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# Matlab Tolerance

if the absolute value of a number is less than 1e-5, you may consider that close enough to be zero. This MATLAB function, where tspan = [t0 tf], integrates the system of differential equations y'=f(t,y) from t0 to tf with initial conditions y0. The element-wise formula for the Gauss-Seidel method is extremely similar to that of the Jacobi method. The Version 5 properties are supported only for backward compatibility. The iterations of the method should stop/terminate when a certain tolerance/convergence level is achieved OR a maximum number of iterations are performed (whichever happens first). The number of iterations in an optimization depends on a solver's stopping criteria. The manufacturer is 95% confident that 99% of all parts will have widths that are between 5 and 8 mm. Achieving fault tolerance. Suppose we want to solve the system of linear equations = for the vector x, where the known n × n matrix A is symmetric (i. Avec l'éditeur de MATLAB il est très simple et très rapide d'indenter proprement son code avec le raccourci : CTRL+A (sélection de tout le code) puis CTRL+I (indentation automatique). I am trying to have a tolerance of 10^-20 instead. Computationally, it is defined as the reciprocal of tolerance: 1 / (1 - R 2). In MATLAB version 5. Bisection method m file, Bisection method for loop, while loop used. Use the satisfiedBy method to implement the tolerance definition. Using the default values of tolerance, vpaintegral can handle values that cause the MATLAB integral function to overflow or underflow. 5' at line 26. gz of package or clone repository Run setup. Use help in MATLAB for more information on how to use any of these commands. whether or not there exists a convex function that may fit the data within a specified residual tolerance. Diagnostic object. The shock response spectrum assumes that the shock pulse is applied as a common base input to an array of independent single-degree-of-freedom systems. Create Custom Tolerance. However, I recently discovered the intersect command that can do this too, but faster. This is a slide-based introduction to techniques for doing Monte Carlo simulation in Matlab. help optimset provides information that defines the different parameters and describes how to use them. Learn more about fsolve. 5, start with a vector of all 1's and use a relative tolerance of 1. Loading Unsubscribe. The value of function can be modified and any function can be given as input. It comes from a course I teach as part of an online Masters degr. Matlab uses a tolerance to determine what is equal to zero. arrays of numbers. The coding style reﬂects something of a compromise between efﬁciency, on the one hand, and brevity and intelligibility, on the other. All other things equal, researchers desire lower levels of VIF, as higher levels of VIF are known to affect adversely the results associated with a multiple. @gnovice: Actually thats incorrect. (Taylor polynomial with integral remainder) Suppose a function f(x) and its ﬁrst n + 1 derivatives are continuous in a closed interval [c,d] containing the point x = a. The number of iterations in an optimization depends on a solver's stopping criteria. I have a problem with ode solver in MATLAB. Our main mission is to help out programmers and coders, students and learners in general, with relevant resources and materials in the field of computer programming. Matlab Practice Exam 2 (piecewise, for loops, while loops, tolerance) Brian Schendt. The relative tolerance is a percentage of the state's value. Change Leading Tolerance in a Baseline Comparison Test. diagnostics. Another was to say "root. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (2. The formulas differ between the calculation of one-sided tolerance limits and two-sided tolerance intervals. 5' at line 26. Tolerances and Stopping Criteria. Related Readings. FUZZY tolerance relation matlab. Get YouTube without the ads. For many years MATLAB used only double precision and it remains our default format. The testing framework uses the diagnostic when the compared values are outside of the allowable tolerance. NET,, Python, C++, C, and more. Then for any value x on this interval. This MATLAB function returns the unique elements in A using tolerance tol. I have two vector with different lenght and I want to compare the values of the vectors one by one with a certain tolerance because the numbers are similar but not equal, e. Programs will be introduced in Chapter 3. MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks. However, I recently discovered the intersect command that can do this too, but faster. Integrate besseli(5,25*u). Therefore, I was looking for another built-in function that could take a tolerance as an input argument, and return “true” when the absolute difference is below the tolerance threshold. For example, an engineer wants to know the range within which 99% of the future product will fall, with 98% confidence. I have stated the tolerance inside fminsearch function as options argument. m file containing % the function whose root you are seeking, guess is the % initial guess of the root, and tolerance is how % accurately you want to know the answer % Note that the default value of tolerance is 1e-10. In many cases, the actual individual part dimensions occur near the center of the tolerance range with very few parts with actual dimensions near the tolerance limits. Before you begin to solve an optimization problem, you must choose the appropriate approach: problem-based or solver-based. The following MATLAB code gives a generalized illustration of numerical integration using Trapezoidal rule. So, fsolve sees a number it thinks is close to zero, and stops. Choose the type of tolerance you want to set (RelTol, AbsTol, or NormControl), use odeset() to define the options for your ODE solver, call the ODE solver and pass the desired options. If it is a row vector then the solution y will be a matrix in which each column is the solution for the corresponding initial value in init. Simple Calculations with MATLAB 1. Inputs A and B must either be the same size or have sizes that are compatible (for example, A is an M-by-N matrix and B is a scalar or 1-by-N row vector). Examples of Dimension Tolerance and Precision You can set tolerance and precision options in the Dimension Value PropertyManager, as shown in these examples. I am doing a computation using fmincon, and it says tolfun=1e-06 and options. Approximation with tolerance = 0. Working Skip trial 1 month free. The default value (1e-3) means that the computed state is accurate to within 0. Entering vectors In Matlab, the basic objects are matrices, i. 273737e-13) at time t. The relative tolerance is a percentage of the state's value. So, fsolve sees a number it thinks is close to zero, and stops. Windows and such MATLAB evolved as an interface to a powerful library of linear algebra routines programmed in FORTRAN. Change Leading Tolerance in a Baseline Comparison Test. The element-wise formula for the Gauss-Seidel method is extremely similar to that of the Jacobi method. Additionally, it is easy to find the roots of the function analytically in this case:. resvec2(1) = norm(b) and resvec2(6) = norm(b-A*x2). It comes from a course I teach as part of an online Masters degr. Other ideas about root finding. The default value (auto) initially sets the absolute tolerance for each state based on the relative tolerance alone. The default tolerance is usually very small, of order 1e-15. Tol is the Tolerance, the max difference permitted between exact and approximate root count is the number of iterations performed Saving and ruunning the program. FUZZY tolerance relation matlab. Distributed under the MIT License. Unless otherwise noted on this page, most scripts stand alone and work in Matlab without further modification. Bisection method m file, Bisection method for loop, while loop used. To validate that the model simulates as expected, I decided to log many signals, and compare them. But you can understand the basic idea of the method and how to implement it using MATLAB. However, I recently discovered the intersect command that can do this too, but faster. optimset with no input or output arguments displays a complete list of parameters with their valid values. Such an interval is called a tolerance interval. In case this tighter tolerance slows down your simulation, the first thing I would recommend is leaving the absolute tolerance to auto, and try increasing the relative tolerance close to its default value of 1e-3 (or 1e-4) to get results of comparable accuracy. tolerance, and jitter transfer. A revision of IEEE 754, published in 2008, defines a floating point format that occupies only 16 bits. x T Ax > 0 for all non-zero vectors x in R n), and real, and b is known as well. The relative tolerance, however, becomes problematic when the solution is around zero, since x/0 is undefined. Compose your optimization problem in a MATLAB environment with familiar MATLAB syntax using the generic optimal control interface. The program solves the following problems: Tolerance analysis of a dimensional chain using the "Worst case" method. S = sum(A,vecdim) sums the elements of A based on the dimensions specified in the vector vecdim. The relative tolerance is a percentage of the state's value. 5, start with a vector of all 1's and use a relative tolerance of 1. I get the following message when I run the function: "fsolve stopped because the relative size of the current step is less than the default value of the step size tolerance, but the vector of function values is not near zero as measured by the selected value of the function tolerance. I need to compare two numeric matrices. A MATLAB package for functional data analysis using the square root velocity framework which performs pair-wise and group-wise alignment as well as modeling using functional component analysis Download zip or tar. It is also possible to write programs in MATLAB that are contained in script ﬁles or M-ﬁles. The satisfiedBy method is used to determine whether the tolerance is met. All can be viewed as prototypes for physical modeling sound synthesis. Construction. Question: Develop A Matlab Function That Finds The Root Of A Function F (x) Within A Given Initial Interval [a, B With A Tolerance In Solution Of At Least E Using The Bisection Method. For a more detailed description of the 'anova1' and 'multcompare' commands, visit the following Mathworks links: anova1 and multcompare. Classes that derive from the Tolerance class also must provide a diagnostic for two compared values. 98% is the confidence level for the tolerance interval. We now examine each of these specifications in turn. Therefore, I was looking for another built-in function that could take a tolerance as an input argument, and return “true” when the absolute difference is below the tolerance threshold. For information on the Version 5 properties, type at the MATLAB command line: more on, type odeset, more off. Create a table that displays the values of a, b, x NS, f (x NS), and the tolerance for each iteration of the bisection process. In this article, we are going to learn about Bisection Method in MATLAB. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, C#, Java, Fortran and Python. I do not understand why AbsTol determines the accuracy when the solution approaches zero (indeed, if the solution of my problem is a circular orbit of 7000 km radius this does not meet) and why RelTol controls the number of correct digits in all solution components, except those smaller than thresholds AbsTol(i). I already reduced the tolerance on the numerical integrals inside the system of equations, which slightly improved the computation time. mat, I have Fd and Fq matrices with 256*256 dimension as inputs and Pfer_c, Pfer_h, Pfes_c, Pfes_h, Ppm as the output of Fq and Fq. This paper presents a new transformer model displaying hysteresis using the MATLAB (TM) Simulink environment. The default value (auto) initially sets the absolute tolerance for each state based on the relative tolerance alone. 