PCGNE is the main aim to show in this project. We basically use many plots and tables to show the better method. Finally, we use a block preconditioning technique known as Block Conjugate Gradient algorithms for least squares for some better and faster convergence.
This document discusses the non-clinical drug development process. It begins with an introduction explaining that developing new drugs requires expertise from many disciplines and takes 10-12 years and over $800 million on average. It then discusses the Investigational New Drug (IND) application process, which allows clinical trials in humans after pre-clinical studies in animals. It describes the types of INDs and provides charts outlining the IND and New Drug Application (NDA) processes. Finally, it briefly discusses the Abbreviated New Drug Application (ANDA) process for generic drugs.
Retrometabolic drug design approaches aim to develop safer drugs by designing drugs (soft drugs or chemical delivery systems) that selectively target tissues and undergo deactivation through predictable metabolism. Soft drugs are active but designed to metabolize into inactive species, while chemical delivery systems are inactive prodrugs activated by sequential metabolism. Examples include soft corticosteroids designed to metabolize quickly into inactive compounds to reduce side effects, and brain-targeting prodrugs designed to cross the blood-brain barrier then metabolize to release the active drug sustained in the brain. These approaches rely on metabolism to control drug distribution and action while increasing safety.
The document discusses gradient and divergence. Gradient is a vector quantity that points in the direction of maximum rate of increase of a scalar function. Divergence is a scalar quantity that measures the spread of a vector field from a point. It gives examples of gradient on a hillside and divergence for a faucet and whirlpool. It also provides mathematical expressions and geometric interpretations for gradient and divergence, and examples of problems calculating them.
This document discusses biostatistics in bioequivalence studies. It covers:
1) The importance of biostatistics in designing and analyzing bioequivalence trials, as well as distinguishing between correlation and causation.
2) Key biostatistical concepts for bioequivalence studies including descriptive statistics, parametric assumptions of normality and homoscedasticity, study designs, and tests of significance.
3) Details on sample size calculation and determining the number of subjects needed in a bioequivalence study based on factors like variability, equivalence bounds, type I and II error rates.
Seminar presentation made by me for the topic of 'Resources for Sentiment Analysis' at IIT Bombay. Includes a set of bonus slides for additional information which was not actually presented.
This document summarizes the process of evaluating floating tablets, including preformulation studies, precompression evaluation, postcompression evaluation, in vitro studies, in vivo studies, and stability studies. Some key points covered include determining particle size and shape, bulk and tapped density measurements, drug release testing using USP apparatus 2, and conducting in vivo x-ray studies in humans to observe floating ability in fasted and fed states. The goal of developing a floating drug delivery system is to provide prolonged gastric retention for controlled release of the drug.
Liouville's theorem and gauss’s mean value theorem.pptxMasoudIbrahim3
This document provides an overview of Liouville's theorem and Gauss's mean value theorem from complex analysis. It includes the statements of both theorems, outlines their proofs, and provides examples and frequently asked questions about Liouville's theorem. Specifically, Liouville's theorem states that every bounded entire function must be constant, while Gauss's mean value theorem relates the derivative of a function to the average value of the derivative over an interval.
This document discusses differential equations and their application. It begins by defining what a differential equation is and provides examples of first order differential equations. It then discusses Newton's Law of Cooling, providing the derivation and formulation of the law. Several applications of Newton's Law of Cooling are presented, including using it to estimate time of death from temperature readings and determining cooling system specifications for computer processors. Other topics covered include the Mean Value Theorem, precalculus concepts, and examples of how calculus is applied in various fields such as credit cards, biology, engineering, architecture, and more.
This document discusses biostatistics in bioequivalence studies. It covers:
1) The importance of biostatistics in designing and analyzing bioequivalence trials, as well as distinguishing between correlation and causation.
2) Key biostatistical concepts for bioequivalence studies including descriptive statistics, parametric assumptions of normality and homoscedasticity, study designs, and tests of significance.
3) Details on sample size calculation and determining the number of subjects needed in a bioequivalence study based on factors like variability, equivalence bounds, type I and II error rates.
Seminar presentation made by me for the topic of 'Resources for Sentiment Analysis' at IIT Bombay. Includes a set of bonus slides for additional information which was not actually presented.
This document summarizes the process of evaluating floating tablets, including preformulation studies, precompression evaluation, postcompression evaluation, in vitro studies, in vivo studies, and stability studies. Some key points covered include determining particle size and shape, bulk and tapped density measurements, drug release testing using USP apparatus 2, and conducting in vivo x-ray studies in humans to observe floating ability in fasted and fed states. The goal of developing a floating drug delivery system is to provide prolonged gastric retention for controlled release of the drug.
Liouville's theorem and gauss’s mean value theorem.pptxMasoudIbrahim3
This document provides an overview of Liouville's theorem and Gauss's mean value theorem from complex analysis. It includes the statements of both theorems, outlines their proofs, and provides examples and frequently asked questions about Liouville's theorem. Specifically, Liouville's theorem states that every bounded entire function must be constant, while Gauss's mean value theorem relates the derivative of a function to the average value of the derivative over an interval.