98% is the confidence level for the tolerance interval. S = sum(A,vecdim) sums the elements of A based on the dimensions specified in the vector vecdim. Single precision has been added gradually over the last several years and is now also fully supported. I am doing a computation using fmincon, and it says tolfun=1e-06 and options. The value of function can be modified and any function can be given as input. For more information about this method please try this. I do not understand why AbsTol determines the accuracy when the solution approaches zero (indeed, if the solution of my problem is a circular orbit of 7000 km radius this does not meet) and why RelTol controls the number of correct digits in all solution components, except those smaller than thresholds AbsTol(i). This is mostly helpful when doing tolerance analysis and sensitivity analysis on the circuit. What is the eigenvalue and how many steps did it take?. It is used to compute a range of values for the fixed proportion of the population. To validate that the model simulates as expected, I decided to log many signals, and compare them. You do not type the symbol ˛. Jitter Generation Given an input data stream with no jitter, the output of the CDR must meet the following jitter requirements: • rms jitter < 10 mUI (i. For that, I saved the Simulink. Tolerances and Stopping Criteria. From this write a matlab function that, given the values of x and a tolerance e, returns the value of k such that the absolute value of the k-th term of the taylor series expansion is less or equal than e. The fzero command finds a point where the function changes sign. In MATLAB version 5. Note This reference page describes the ODE properties for MATLAB, Version 7. Gauss-Seidel Method in MATLAB:. Learn more about fuzzy_relation, tolerance Fuzzy Logic Toolbox. I get the following message when I run the function: "fsolve stopped because the relative size of the current step is less than the default value of the step size tolerance, but the vector of function values is not near zero as measured by the selected value of the function tolerance. 1 Introduction and a Word of Warning MATLAB is an incredibly powerful tool, but in order to use it safely you need to be able to understand how it works and to be very precise when you enter commands. A revision of IEEE 754, published in 2008, defines a floating point format that occupies only 16 bits. The formulas differ between the calculation of one-sided tolerance limits and two-sided tolerance intervals. MATLAB 2019 Overview MATLAB 2019 Technical Setup Details MATLAB 2019 Free Download MATLAB Deep Learning: With Machine Learning, Neural Networks and Artificial Intelligence by Phil Kim Get started with MATLAB for deep learning and AI with this in-depth primer. In the Loss. There is also a way to cover a fixed proportion of the population with a stated confidence. For two DNA sequences of the same length, the Hamming distance is the number of positions in which the nucleotides (letters) of one sequence differ from the other. Windows and such MATLAB evolved as an interface to a powerful library of linear algebra routines programmed in FORTRAN. - Mike Middleton, www. The procedure is generally continued until the changes made by an iteration are below some tolerance, such as a sufficiently small residual. The Version 5 properties are supported only for backward compatibility. The testing framework uses the diagnostic when the compared values are outside of the allowable tolerance. It is also possible to write programs in MATLAB that are contained in script ﬁles or M-ﬁles. Changing the way you enter a command, even subtly can completely change its meaning. I used all ode solver like ode23s, ode23, ode15s, ode45 and so on. The data types of the inputs to the AbsoluteTolerance constructor determines which data types the tolerance supports. The program for bisection method in MATLAB works in similar manner. Thus, it makes sense to also look at the absolute change in value, and quit optimizing when abs(x(i)-x(i-1))> optimizationalgorithm. AbsoluteTolerance(tolVals) creates an absolute tolerance object that assesses the magnitude of the difference between the actual and expected values. function approximateZero = newtonsMethod( fnc, x0, tol ) % implementation of Newton's Method for finding a zero of a function % requires a symbolic expression, a starting point, and a tolerance as input % produces either an input, which when substituted into the given expression, % yields an output with absolute value less than the specified. Newton's method: Matlab code In the next exercise, you will get down to the task of writing Newton's method as a function m-file. Toggle Main Navigation. Get YouTube without the ads. Simulink software resets the counter each time it detects nonconsecutive zero crossings (successive zero crossings that fail to meet the relative tolerance setting); therefore, decreasing the relative tolerance value may afford your model's behavior more time to recover. When creating a custom tolerance, the class author must implement the getDiagnosticFor method so that it analyzes the two values, actVal and expVal, against the tolerance, tolObj, and instantiates and returns a matlab. The process of evaluating a definite integral from a set of tabulated values of integrand f(t) is called numerical integration. How to add tolerance to my code ? I think the reason is that I need to add a tolerance to the result of desired_line so Matlab can find it and add it to the. This video implements the secant method in MATLAB. There is also a way to cover a fixed proportion of the population with a stated confidence. This is the required formula which will also be used in the program for secant method in Matlab. Additionally, it is easy to find the roots of the function analytically in this case:. When creating a custom tolerance, the class author must implement the getDiagnosticFor method so that it analyzes the two values, actVal and expVal, against the tolerance, tolObj, and instantiates and returns a matlab. In many cases, the actual individual part dimensions occur near the center of the tolerance range with very few parts with actual dimensions near the tolerance limits. 1 Introduction and a Word of Warning MATLAB is an incredibly powerful tool, but in order to use it safely you need to be able to understand how it works and to be very precise when you enter commands. Suppose we want to solve the system of linear equations = for the vector x, where the known n × n matrix A is symmetric (i. x T Ax > 0 for all non-zero vectors x in R n), and real, and b is known as well. The main purpose of this section is to document the syntax and unique features of the Matlab API; for more detail on the underlying features, please refer to the C documentation in the NLopt Reference. Classes that derive from the Tolerance class also must provide a diagnostic for two compared values. % [root, steps] = bisect(‘function’,guess,tolerance) % where ‘function’ is the name of the. This MATLAB function returns the rank of matrix A. Windows and such MATLAB evolved as an interface to a powerful library of linear algebra routines programmed in FORTRAN. So, fsolve sees a number it thinks is close to zero, and stops. Discussion. Set tolerances and other criteria using optimoptions as explained in Set and. The default value (auto) initially sets the absolute tolerance for each state based on the relative tolerance alone. If the relative tolerance is larger than 1e-3, then the initial absolute tolerance is set to 1e-6. For a more detailed description of the 'anova1' and 'multcompare' commands, visit the following Mathworks links: anova1 and multcompare. Distributed under the MIT License. All can be viewed as prototypes for physical modeling sound synthesis. MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks. The choice of Matlab as. Solving Nonlinear Equation(s) in MATLAB 1 Introduction This tutorial helps you use MATLAB to solve nonlinear algebraic equations of single or multiple variables. For example, an engineer wants to know the range within which 99% of the future product will fall, with 98% confidence. The root sum square or RSS or statistical tolerance stack up method is useful for tolerance stack up analysis of an assembly having a large numbers of components. Classes that derive from the Tolerance class also must provide a diagnostic for two compared values. Optimization Browse through the Tolerance Editor and alter what you think is necessary. The following commands can serve as an introduction to MATLAB and allow you to get help:. The program solves the following problems: Tolerance analysis of a dimensional chain using the "Worst case" method. Construction. The program for bisection method in MATLAB works in similar manner. Use the getDiagnosticFor method to implement this condition. The coding style reﬂects something of a compromise between efﬁciency, on the one hand, and brevity and intelligibility, on the other. For more information about this method please try this. MATLAB Functions What is a MATLAB function? A MATLAB "function" is a MATLAB program that performs a sequence of operations specified in a text file (called an m-file because it must be saved with a file extension of *. This MATLAB function, where tspan = [t0 tf], integrates the system of differential equations y'=f(t,y) from t0 to tf with initial conditions y0. Bisection Method in MATLAB Code:. Use the getDiagnosticFor method to implement this condition. AbsoluteTolerance(tolVals) creates an absolute tolerance object that assesses the magnitude of the difference between the actual and expected values. The following is a sample program to understand finding solution of a non linear equation using Newton Raphson Method. The tolerance interval states with 95% confidence that 99% of the population have widths that fall within the interval [5, 8]. This is the required formula which will also be used in the program for secant method in Matlab. All the processes are dealt with and tested by computer. What is the eigenvalue and how many steps did it take?. The proposed model displays a complete scheme for the simulation of 3-phase transformers. Integrate besseli(5,25*u). Trying to find same values in 2 different vectors with a tolerance (self. The program for bisection method in MATLAB works in similar manner. 3 and earlier, the quad function used a less reliable algorithm and a default relative tolerance of 1. Learn more about fsolve. Generally, a tolerance is a threshold which, if crossed, stops the iterations of a solver. Entering vectors In Matlab, the basic objects are matrices, i. Written for the practicing electronics professional, Tolerance Analysis of Electronic Circuits Using MATLAB offers a comprehensive, step-by-step treatment of methods used to perform analyses essential to the design process of circuit cards and systems of cards, including:worst-case analysis,limits f. So, fsolve sees a number it thinks is close to zero, and stops. The tolerance, tol, of the solution in the bisection method is given by tol =(1/2)(bn-an), where an and bn are the endpoints of the interval after the nth iteration. When creating a custom tolerance, the class author must implement the getDiagnosticFor method so that it analyzes the two values, actVal and expVal, against the tolerance, tolObj, and instantiates and returns a matlab. Therefore, I was looking for another built-in function that could take a tolerance as an input argument, and return "true" when the absolute difference is below the tolerance threshold. The root sum squared (RSS) method is a statistical tolerance analysis method. The program solves the following problems: Tolerance analysis of a dimensional chain using the "Worst case" method. The iterations of the method should stop/terminate when a certain tolerance/convergence level is achieved OR a maximum number of iterations are performed (whichever happens first). The same procedure aforementioned is followed in the MATLAB program for this method. Set tolerances and other criteria using optimoptions as explained in Set and. How to add tolerance to my code ? I think the reason is that I need to add a tolerance to the result of desired_line so Matlab can find it and add it to the. Input arrays, specified as scalars, vectors, matrices, or multidimensional arrays. Suppose we want to solve the system of linear equations = for the vector x, where the known n × n matrix A is symmetric (i. Definition of a tolerance interval: A confidence interval covers a population parameter with a stated confidence, that is, a certain proportion of the time. Before trying to find all of the roots of this function in MATLAB I think it's worth understanding that it has infinitely many roots due to the inclusion of the $\cos()$ term. The testing framework uses the diagnostic when the compared values are outside of the allowable tolerance. The following is a sample program to understand finding solution of a non linear equation using Newton Raphson Method. Write a MATLAB program, in a script file, that determines the solution of the equation 8 - 4. So, the thickness dimension (X) with the tolerance zone of assembly would be: X = 72 ± 0. 5(x - sin x) = 0 by using the bisection method. MATLAB 2019 Overview MATLAB 2019 Technical Setup Details MATLAB 2019 Free Download MATLAB Deep Learning: With Machine Learning, Neural Networks and Artificial Intelligence by Phil Kim Get started with MATLAB for deep learning and AI with this in-depth primer. This MATLAB function specifies a numeric tolerance for the output signal specified by block_path and port_index, with the tolerance type specified by tolerance_type and value specified by tolerance_value. Function Handles in the MATLAB Programming documentation for more information. You can inspect the code of this function by executing the following command in the MATLAB Command Window: >> edit phase The tolerance used by the "phase" function is '3. The iterations of the method should stop/terminate when a certain tolerance/convergence level is achieved OR a maximum number of iterations are performed (whichever happens first). Newton's method: Matlab code In the next exercise, you will get down to the task of writing Newton's method as a function m-file. If the part has multiple configurations, click Configurations to change selected configurations. The initial search point, x0, has to be given by the user based upon the problem. Cube Root Algorithm in Matlab % p0 is the initial approximation to a zero of f % delta is the tolerance for p0 % epsilon is the tolerance for the function values. Inputs A and B must either be the same size or have sizes that are compatible (for example, A is an M-by-N matrix and B is a scalar or 1-by-N row vector). The shock response spectrum gives the peak response of each system with respect to the natural frequency. There is also a way to cover a fixed proportion of the population with a stated confidence. FUZZY tolerance relation matlab. This section describes the arithmetic operators' support for data types other than double. A function accepts one or more MATLAB variables as inputs, operates on them in some way, and then. Create Custom Tolerance. Intersect with tolerance idea I have been using a homegrown tool to find the indices to relate two arrays/sets for filing information, etc. Such an interval is called a tolerance interval. MATLAB 2019 Overview MATLAB 2019 Technical Setup Details MATLAB 2019 Free Download MATLAB Deep Learning: With Machine Learning, Neural Networks and Artificial Intelligence by Phil Kim Get started with MATLAB for deep learning and AI with this in-depth primer. • set tolerance value, etc. I was using the command intersect but it only gives me the numbers that are exactly the same. For example, fzero(@tan,1) returns 1. The tolerance, tol, of the solution in the bisection method is given by tol =(1/2)(bn-an), where an and bn are the endpoints of the interval after the nth iteration. If the relative tolerance is larger than 1e-3, then the initial absolute tolerance is set to 1e-6. It comes from a course I teach as part of an online Masters degr. Integration tolerances ode15s. Fault tolerance is the realization that we will always have faults (or the potential for faults) in our system and that we have to design the system in such a way that it will be tolerant of those faults. Find out why Close. Note If you have purchased the Optimization Toolbox, you can also use optimset to create an expanded options structure containing additional options specifically designed for the functions provided in that toolbox. The power method gives the largest eigenvalue as about 4. m file containing % the function whose root you are seeking, guess is the % initial guess of the root, and tolerance is how % accurately you want to know the answer % Note that the default value of tolerance is 1e-10. Newton's method: Matlab code In the next exercise, you will get down to the task of writing Newton's method as a function m-file. function approximateZero = newtonsMethod( fnc, x0, tol ) % implementation of Newton's Method for finding a zero of a function % requires a symbolic expression, a starting point, and a tolerance as input % produces either an input, which when substituted into the given expression, % yields an output with absolute value less than the specified. For example The default test wavelength is 632. For example, an engineer wants to know the range within which 99% of the future product will fall, with 98% confidence. That is, the system should compensate for the faults and continue to function. 5(x - sin x) = 0 by using the bisection method. If the simulation takes too long, you can increase (or loosen) the values of RelativeTolerance and AbsoluteTolerance at the cost of some accuracy. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (2. NET,, Python, C++, C, and more. If the relative tolerance is larger than 1e-3, then the initial absolute tolerance is set to 1e-6. x T Ax > 0 for all non-zero vectors x in R n), and real, and b is known as well. I have two vector with different lenght and I want to compare the values of the vectors one by one with a certain tolerance because the numbers are similar but not equal, e. How can I know the value I set is relative or absolute tolerance? How can I set a relative tolerance? since I don't know if the auto tolerance setting updates in 2017a onwards has affected fminsearch or not. Inputs A and B must either be the same size or have sizes that are compatible (for example, A is an M-by-N matrix and B is a scalar or 1-by-N row vector). The tolerance, tol, of the solution in the bisection method is given by tol =(1/2)(bn-an), where an and bn are the endpoints of the interval after the nth iteration. Its methods may be used on other types of systems subject to accumulated variation, such as mechanical and electrical systems. Bisection Method in MATLAB Code:. Approximation with tolerance = 0. This paper presents a new transformer model displaying hysteresis using the MATLAB (TM) Simulink environment. How to add tolerance to my code ? I think the reason is that I need to add a tolerance to the result of desired_line so Matlab can find it and add it to the. For details, see First Choose Problem-Based or Solver-Based Approach. The shock response spectrum gives the peak response of each system with respect to the natural frequency. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (2. 5, start with a vector of all 1's and use a relative tolerance of 1. This program for Regula Falsi method in MATLAB finds the root of the function f(x) = x 3 - 2x - 5 within the desired limit of accuracy as input by the user. - Mike Middleton, www. Though it is a very modern computer package, MATLAB's roots are still evident in the way that you interact with it. Generally, a tolerance is a threshold which, if crossed, stops the iterations of a solver. The example finds a root of the sin() function in the proximity of 4, which of course turns out to be 3. AbsoluteTolerance(tolVals) creates an absolute tolerance object that assesses the magnitude of the difference between the actual and expected values. The testing framework uses the diagnostic when the compared values are outside of the allowable tolerance. For two DNA sequences of the same length, the Hamming distance is the number of positions in which the nucleotides (letters) of one sequence differ from the other. Newton's method: Matlab code In the next exercise, you will get down to the task of writing Newton's method as a function m-file. Use the getDiagnosticFor method to implement this condition. So, fsolve sees a number it thinks is close to zero, and stops. Create Custom Tolerance. tolerance, and jitter transfer. What is "tolerance. Construction. Working Skip trial 1 month free. The default value (1e-3) means that the computed state is accurate to within 0. function approximateZero = newtonsMethod( fnc, x0, tol ) % implementation of Newton's Method for finding a zero of a function % requires a symbolic expression, a starting point, and a tolerance as input % produces either an input, which when substituted into the given expression, % yields an output with absolute value less than the specified. If the simulation takes too long, you can increase (or loosen) the values of RelativeTolerance and AbsoluteTolerance at the cost of some accuracy. For more information about this method please try this. The iterations of the method should stop/terminate when a certain tolerance/convergence level is achieved OR a maximum number of iterations are performed (whichever happens first). The manufacturer is 95% confident that 99% of all parts will have widths that are between 5 and 8 mm. And my code can not be calculated, because of error-warning: Warning: Failure at t=8. m to setup paths and compile MEX functions. Tolerance Interval Calculator. Optimization Toolbox™ solvers use tolerances to decide when to stop iterating and to measure solution quality. ; Uses object-oriented TestCase, TestSuite and TestResult classes, allowing for user-defined extensions. If the part has multiple configurations, click Configurations to change selected configurations. Simulink software resets the counter each time it detects nonconsecutive zero crossings (successive zero crossings that fail to meet the relative tolerance setting); therefore, decreasing the relative tolerance value may afford your model's behavior more time to recover. A function accepts one or more MATLAB variables as inputs, operates on them in some way, and then. I already reduced the tolerance on the numerical integrals inside the system of equations, which slightly improved the computation time. 1) We can use MATLAB's built-in dsolve(). Diagnostic object. It is likely to cover the specified or fixed proportion of the future population with a stated confidence. Use the getDiagnosticFor method to implement this condition. *exp(-u*25) by using both integral and vpaintegral. Your Assignment. Changing the way you enter a command, even subtly can completely change its meaning. In the Loss. Advantages of Secant Method over other Root Finding Methods: Its rate of convergence is more rapid than that of bisection method. The default value (1e-3) means that the computed state is accurate to within 0. This MATLAB function specifies a numeric tolerance for the output signal specified by block_path and port_index, with the tolerance type specified by tolerance_type and value specified by tolerance_value. Avec l'éditeur de MATLAB il est très simple et très rapide d'indenter proprement son code avec le raccourci : CTRL+A (sélection de tout le code) puis CTRL+I (indentation automatique). Programs will be introduced in Chapter 3. Taylor Series in MATLAB First, let's review our two main statements on Taylor polynomials with remainder. 273737e-13) at time t. As the simulation progresses, Simulink resets the absolute tolerance for each state to the maximum value that the state has assumed thus far times the relative tolerance for that state. Data Type single. tolerance, and jitter transfer. Approximation with tolerance = 0.