This document discusses differential equations and their application. It begins by defining what a differential equation is and provides examples of first order differential equations. It then discusses Newton's Law of Cooling, providing the derivation and formulation of the law. Several applications of Newton's Law of Cooling are presented, including using it to estimate time of death from temperature readings and determining cooling system specifications for computer processors. Other topics covered include the Mean Value Theorem, precalculus concepts, and examples of how calculus is applied in various fields such as credit cards, biology, engineering, architecture, and more.
1. 江前敏晴, 紙の基礎と印刷適性(Part 3).
4 紙の印刷適性
インキが紙に接触することが印刷の第 1 段階であるが、接触しただけではイン
キは紙に定着しない。その後のインキの広がり、すなわち浸透が第 2 段階として
起こり、最後の段階が定着である。ここではインキが浸透する過程を測定・解析
する上で基礎となる液体の吸収理論及びその測定技術を中心に論ずることにす
る。また併せて、紙の持つ様々な特性が液体浸透のどのような影響を及ぼすのか
も見ていくことにする。ここで扱う液体の吸収性は、印刷だけではなく紙を製造
する際のサイズプレスや塗工工程での原紙の吸水挙動を推測する上でも重要で
ある。
4-1 液体吸収性
4-1-1 基礎理論
液体の吸収・浸透に関連した理論をここでは扱う。
4-1-1-1 Lucas-Washburn 式に基づく毛管吸収
ルーカス-ウォッシュバーン(Lucas-Washburn)の式(以下 L-W 式と略記)が
古くから適用され、現在でも液体浸透の解析の基本式として用いられる。これは
次の式(1.1)で表される。
rγ cos θ
l= t (Lucas-Washburn の式) 式 (20)
2η
ここで、l:浸透深さ、r:毛管半径、γ:液体の表面張力、θ:接触角、η:粘度、t:時
間である。
L-W 式は次のようにして求められる。非圧縮性ニュートン流体に対する運動
の基礎方程式はナビエ-ストークス(Navier-Stokes)の式と呼ばれ、空間上の xyz で
示される直交座標軸で考えると、z 軸方向には次式で示される。
⎛ ∂v z ∂v ∂v ∂v ⎞ ⎛ ∂ 2 v ∂ 2 v ∂ 2 v ⎞ ∂p
ρ⎜
⎜ +v x z + v y z +v z z ⎟=η ⎜ 2z + 2z + 2 z ⎟− + ρg z 式 (21)
⎝ ∂t ∂x ∂y ∂z ⎟ ⎜ ∂x
⎠ ⎝ ∂y ∂z ⎟ ∂z
⎠
ここで、v は液体の速度で添え字 x,y,z は空間上の直交座標軸方向、ρは液体の
密度、ηは液体の粘度、gz は重力加速度の z 軸方向成分である。
図 78 で示されるような半径が r で長さが l の円管内を粘度ηの液体が安定し
1
2. 江前敏晴, 紙の基礎と印刷適性(Part 3).
て一定速度で流れる(定常流という)場合、水平に置かれた円管では x,y 方向に
流れがなく vx=vy=0 となる。また、z 方向には速度勾配がないので∂2vz/∂z=0 が、
また定常流であることから∂2vz/∂t=0 が成り立つ。よって、
∂p ⎛ ∂ 2 v z ∂ 2 v z ⎞
=η ⎜ + ⎟ 式 (22)
∂z ⎜ ∂y 2 ∂y 2 ⎟
⎝ ⎠
y
x
r
θ
z
flow in z direction
図 79 左端に張った白金線をマイ
ナス極とし、 流れの中で電
図 78 円管を流れるハーゲンポア
圧をかけると、 白金線から
ゼイユの流れを示す模式図
水素の微小な気泡が発生
し、それが右方に流され
る。電圧をパルス的に加え
ると、図のような放物線上
の気泡の列ができる。 これ
から上下の平行な壁面で
流速は 0 であることが判断
できる。
これを極座標で表示するには次のように置き換えればよい。
y
z=z x = r cosθ y = r sin θ r = + x2 + y2 θ = tan −1 式 (23)
x
これを式(22)に代入し、
1 dp ∂ 2 v z 1 ∂v z 1 ∂ 2 v z
= + + 式 (24)
μ dz ∂ r 2 r ∂ r r 2 ∂θ 2
この座標系の方が変微分の計算がやりやすい。どのθの位置でも vz は一定なの
で∂2vz/∂θ2=0 が成り立ち、また dp/dz は一定なので、次のようになる。
1 dp d 2 v z 1 dv z 1 d ⎛ dv z ⎞
= const = + = ⎜r ⎟ 式 (25)
μ dz dr2 r d r r d r ⎝ dr ⎠
2