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# Distance Traveled Formula

Distance Traveled defines how much path an object has covered to reach its destination in a given period. The formula for distance travelled is given

$d=vt$

Where,

d = distance travelled

v = Velocity

t = time taken to travel

The distance-travelled formula can be applied to calculate the distance of driving a car or swimming laps in a pool. While driving a car, the distance will be calculated in miles or kilometres, the rate is in miles per hour or kilometres per hour, and time is in hours. While swimming laps in a pool, the distance will be calculated in laps.

Solved Examples

Question 1: A heavily loaded truck travels at a velocity of 60 miles per hour. Calculate the total time taken by the truck to travel a distance of 200 miles?

Given: Velocity = 60 miles per hour

Displacement d = 200 miles

we know,

displacement d = vt

The time taken is given by

t = d/v

= 200/60

t = 3.33 hours

format: plain


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## SPTK Addendum: Problems with resampling using MATLAB’s resample.m

Sometimes MATLAB’s resample.m gives results that can be trouble for subsequent CSP.

Previous SPTK Post: Echo Detection Next SPTK Post: TBD

In this brief Signal Processing Toolkit note, I warn you about relying on resample.m to increase the sampling rate of your data. It works fine a lot of the time, but when the signal has significant energy near the band edges, it does not.

## SPTK: Echo Detection and the Prisoner’s Dilemma

Let’s apply some of our Signal Processing ToolKit tools to a problem in forensic signal processing!

Previous SPTK Post: The Sampling Theorem Next SPTK Post: Resampling in MATLAB

No, not that prisoner’s dilemma. The dilemma of a prisoner that claims, steadfastly, innocence. Even in the face of strong evidence and a fair jury trial.

In this Signal Processing ToolKit cul-de-sac of a post, we’ll look into a signal-processing adventure involving a digital sting recording and a claim of evidence tampering. We’ll be able to use some of our SPTK tools to investigate a real-world data record that might, just might, have been tampered with. (But most probably not!)

Continue reading “SPTK: Echo Detection and the Prisoner’s Dilemma”

## SPTK: Sampling and The Sampling Theorem

The basics of how to convert a continuous-time signal into a discrete-time signal without losing information in the process. Plus, how the choice of sampling rate influences CSP.

Previous SPTK Post: Random Processes Next SPTK Post: Echo Detection

In this Signal Processing ToolKit post we take a close look at the basic sampling theorem used daily by signal-processing engineers. Application of the sampling theorem is a way to choose a sampling rate for converting an analog continuous-time signal to a digital discrete-time signal. The former is ubiquitous in the physical world–for example all the radio-frequency signals whizzing around in the air and through your body right now. The latter is ubiquitous in the computing-device world–for example all those digital-audio files on your Discman Itunes Ipod DVD Smartphone Cloud Neuralink Singularity.

So how are those physical real-world analog signals converted to convenient lists of finite-precision numbers that we can apply arithmetic to? For that’s all [digital or cyclostationary] signal processing is at bottom: arithmetic. You might know the basic rule-of-thumb for choosing a sampling rate: Make sure it is at least twice as big as the largest frequency component in the analog signal undergoing the sampling. But why, exactly, and what does ‘largest frequency component’ mean?

Continue reading “SPTK: Sampling and The Sampling Theorem”

## SPTK (and CSP): Random Processes

The merging of conventional probability theory with signal theory leads to random processes, also known as stochastic processes. The ideas involved with random processes are central to cyclostationary signal processing.

Previous SPTK Post: Examples of Random Variables Next SPTK Post: The Sampling Theorem

In this Signal Processing ToolKit post, I provide an introduction to the concept and use of random processes (also called stochastic processes). This is my perspective on random processes, so although I’ll introduce and use the conventional concepts of stationarity and ergodicity, I’ll end up focusing on the differences between stationary and cyclostationary random processes. The goal is to illustrate those differences with informative graphics and videos; to build intuition in the reader about how the cyclostationarity property comes about, and about how the property relates to the more abstract mathematical object of a random process on one hand and to the concrete data-centric signal on the other.

So … this is the first SPTK post that is also a CSP post.

Continue reading “SPTK (and CSP): Random Processes”

## SPTK: Examples of Random Variables in Communication-Signal Contexts

Some examples of random variables encountered in communication systems, channels, and mathematical models.

Previous SPTK Post: Random Variables Next SPTK Post: Random Processes

In this Signal Processing ToolKit post, we continue our exploration of random variables. Here we look at specific examples of random variables, which means that we focus on concrete well-defined cumulative distribution functions (CDFs) and probability density functions (PDFs). Along the way, we show how to use some of MATLAB’s many random-number generators, which are functions that produce one or more instances of a random variable with a specified PDF.

Continue reading “SPTK: Examples of Random Variables in Communication-Signal Contexts”

## SPTK: The Analytic Signal and Complex Envelope

In signal processing, and in CSP, we often have to convert real-valued data into complex-valued data and vice versa. Real-valued data is in the real world, but complex-valued data is easier to process due to the use of a substantially lower sampling rate.

Previous SPTK Post: The Moving-Average Filter    Next SPTK Post: Random Variables

In this Signal-Processing Toolkit post, we review the signal-processing steps needed to convert a real-valued sampled-data bandpass signal to a complex-valued sampled-data lowpass signal. The former can arise from sampling a signal that has been downconverted from its radio-frequency spectral band to a much lower intermediate-frequency spectral band. So we want to convert such data to complex samples at zero frequency (‘complex baseband’) so we can decimate them and thereby match the sample rate to the signal’s baseband bandwidth. Subsequent signal-processing algorithms (including CSP of course) can then operate on the relatively low-rate complex-envelope data, which is beneficial because the same number of seconds of data can be processed using fewer samples, and computational cost is determined by the number of samples, not the number of seconds.

Continue reading “SPTK: The Analytic Signal and Complex Envelope”

## SPTK: The Moving-Average Filter

A simple and useful example of a linear time-invariant system. Good for smoothing and discovering trends by averaging away noise.

Previous SPTK Post: Ideal Filters             Next SPTK Post: The Complex Envelope

We continue our basic signal-processing posts with one on the moving-average, or smoothing, filter. The moving-average filter is a linear time-invariant operation that is widely used to mitigate the effects of additive noise and other random disturbances from a presumably well-behaved signal. For example, a physical phenomenon may be producing a signal that increases monotonically over time, but our measurement of that signal is corrupted by noise, interference, or flaws in the measurement process. The moving-average filter can reveal the sought-after trend by suppressing the effects of the unwanted disturbances.

Continue reading “SPTK: The Moving-Average Filter”

## SPTK: Ideal Filters

Ideal filters have rectangular or unit-step-like transfer functions and so are not physical. But they permit much insight into the analysis and design of real-world linear systems.

We continue with our non-CSP signal-processing tool-kit series with this post on ideal filtering. Ideal filters are those filters with transfer functions that are rectangular, step-function-like, or combinations of rectangles and step functions.

## SPTK: Convolution and the Convolution Theorem

Convolution is an essential element in everyone’s signal-processing toolkit. We’ll look at it in detail in this post.

This installment of the Signal Processing Toolkit series of CSP Blog posts deals with the ubiquitous signal-processing operation known as convolution. We originally came across it in the context of linear time-invariant systems. In this post, we focus on the mechanics of computing convolutions and discuss their utility in signal processing and CSP.

Continue reading “SPTK: Convolution and the Convolution Theorem”

## SPTK: Interconnection of Linear Systems

Real-world signal-processing systems often combine multiple kinds of linear time-invariant systems. We look here at the general kinds of connections.

Previous Post: Frequency Response Next Post: Convolution

It is often the case that linear time invariant (or for discrete-time systems, linear shift invariant) systems are connected together in various ways, so that the output of one may be the input to another, or two or more systems may share the same input. In such cases we can often find an equivalent system impulse response that takes into account all the component systems. In this post we focus on the serial and parallel connections of LTI systems in both the time and frequency domains.

Continue reading “SPTK: Interconnection of Linear Systems”

## SPTK: Frequency Response of LTI Systems

The frequency response of a filter tells you how it scales each and every input sine-wave or spectral component.

We continue our progression of Signal-Processing ToolKit posts by looking at the frequency-domain behavior of linear time-invariant (LTI) systems. In the previous post, we established that the time-domain output of an LTI system is completely determined by the input and by the response of the system to an impulse input applied at time zero. This response is called the impulse response and is typically denoted by $h(t)$.

## SPTK: Linear Time-Invariant Systems

LTI systems, or filters, are everywhere in signal processing. They allow us to adjust the amplitudes and phases of spectral components of the input.

In this Signal Processing Toolkit post, we’ll take a first look at arguably the most important class of system models: linear time-invariant (LTI) systems.

What do signal processors and engineers mean by system? Most generally, a system is a rule or mapping that associates one or more input signals to one or more output signals. As we did with signals, we discuss here various useful dichotomies that break up the set of all systems into different subsets with important properties–important to mathematical analysis as well as to design and implementation. Then we’ll look at time-domain input/output relationships for linear systems. In a future post we’ll look at the properties of linear systems in the frequency domain.

## SPTK: The Fourier Series

A crucial tool for developing the temporal parameters of CSP.

This installment of the Signal Processing Toolkit shows how the Fourier series arises from a consideration of representing arbitrary signals as vectors in a signal space. We also provide several examples of Fourier series calculations, interpret the Fourier series, and discuss its relevance to cyclostationary signal processing.

## SPTK: Signal Representations

A signal can be written down in many ways. Some of them are more useful than others and can lead to great insights.

In this Signal Processing ToolKit post, we’ll look at the idea of signal representations. This is a branch of signal-processing mathematics that expresses one signal in terms of one or more signals drawn from a special set, such as the set of all sine waves, the set of harmonically related sine waves, a set of wavelets, a set of piecewise constant waveforms, etc.

Signal representations are a key component of understanding stationary-signal processing tools such as convolution and Fourier series and transforms. Since Fourier series and transforms are an integral part of CSP, signal representations are important for all our discussions at the CSP Blog.

## Signal Processing Toolkit: Signals

Introducing the SPTK on the CSP Blog. Basic signal-processing tools with discussions of their connections to and uses in CSP.

Next SPTK Post: Signal Representations

This is the inaugural post of a new series of posts I’m calling the Signal Processing Toolkit (SPTK).  The SPTK posts will cover relatively simple topics in signal processing that are useful in the practice of cyclostationary signal processing. So, they are not CSP posts, but CSP practitioners need to know this material to be successful in CSP. The CSP Blog is branching out! (But don’t worry, there are more CSP posts coming too.)


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# Yumminess has asked Jordon and Taylor to consider making Extra Attack Brownies and Nutty Attack B...

Yumminess has asked Jordon and Taylor to consider making Extra Attack Brownies and Nutty Attack Brownies, in addition to Chocolate Attack Brownies. The selling price to Yumminess would be $12 and$14.50 per tin, respectively, compared to the original $10 for Chocolate Attach Brownies. In addition to the current fixed common cost of$79,000, you have figured the additional costs to manufacture each new recipe. For 50,000 tins of Extra Attack Brownies, additional variable costs would be $75,000. For 20,000 tins of Nutty Attack Brownies, additional variable costs would be$100,000. Remember that the contribution margin for Chocolate Attack Brownies per tin is \$1.995.

Answer questions 1 and 2 as a sell now or process further scenario. Question 3 is sales mix with a weighted-average contribution margin.

1. What would be the incremental income/loss per tin for manufacturing Extra Attack Brownies? (If a net loss, use “( )” or “-“ in your answer.)

2. What would be the incremental income/loss per tin for manufacturing Nutty Attack Brownies? (If a net loss, use “( )” or “-“ in your answer.)

3. If Jordan and Taylor sold 100,000 tins of Chocolate Attach Brownies, 70,000 tines of Extra Attack Brownies, and 30,000 tins of Nutty Attack Brownies to Yumminess, what would be the weighted-average contribution margin per tin.


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Relevant drawbacks of the molecular structure and mechanism of the action of camptothecins are the instability of the E ring lactone and the reversibility of drug-target interaction. Such features are expected to limit the clinical efficacy of conventional camptothecins. In an attempt to overcome these limitations and to improve the pharmacological profile of camptothecins, a novel series of seven modified lipophilic analogues was synthesized based on the hypothesis that lipophilicity could promote a rapid cellular accumulation and stabilization of drug-target interaction. A novel analogue (ST1481) of the series, characterized by a potent antitopoisomerase and cytotoxic activity, was selected for preclinical development. A detailed preclinical study of ST1481 was performed in the H460 non-small cell lung tumor model using oral administration and various treatment schedules. Under all of the conditions, ST1481 exhibited an impressive efficacy in terms of tumor growth inhibition (tumor volume inhibition percentage > 99%), log10 cell kill, rate of complete responses (including “cures”), and an improvement of the therapeutic index compared with topotecan (used as the reference drug). The cytotoxic potency was also reflected by the in vivo potency, because the drug activity was observed at doses as low as 0.25 mg/kg with the daily schedule. In contrast to topotecan, no cross-resistance to ST1481 was found in ovarian carcinoma cells overexpressing P-glycoprotein (A2780/DX). A similar trend in the improvement of activity was also observed in the same tumor model growing in vivo with a 100% rate of complete tumor regressions. A rapid intestinal absorption and good oral bioavailability were supported by in vivo distribution studies, because the peak values of drug accumulation were found from 1 to 2 h after administration. The relevant liver accumulation may account for a marked effect of ST1481 against liver metastases induced by the ovarian carcinoma IGROV-1. In conclusion, the results support the hypothesis that a potent lipophilic camptothecin with a proper substituent at the position 7 may have therapeutic advantages likely related to a rapid intracellular uptake and tissue distribution, stabilization of the drug-target complex, and good oral bioavailability. Overall, the results support the preclinical interest of ST1481 in terms of efficacy, potency, toxicity profile, and ability to overcome multidrug resistance.

The antitumor activity of camptothecins has been ascribed to their ability to interfere with the catalytic cycle of DNA topoisomerase I and stabilize the covalent DNA-enzyme complex by inhibiting DNA religation (1). During DNA synthesis, the reversible drug-enzyme-DNA complex (ternary complex) causes arrest of the replication fork and formation of double-strand DNA breaks (2). Although replication-independent effects have been described (3), camptothecins are recognized as S phase-specific agents (4).

The primary limitations of camptothecins are the formation of a labile drug target complex and instability of the lactone ring. On the basis of the reversibility of the ternary complex and formation of lethal lesions during DNA replication (5), optimal cytotoxic effects are expected with prolonged exposure to the drug. The validity of such expectation has been supported by preclinical and clinical studies using schedules with prolonged treatment (6, 7) or with formulations such as liposomal or conjugated camptothecins that allow a slow drug release (8, 9). In an attempt to optimize drug efficacy, possible strategies may involve chemical modifications of molecular structure. Analogues endowed with increased ability to induce topoisomerase I-mediated DNA cleavage and/or more persistent stabilization of the ternary complex compared with conventional camptothecins may result in more cytotoxic and possibly more effective antitumor drugs. A common feature of natural camptothecins is the intrinsic instability of the α-hydroxylactone, which in physiological conditions gives the ring-opened carboxylate form (10). The preferential binding of the carboxylate form to HSA shifts the hydrolysis equilibrium toward the inactive carboxylate in plasma. Such behavior represents a major drawback of drug activity, because a small amount of lactone is expected in plasma at equilibrium.

Thus, possible modifications can be aimed at: (a) stabilizing the lactone form of camptothecins and/or reducing the affinity of the drug for albumin; and (b) favoring the rapid drug uptake and/or enhancing drug interaction with the intracellular target. The latter approach was preferred in our design of novel molecules, because the lactone ring instability is a common feature of all of the camptothecins. Indeed, rapid uptake, enhanced intracellular accumulation, and stabilization of the drug-target complex are expected to stabilize the active lactone form (11) and to result in a potent cytotoxic activity. On the basis of such rationale, a novel series of camptothecins substituted in position 7 with lipophilic chains has been developed (12, 13).

Using as the screening system the NCI-H460 lung carcinoma cell line characterized by overexpression of topoisomerase I, a new analogue of the series (ST1481) was selected as a promising candidate for additional investigation. The analogue is endowed with markedly increased cytotoxic activity compared with camptothecin and is more effective in stimulation of topoisomerase I-mediated DNA cleavage. The topoisomerase I-DNA-cleavable complexes formed in the presence of ST1481 are less reversible than those induced by conventional camptothecins (13). The aim of the study was to investigate relevant aspects of the pharmacological profile and therapeutic features of ST1481 in preclinical systems. Oral administration was used to assess in athymic nude mice bearing the NCI-H460 lung tumor: (a) the potency and efficacy of ST1481; (b) the TI of ST1481; and (c) the schedule dependency of antitumor activity. The results of antitumor efficacy studies, together with the ability to completely overcome MDR3 mediated by P-glycoprotein in in vivo models, indicate ST1481 as a promising compound for clinical development.

Drugs

The synthesis of ST1481 (7-t-butoxyiminomethylcamptothecin) has been already described (13). The drug was dissolved in DMSO and stored at −20°C until use. Immediately before treatment, the drug was additionally diluted in sterile, distilled water (DMSO 10% final concentration). TPT, kindly supplied by Smith-Kline Beecham Pharmaceuticals, was dissolved in sterile, distilled water. Drugs were administered by gavage in a volume of 10 ml/kg according to three schedules: q4dx4, qdx5/w for 5–10 weeks (see “Results”), and q8–10d for 10 times.

Cell Lines and Drug Sensitivity Studies

The human tumor cell lines used in the study included: the non-small cell lung carcinoma NCI-H460 cell line; the ovarian carcinoma A2780 and IGROV-1 cell lines and the doxorubicin-resistant A2780/DX and IGROV-1/DX1 sublines, characterized by P-glycoprotein-mediated MDR phenotype (14); the prostate carcinoma PC-3 cell line; and the breast carcinoma MCF-7 cell line. All of the cell lines were maintained as monolayer cultures in RPMI 1640 supplemented with 10% FCS.

Cellular sensitivity to drugs was assessed by the growth-inhibition assay. Briefly, cells in the logarithmic phase of growth were seeded in duplicate in six-well plates and, 24 h after seeding, were exposed to drug for 1 h. When the effects of HSA were studied, it was added to the medium just before exposure to the drug. HSA itself at the used concentrations (≤30 mg/ml) did not affect cell proliferation. Cells were then washed and incubated in drug-free medium for 72 h. Adherent cells were trypsinized and counted by using a cell counter (Coulter Electronics, Luton, United Kingdom). IC50 was defined as the concentration required for 50% cell growth inhibition compared with control cells.

Animals

All of the antitumor activity experiments were carried out using female athymic Swiss nude mice, 8–10 weeks old (Charles River, Calco, Italy). Mice were maintained in laminar flow rooms, keeping temperature and humidity constant. Mice had free access to food and water. Experiments were approved by the Ethics Committee for Animal Experimentation of the Istituto Nazionale Tumori of Milan. For drug distribution studies, 5–6 week-old female BALB/c mice (Charles River) were used.

Cellular Pharmacokinetic Studies

Cells were plated in six-well plates at a subconfluent density corresponding to 6 × 105 and 8 × 105 cells/well for PC-3 and MCF-7, respectively. Cells (3 wells/sample) were then washed with serum-free medium and exposed for 1 h to 10 μm of ST1481 or TPT dissolved in 1% DMSO. Treated cells were washed three times with PBS to remove the drug, and they were maintained in drug-free medium for 24 h. At different times, washed cells were incubated for 30 min with TE buffer [10 mm Tris-HCl (pH 7.5) and 1 mm EDTA] and 1% NP-40 (30 μl/well). Cell lysates were collected and frozen at −20°C.

The extraction of ST1481 was performed according to a modified method described by Koshkina et al.(15). Briefly, 700 μl of 0.1% acetic acid:acetonitrile (1:4), pH 4.5, were added to each sample and extracted with 4 ml of methylene chloride. The mixture was centrifuged at 4500 × g for 5 min, and the organic phase was dried under vacuum. Dried extracts were reconstituted in 150 μl of acetonitrile, and 50 μl was injected into the HPLC column (Licrosphere 100; RP-18; 5 μm; Merck). The mobile phase consisted of water:acetonitrile (1:1), and the flow rate was 1.5 ml/min.

The extraction of TPT was performed according to the method described previously (16). Briefly, 450 μl of methanol, cooled at −20°C, was added to each sample. After centrifugation at 10,000 rpm for 10 min at 4°C, 50 μl of the supernatant was injected into the HPLC column (Nova-Pack C18; 3.9 × 150 mm; Waters). The mobile phase consisted of 0.1 m acetic acid (pH 3.5) with triethylammine:acetonitrile (20:80), and the flow rate was 1 ml/min. Analyses were performed at room temperature using a BioSys HPLC (Model PP-510; Beckman Coulter) and a Fluorescence Detector (Model RF10AxL; Shimadzu) using an excitation wavelength of 370 nm and emission at 510 nm for detection. Known amounts of drug were added to untreated samples processed as described above to estimate the extraction efficiency of the methods. Efficiency was calculated as: (amount of the drug added/amount of the drug obtained by HPLC analysis) × 100.

Pharmacokinetic Analysis and Tissue Distribution of ST1481

Healthy athymic Swiss mice were treated p.o. with 5 mg/kg of ST1481. Plasma levels of the drug were determined as the total lactone forms by using an HPLC fluorimetric method. The HPLC system consisted of two Model PU-980 pumps (Jasco International Co. Ltd., Tokyo, Japan), a Model FP-920 fluorescence detector (Jasco International Co. Ltd.), and a Model AS-950 autosampler (Jasco International Co. Ltd.). For the determination of plasma levels of ST1481, 50 μl of plasma were diluted with 50 μl of 0.2 n HCl, then 10 μl of internal standard solution were added. After vortexing, samples were transferred into autosampler vials and injected. The method consisted of an on-line purification of plasma sample followed by isocratic elution chromatography. The sample purification was obtained with a BioTrap 500 C18 20 × 4.0 mm column (ChromTech Ltd., Congleton, United Kingdom). The HPLC mobile phase for purification was prepared by mixing 900 ml of water with 100 ml of acetonitrile. The chromatographic separation was obtained with a Luna 5 μm Phenyl-Hexyl 150 × 4.60 mm column (Phenomenex, Torrance, CA). The HPLC mobile phase for chromatographic separation was prepared by mixing 500 ml of water and 500 ml of acetonitrile. The column eluate was monitored by fluorescence with the excitation wavelength set at 370 nm and the emission wavelength set at 510 nm, a gain of 1000. Chromatographic data processing was performed with Borwin Ver. 1.2.6 software (Jasco International Co. Ltd.) working on a Pentium PC. Using 50 μl of plasma, the lower limit of quantification for ST1481 was 2.5 ng/ml. The pharmacokinetic parameters were obtained using a model-independent approach. The pharmacokinetic analysis was carried out using WinNonlin Professional Edition, version 1.5 software (Scientific Consulting Inc.).

For in vivo distribution experiments, exponentially growing M109 murine lung carcinoma cells (3 × 105 cells/mouse) were injected i.m. into the right hind leg muscle of female BALB/c mice. A single dose of ST1481 (1.2 mg/kg in 10% DMSO) was administered by the oral route on day 13 from tumor injection. At various times after treatment, 5 mice/group were sacrificed. Selected tissues were homogenized in 1 ml of 0.1% acetic acid:acetonitrile, (1:4, v/v), pH 4.5, and centrifuged at 16,000 rpm for 10 min. Supernatant fractions were extracted by adding 10 ml of methylene chloride and processed as described above for cellular pharmacokinetics studies.

Antitumor Activity Studies on s.c. Growing Tumors

The NCI-H460 human lung carcinoma and the A2780/DX human ovarian carcinoma were used. Exponentially growing tumor cells were injected s.c. (8–10 × 106 cells/flank) into nude athymic mice. The tumor line was maintained by serial s.c. passages of tumor fragments (∼2 × 2 × 6 mm) in healthy mice, as described previously (14).

Antitumor Efficacy Studies.

Experimental groups included four or five mice bearing bilateral s.c. tumors, if not otherwise indicated. Tumor fragments were implanted on day 0, and tumor growth was followed by biweekly measurements of tumor diameters with a Vernier caliper. TV was calculated according to the formula:

$$TV\ (mm^{3})\ {=}\ d^{2}\ {\times}\ D/2$$
, where d and D are the shortest and the longest diameters, respectively. Treatments started at different times after tumor injection, depending on the experimental design. For ethical reasons experimental groups were eliminated when the TV in the group was about 2000–3000 mm3.

The efficacy of the drug treatment was assessed as: (a) TVI % in treated versus control mice, calculated as TVI % = 100 − (mean TV treated/mean TV control × 100); (b) LCK calculated by the formula LCK = (T − C)/3.32 × DT, where T and C are the mean times (days) required for treated (T) and control (C) tumors, respectively, to reach 1000 mm3, and DT is the doubling time of control tumors (an LCK value >1 is indicative of an active compound); and (c) CR meaning no evidence of tumor lasting for ≥10 days [CRs at the end of the experiment (≥100 days) are considered “cures”].

The toxicity of the drug treatment was assessed as: (a) BWL calculated as BWL % = 100 − (mean BWdayx/mean BWday1x100), where day 1 is the first day of treatment and day x is any day after (maximum BWL % values are reported in the “Tables;” mice were weighed twice/week throughout the experimental frame); and (b) lethal toxicity, i.e., any death in treated groups occurring before any control death (mice were inspected daily for mortality).

For statistical analysis, Fisher’s exact test was used for comparison of CR rates.

Assessment of TI.

To evaluate the TI of the two drugs, a wide range of doses was tested according to the q4dx4 schedule on NCI-H460 tumor-bearing mice. TI was calculated by the formula TI = LD10/ED90, where LD10 is the dose causing 10% lethal toxicity and ED90 is the drug dose causing 90% TVI.

Activity Against Liver Metastases

The IGROV-1 human ovarian carcinoma was adapted to grow in mice as an i.p. model, where the tumor grows as diffuse carcinomatosis and ascites (17). Ascitic tumor cells were inoculated (106 cells in 0.5 ml of saline) in the spleen. Briefly, mice were anesthetized and the left flank opened. The spleen was carefully exposed, and tumor cells were injected under the spleen capsule via a 27-gauge needle. After cell injection (1 min), the spleen was removed, and the wound was closed (18). All of the mice developed liver tumor foci and ascites. Six days after surgery, drugs were given p.o. qdx5/wx4w. Control mice were treated with 10% DMSO. A few days after ascites onset, mice were sacrificed and livers removed and weighed. At day 80, all of the mice were sacrificed, including those without evidence of ascites.

Cellular Sensitivity Studies

Table 1 shows a comparison of sensitivity of the NCI-H460 cell line to ST1481 and to clinically relevant camptothecins after short-term exposure (1 h). The novel analogue was markedly more potent than camptothecin and TPT and substantially more potent than other molecules modified at the position 7 and containing a hydroxyl group at the position 10 (i.e., SN38 and ST1602). Thus, because an appreciable reduction of the antiproliferative effect by the presence of the 10-hydroxy group was evident, the ST1481 compound, lacking modifications in the A ring, was selected for additional development despite expected affinity for serum albumin (19). Indeed, the antiproliferative effect was reduced in the presence of 30 mg/ml of HSA. However, under such conditions, drug potency was still higher than that of TPT or SN-38 in the absence of albumin.

Activity Against NCI-H460 Human Lung Carcinoma Xenograft

The effects of oral ST1481 against the NCI-H460 human lung tumor xenografts were investigated with various schedules in comparison with oral TPT used as the reference drug.

Effect of Protracted Daily Treatment (qdx5/w).

The results of the antitumor activity studies with the qdx5/w schedule for several weeks are reported in Table 2 and Fig. 1 A. Treatment with the lowest tested dose of TPT (1.2 mg/kg) was effective in slowing tumor growth (LCK = 2.4) but did not achieve CR. In animals treated with 2 mg/kg of TPT, 4 of 10 tumors regressed ∼30 days from the start of treatment. Moreover, despite continuing drug delivery (≤10 weeks), the tumors started to regrow and all of the tumors were present at the end of the experiment (day 100). In mice treated with the low dose of ST1481 (0.25 mg/kg), 4 of 8 tumors completely regressed ∼15 days, but all of the tumors started to regrow by the end of the experiment. When a higher dose (0.5 mg/kg) was delivered, all of the tumors (8/8) disappeared by day 30, and 5 of 8 were cured at day 100 despite the shorter treatment duration compared with that of TPT (5 versus 10 weeks). The cumulative doses delivered were 100 and 12.5 mg/kg for TPT and ST1481, respectively. No significant toxicity was induced by the tested doses of the two drugs according to this schedule.

Effect of Every 8th-10th Day Treatment (q8–10d × 10 Times).

The results of the antitumor activity studies delivering the drugs by a very spaced schedule are reported in Table 2. Two dose levels of TPT were investigated: they were effective in reducing tumor growth (LCK values of 2.5 and 3.1 with 18 and 22 mg/kg, respectively) but not in achieving CR. Both doses were slightly toxic. In contrast, the two investigated doses of ST1481 (5 and 6 mg/kg) induced a very high rate of CR, most of which resulted in no evidence of disease at the end of the experiment (day 100). As a consequence, LCK values were much higher than in TPT-treated tumors. The marked differences in antitumor activity between the two drugs are clearly documented by the growth curves (Fig. 1 B).

Effect of Every 4th Day Treatment (q4dx4).

With the q4dx4 schedule, four dose levels of TPT were investigated, and a clear dose-dependent antitumor effect was observed in terms of TVI % and LCK values (Table 3). Tumor growth was stopped (≤20 days) by the highest tolerated dose, i.e., 15 mg/kg (total dose, 60 mg/kg), but no CR was achieved. The dose of 18 mg/kg was highly toxic. The analogue ST1481 induced CR in 5 of 8 tumors at a well-tolerated dose (2 mg/kg) and in all of the surviving animals at a higher toxic level (2/5 toxic deaths among mice treated with 4 mg/kg).

Assessment of TI.

To better define the potential advantages in the therapeutic profile of ST1481, the relation between drug tolerability and efficacy was evaluated in NCI-H460 tumor-bearing mice. The MTDs of TPT and ST1481 delivered p.o. according to the q4dx4 schedule were deduced by observations of lethal toxicity in several independent experiments. Pooling together these observations the MTDs (roughly corresponding to the LD10) were 3 mg/kg for ST1481 (4 dead in 52 treated mice) and 15 mg/kg for TPT (6 dead in 173 treated mice), thus indicating that the novel analogue is ∼5-fold more potent than TPT. The MTD was confirmed also in nontumor-bearing mice (data not shown). When we calculated the TI for each drug as LD10:ED90 (dose inducing 90% TVI %, see Table 3), a favorable profile of tolerability at effective doses was found for the novel analogue, because the TI was 3 for ST1481 (i.e., 3/1) and 1.7 for TPT (i.e., 15/9).

Activity Against Doxorubicin-resistant Human Ovarian Carcinoma Models

To examine the ability of ST1481 to overcome drug resistance in tumor cells with the MDR phenotype, we used human ovarian carcinoma variants selected for resistance to doxorubicin. Both sublines displayed a pronounced resistance to the selecting agent (Table 4) and were characterized by a typical MDR phenotype. A marked cross-resistance to TPT was observed only in IGROV-1/DX. The higher degree of resistance of IGROV-1/DX cells was likely related to an increased level of P-glycoprotein expression as compared with A2780/DX. BCRP expression was not detected in these cell systems. In both cell systems, no cross-resistance to ST1481 was observed. The lack of influence of P-glycoprotein expression on tumor response to ST1481 was confirmed in the A2780/DX tumor xenografts. In this model all of the tumors (8/8) completely regressed under treatment with the MTD (3 mg/kg; q4dx4 schedule) of the novel camptothecin. TPT, in the same experimental conditions, was significantly less effective against the tumor (2/10 CR).

Activity Against Liver Metastases

The high efficacy exhibited by ST1481 delivered by the oral route suggested the potential therapeutic interest of the novel analogue in the treatment of liver metastases. The study was performed with the ovarian carcinoma IGROV-1 model characterized by low level of expression of P-glycoprotein and only moderate responsiveness to agents recognized by this transport-system (e.g., Taxol® and doxorubicin; Ref. 14). Mice developed lethal ascites because of liver invasion by tumor with formation of multiple foci. A daily oral treatment with TPT or ST1481 strongly influenced the onset of ascites as a consequence of a substantial reduction in liver tumor burden. The effect was more marked in ST1481-treated mice, because only 1/5 mice presented visible liver foci at the end of the experiment (day 80). The pattern was reflected by marked differences in liver weight of treated animals (Table 5).

Cellular Accumulation Studies

Cellular drug contents were determined in MCF-7 breast carcinoma cells and in PC-3 prostate carcinoma cells after 1-h exposure to equimolar concentrations of each drug (10 μm). The drug concentration was used because it allowed a reproducible determination of cellular drug content under our conditions. The results presented in Table 6 indicated a markedly (20-fold) higher intracellular accumulation of ST1481 than TPT, suggesting a rapid drug uptake. In addition, after a 24-h incubation in drug-free medium, the intracellular content of ST1481 was still higher than that found immediately after a 1-h exposure to TPT.

Tissue Distribution and Pharmacokinetic Analysis

The cellular behavior was consistent with the in vivo distribution of the drug (Fig. 2). Again, a rapid tissue distribution was found in all of the examined organs. The extent of drug content in these tissues was clearly related to the route of administration. Indeed, the highest concentration found in the liver was expected after oral administration. The drug levels achieved in 1 h were persistent for ≥4 h. A relevant observation of this study was the appreciable amount of drug found in the central nervous system.

The pharmacokinetic analysis of ST1481 in plasma was assessed after oral administration of 5 mg/kg (Table 7). For purpose of comparison, the results achieved by TPT administered p.o. at the dose of 15 mg/kg are also reported (16). Both agents reached the maximum plasma concentrations within 1 h after administration. Despite a lower dose, ST1481 reached a substantially higher plasma concentration, thus suggesting a good bioavailability. An additional advantage of ST1481 was the long persistence as documented by area under the curve and t½ values.

Whereas previous chemical efforts to exploit substitutions at the C-7 position focused on development of water-soluble derivatives of camptothecin, recent studies have suggested pharmacological interest of lipophilic camptothecins (20, 21). Among a series of 7 substituted camptothecins, the novel lipophilic analogue ST1481 was selected for preclinical development on the basis of promising features at cellular and molecular levels, including potent inhibition of topoisomerase I, persistence of DNA cleavage (13), and rapid cellular uptake of the drug. It is likely that the cytotoxic potency exhibited by ST1481 is the result of the combination of these features rather than of the stability of the active lactone form, although lipophilicity is expected to improve the stability profile (19). The present study provides evidence that such features are also reflected by a promising pharmacological profile and therapeutic behavior.

Indeed, ST1481 retained a strong potency and a superior antitumor efficacy in terms of tumor growth inhibition and rate of complete response against the NCI-H460 tumor xenograft. ST1481 was ∼5-fold more potent than TPT when delivered by intermittent treatment schedules (every 4–8 days), whereas with the daily schedule a marked activity was observed at doses as low as 0.25 mg/kg/day and cumulative doses in the range of 6–12 mg/kg, i.e., ∼10 times lower than those of TPT.

The marked potency and outstanding efficacy of ST1481 were observed with all of the tested schedules; however, as expected for camptothecins, the best schedule was the daily prolonged treatment, which produced CR in all of the treated animals with a high rate of long-term disease-free survivors. A comparable therapeutic effect was achieved with an intermittent treatment schedule (every 8–10 days) using higher dose levels. The latter schedule was substantially less effective for TPT, because no CR was achieved by the drug under such conditions.

Favorable pharmacokinetic and pharmacodynamic properties have been described for camptothecins in mice compared with humans, and they are possibly responsible for the discrepancies in antitumor efficacy between the two species (22). Considering that camptothecins are more myelosuppressive in humans than in mice (23), an improvement of the TI in mice may represent a promising feature for the therapeutic use in humans. ST1481 exhibited an improvement of the TI as compared with TPT, because it exhibited a marked efficacy (TVI % ≥ 90) in a wide range of tolerated doses and with different schedules. Moreover, in contrast to the strong increase in cytotoxic potency of ST1481 versus TPT in tumor cells (Table 1), the two compounds exhibited comparable IC50 values in human bone marrow progenitor cells in vitro (data not shown).4

The enhanced lipophilicity of ST1481 compared with TPT, resulted in a more efficient drug uptake by tumor cells and in a favorable tissue distribution, with particular reference to the ability to cross the blood-brain barrier, as supported by in vivo distribution studies. The ability may represent a favorable feature for the treatment of central nervous system tumors, as already documented in preclinical models of glioma with the use of silatecans, a novel series of lipophilic camptothecins (24). Despite the expected lactone hydrolysis and drug interaction with serum albumin, ST1481 in the presence of HSA retained a marked cytotoxic activity higher than that of TPT and SN-38 in the absence of albumin. The reduction of cytotoxic potency was apparently less marked than that reported for other lipophilic camptothecins (19).

It is likely that the cytotoxic potency of ST1481 is the result of a combination of multiple factors, including a potent topoisomerase I inhibitory activity, stability of DNA-topoisomerase I cleavable complexes, and lipophilicity, resulting in enhanced drug uptake and lactone stability. The cytotoxic potency may be a critical requirement for in vivo drug efficacy, because a substantial reduction in the amount of the active lactone form in human plasma is conceivable even for camptothecins with an improved stability profile (19, 25).

An additional therapeutic advantage of ST1481 is a complete lack of recognition by transport systems involved in the typical MDR phenotype. Overexpression of P-glycoprotein plays a variable role in sensitivity to camptothecins. Indeed, a number of well-known camptothecins (TPT, 9-amino-camptothecin, and CPT11/SN38) shows a partial cross-resistance in P-glycoprotein-mediated drug resistance (26, 27). In contrast, the cytotoxic activity of ST1481 was not influenced by P-glycoprotein in ovarian carcinoma cells, which overexpress the MDR-1 gene, and the feature was also reflected by the impressive responsiveness of A2780/DX tumor growing s.c. and of liver metastases produced by the P-glycoprotein-positive IGROV-1 tumor. These resistant cell sublines did not express detectable levels of BCRP that is important in the transport of TPT and SN38 (28). We have recently found that the novel camptothecin ST1481 is able to overcome cellular resistance in the mitoxantrone-selected cell line characterized by high level of BCRP expression (29). The lack of recognition by BCRP is consistent with the oral efficacy, because this transport system is likely implicated in the regulation of intestinal absorption of camptothecins.

The in vivo study was performed using the oral route of administration, which has been reported as favorable for TPT in human tumor xenografts (16) as well as in clinical studies (30). A formulation suitable for i.v. injection is being developed and should allow a comparative pharmacokinetic analysis after i.v. or oral administration. Additionally, the antitumor efficacy observed for ST1481 at low dose levels (≪1 mg/kg) and pharmacokinetic analysis suggest a good oral bioavailability. The oral administration should be regarded as an advantage rather than as a limitation for the clinical use of camptothecins, because the optimal activity of this class of drugs can be achieved by multiple daily doses, which ensure a prolonged exposure time (31, 32). An outstanding efficacy of ST1481 against liver metastases produced by the IGROV-1 ovarian carcinoma suggests an additional advantage of the oral treatment, because intestinal absorption could ensure a high drug concentration in the liver, which is a common site of metastatic involvement for several tumor types.

In conclusion, the preclinical profile of ST1481 compares favorably with known camptothecins; indeed, the 7-modified analogue exhibited an impressive antitumor efficacy in preclinical models of human tumors, as documented by its striking curative potential. The comparison of antitumor effects of ST1481 and TPT clearly evidenced a superior antitumor activity of the novel analogue, because a high rate of complete tumor regressions was observed. In particular, the pharmacological interest in ST1481 is related to its ability to overcome drug resistance mediated by P-glycoprotein, to an improved TI, and to obvious advantages related to drug potency, thereby allowing the oral delivery of substantially lower doses than those required for TPT. On the basis of this preclinical efficacy profile, ST1481 is a promising candidate for clinical evaluation.

Fig. 1.

Effects on tumor growth of TPT and ST1481 delivered p.o. (from day 3) against the NCI-H460 non-small cell lung carcinoma. A, treatment schedule qdx5/w administrations: TPT, 1.2 (□) and 2 (▪) mg/kg × 10 weeks; ST1481, 0.25 (○) and 0.5 (•) mg/kg × 5 weeks. B, treatment schedule q8–10dx10 administrations: TPT, 18 (□) and 22 (▪) mg/kg; ST1481, 5 (○) and 6 (•) mg/kg.

Fig. 1.

Effects on tumor growth of TPT and ST1481 delivered p.o. (from day 3) against the NCI-H460 non-small cell lung carcinoma. A, treatment schedule qdx5/w administrations: TPT, 1.2 (□) and 2 (▪) mg/kg × 10 weeks; ST1481, 0.25 (○) and 0.5 (•) mg/kg × 5 weeks. B, treatment schedule q8–10dx10 administrations: TPT, 18 (□) and 22 (▪) mg/kg; ST1481, 5 (○) and 6 (•) mg/kg.

Close modal
Fig. 2.

Tissue level of ST1481 after a single oral administration (1.2 mg/kg) in M109 tumor-bearing BALB/c mice. Values refers to the mean of drug content in tissues from five animals; bars, ± SD.

Fig. 2.

Tissue level of ST1481 after a single oral administration (1.2 mg/kg) in M109 tumor-bearing BALB/c mice. Values refers to the mean of drug content in tissues from five animals; bars, ± SD.

Close modal

The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

1

Supported in part by the Ministero della Sanita’ (Rome), the Consiglio Nazionale delle Ricerche (Rome), and the Associazione Italiana Ricerca sul Cancro (Milan), Italy.

3

The abbreviations used are: q4dx4, every 4th day for 4 times; qdx5/w, daily for 5 days/week; q8–10d, every 8th-10th day; TVI %, tumor volume inhibition percentage; MDR, multidrug-resistance; HSA, human serum albumin; HPLC, high-performance liquid chromatography; TPT, topotecan; TV, tumor volume; LCK, log10 cell kill; CR, complete regression; BWL, body weight loss; TI, therapeutic index; MTD, maximum tolerated dose; BCRP, breast cancer resistance protein.

4

Investigator brochure.

Table 1

Cellular sensitivity of non-small-cell lung carcinoma H460 cell line to camptothecins and influence of HSA

Table 2

Effects of ST1481 and TPT, delivered orally (for day 3), using daily or intermittent schedule on the NCI-H460 human tumor xenograft

DrugScheduleDose (mg/kg)CR at dayaLCKb (1000 mm3)Maximum BWLc %Lethal toxicityd (day)
SingleTotal153060100
TPT qdx5/wx10w 1.2 60 0/8 0/8 0/8 NDe 2.4 0/4
100 0/10 4/10 2/10 0/10 6.0 0/5
q8-10dx10 18 180 0/8 0/6 0/6 NDe 2.5 1/4 (24)
22 220 0/10 0/8 0/8 NDe 3.1 14 1/5 (27)
ST1481 qdx5/wx5w 0.25 6.25 4/8 4/8 2/8 NDe 4.0 0/4
0.5 12.5 7/8 8/8 6/8 5/8 6.3 0/4
q8-10dx10 50 0/8 4/8 5/8 5/8 8.6 0/4
60 0/10 6/10 7/10 4/8 7.9 1/5 (61)
DrugScheduleDose (mg/kg)CR at dayaLCKb (1000 mm3)Maximum BWLc %Lethal toxicityd (day)
SingleTotal153060100
TPT qdx5/wx10w 1.2 60 0/8 0/8 0/8 NDe 2.4 0/4
100 0/10 4/10 2/10 0/10 6.0 0/5
q8-10dx10 18 180 0/8 0/6 0/6 NDe 2.5 1/4 (24)
22 220 0/10 0/8 0/8 NDe 3.1 14 1/5 (27)
ST1481 qdx5/wx5w 0.25 6.25 4/8 4/8 2/8 NDe 4.0 0/4
0.5 12.5 7/8 8/8 6/8 5/8 6.3 0/4
q8-10dx10 50 0/8 4/8 5/8 5/8 8.6 0/4
60 0/10 6/10 7/10 4/8 7.9 1/5 (61)
a

CR, no. of completely regressed tumors/total no. of tumors. Days are calculated from the day of tumor implantation.

b

See “Materials and Methods” for LCK formula.

c

Maximum BWL % after drug treatment.

d

No. of mice dead for toxicity/total no. of mice. Days are calculated from the day of tumor implantation.

e

ND, not determined. Mice were eliminated by this time because of tumor burden.

Table 3

Effects of ST1481 and TPT, delivered orally q4dx4 times (days 3, 7, 11, and 15), on the NCI-H460 human tumor xenograft

DrugDose/injection (mg/kg)TVI %a (day 21)CRb (day 25)LCKc (1000 mm3)Maximum BWLd %Lethal toxicitye (day)
SingleTotal
TPT 20 80 0/8 1.3 0/4
36 91 0/8 1.7 0/4
15 60 98 0/8 2.1 0/4
18 72 NDf NDf NDf 23 4/5 (18, 18, 19, 20)
ST14781 90 0/8 1.4 0/4
99 5/8 2.4 0/4
16 100 8/8 2.5 23 2/5 (17, 31)
DrugDose/injection (mg/kg)TVI %a (day 21)CRb (day 25)LCKc (1000 mm3)Maximum BWLd %Lethal toxicitye (day)
SingleTotal
TPT 20 80 0/8 1.3 0/4
36 91 0/8 1.7 0/4
15 60 98 0/8 2.1 0/4
18 72 NDf NDf NDf 23 4/5 (18, 18, 19, 20)
ST14781 90 0/8 1.4 0/4
99 5/8 2.4 0/4
16 100 8/8 2.5 23 2/5 (17, 31)
a

TVI % in treated versus control mice.

b

CR, no. of completely regressed tumors/total no. of tumors in surviving animals at the indicated day. Days are calculated from the day of tumor implantation.

c

See “Materials and Methods” for LCK formula.

d

Maximum BWL % because of the drug treatment.

e

Days of death in parentheses.

f

ND, not determined.

Table 4

Cellular sensitivity of ovarian carcinoma cell lines with MDR phenotype to camptothecinsa

IC50 (μg/ml)RIbIC50 (μg/ml)RIb
A2780A2780/DXIGROV-1IGROV-1/DX
TPT 0.14 ± 0.04 0.21 ± 0.1 1.5 0.30 ± 0.05 8.15 ± 2.6 27
ST1481 0.015 ± 0.002 0.013 ± 0.01 0.9 0.017 ± 0.008 0.018 ± 0.002
Doxorubicin 0.24 ± 0.12 2.3 ± 1.8 10 0.39 ± 0.06 8.8 ± 1.6 22
IC50 (μg/ml)RIbIC50 (μg/ml)RIb
A2780A2780/DXIGROV-1IGROV-1/DX
TPT 0.14 ± 0.04 0.21 ± 0.1 1.5 0.30 ± 0.05 8.15 ± 2.6 27
ST1481 0.015 ± 0.002 0.013 ± 0.01 0.9 0.017 ± 0.008 0.018 ± 0.002
Doxorubicin 0.24 ± 0.12 2.3 ± 1.8 10 0.39 ± 0.06 8.8 ± 1.6 22
a

Assessed by growth inhibition assay after 1 h of drug exposure. Values are the mean (±SD) of at least three experiments.

b

RI, resistant index: ratio between the IC50 values of the resistant and parental cell lines.

Table 5

Effects of ST1481, 0.5 mg/kg, and TPT, 2 mg/kg, (oral administration, from day 6, qdx5/wx4w) on experimental liver metastases of the human ovarian tumor IGROV-1

DrugMedian day of ascites onsetaDay of evaluationbNo. of mice with metastases/totalLiver weight (g)
Mean ± SDMedianRange
Solvent 20 24 8/8 3.7 ± 1.6 3.4 1.6–7.1
TPT 76 80 3/5 2.1 ± 1 2.5 1.2–3.9
ST1481 >80 80 1/5 1.8 ± 0.6 1.5 1.4–2.9
DrugMedian day of ascites onsetaDay of evaluationbNo. of mice with metastases/totalLiver weight (g)
Mean ± SDMedianRange
Solvent 20 24 8/8 3.7 ± 1.6 3.4 1.6–7.1
TPT 76 80 3/5 2.1 ± 1 2.5 1.2–3.9
ST1481 >80 80 1/5 1.8 ± 0.6 1.5 1.4–2.9
a

Mice develop ascites as a consequence of tumor growth in the liver. Mice with no evidence of ascites at the end of the experiment are indicated as >80.

b

Time at which mice are sacrificed for liver inspection.

Table 6

Intracellular content of ST1481 and TPT in PC-3 and MCF-7 human tumor cellsa

Cell lineTime (h)ng/mg proteinb
ST1481TPT
Prostate cancer PC-3 52 ± 4 2.6 ± 0.1
3.7 ± 0.3 0.3 ± 0.02
24 4.1 ± 0.2 0.2 ± 0.03
Breast cancer MCF-7 28 ± 1 1.4 ± 0.06
2.6 ± 0.3 0.3 ± 0.07
24 1.5 ± 0.1 0.3 ± 0.04
Cell lineTime (h)ng/mg proteinb
ST1481TPT
Prostate cancer PC-3 52 ± 4 2.6 ± 0.1
3.7 ± 0.3 0.3 ± 0.02
24 4.1 ± 0.2 0.2 ± 0.03
Breast cancer MCF-7 28 ± 1 1.4 ± 0.06
2.6 ± 0.3 0.3 ± 0.07
24 1.5 ± 0.1 0.3 ± 0.04
a

Intracellular drug content was determined after 1 h exposure to 10 μm drug. Drug content at 6 and 24 h refers to the amount of drug retained by the cell after removal of extracellular drug.

b

The values are expressed as mean ± SE of three independent experiments.

Table 7

Pharmacokinetic parameters of ST1481 and TPT obtained after oral administration of therapeutic doses

DrugDose (mg/kg)C maxa (ng/ml)AUC0-infbt1/2c (h)
TPT 15 118.91 ± 30.64 552.29 2.77
ST1481 307.46 ± 69.79 2458.66 11.8
DrugDose (mg/kg)C maxa (ng/ml)AUC0-infbt1/2c (h)
TPT 15 118.91 ± 30.64 552.29 2.77
ST1481 307.46 ± 69.79 2458.66 11.8
a

Maximal plasma concentration. Mean ± SD from three mice.

b

Area under the concentration-time curve from 0 to infinity.

c

Apparent terminal half-life.

We thank Loredana Cleris for technical assistance and Laura Zanesi and Elena Morittu for editorial assistance.

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