Wave2500™ is a stand-alone computer software program for computational ultrasonics for problems that are 3D-axisymmetric -- in cylindrical coordinates. It was produced to bring numerical simulation to the ultrasound engineering community. This page provides some basic information about Wave2500™ including a general Program Overview, Hardware/Software/Memory Requirements, and a brief description of the Wave Equation that is being simulated.

Program Overview

Wave2500™ is a stand-alone software package for computational ultrasonics. It operates by solving the three-dimensional (3D) acoustic (viscoelastic) axisymmetric wave equation based on a method of finite differences. The solution is computationally intensive. However, thanks to the ever increasing power and speed of computer hardware, it is now possible to bring such software packages to the desktop and personal computer of the ultrasound engineer and researcher.

Wave2500™ allows the user to compute the full viscoelastic wave solution (both longitudinal and shear displacements) in an arbitrary three-dimensional (3D) object that is axisymmetric (that is, does not have any changes in materials as a function of the angle phi around the axis, when the radius, r, and height, z, are constant), subjected to user-specified acoustic sources (which themselves must also be axisymmetric; that is either circular disks or annuli). The program, besides simulating the complete spatial and time-dependent acoustic solution, allows the user to simulate ultrasound measurements in a variety of source and receiver configurations. Wave2500™ will prove useful to researchers and applications engineers in such diverse fields as non-destructive testing, materials evaluation, medical imaging and biological tissue characterization. The software is useful also in basic mechanistic studies and for academic applications. With Wave2500™ the user can compute solutions (e.g., scattered and reflected waveforms) to virtually an unlimited variety of distinct physical problems without ever leaving the computer keyboard.

Wave2500™ provides solutions to a broad range of 3D axisymmetric ultrasound problems. The program allows the user to specify an arbitrary object which is ultrasonically interrogated. The object is specified in a "PCX" (2D) image file. The objects are by definition cylindrical (or annular); however owing to the assumed axisymmetric property, a 2D image is sufficient to describe the entire 3D object; that is, any cross-section through the cylinder axis -- as represented by a 2D image file -- is sufficient to describe the object. Thus, for those users already familiar with Wave2000® (our 2D ultrasound simulation software), the similarity of the two programs will be apparent in terms of the 2D image representing the object; however, the equations for Wave2500™ ensure that the simulated data obtained will actually represent propagation of ultrasound in the 3D (cylindrical and axisymmetric) object.

"PCX" is a "tried-and true" graphics file format which includes within it absolute size information, a useful feature for the ultrasound simulations. The image data or object is composed of individual pixels which can have 1 of 256 gray levels (0-255). Each pixel value represents a physical material (e.g., water, steel, etc.) that is set by the user. Gray level 255 is reserved by Wave2500™ to denote void (i.e., vacuum). There is thus a vast variety of 3D axisymmetric structures in which ultrasound propagation can be simulated using Wave2500™.

The 2D object or image representing the cross-section of the 3D object to be simulated can be generated either internally using Wave2500 "Geometry" routines or externally using any graphics program (commercial or "in-house") which can output files in 8 bit monochrome "PCX" format. Additionally, the image may be obtained from various scan modalities, for example CT or MRI slice data, which has been converted to "PCX" format. Usually, a segmentation algorithm of some kind would be necessary to properly associate various regions of the image with a particular material (i.e., grey level).

The attractiveness of Wave2500™ is that it is very easy to generate solutions to a wide variety of 3D axisymmetric ultrasound problems within a simple graphical interface. The user has access to features designed to mimic reasonably closely many practical situations. For example, there are source and receiver configurations that the ultrasound engineer will notice are similar to real ultrasound experimental configurations, for example the use of signals that characterize many transducer generated waveforms. As one application, Wave2500™ may be useful for analyzing ultrasound propagation in cladded rods (e.g., a plastic rod surrounded by an aluminum sheath). In addition, the software could be used to explore the use of circumferential transducer sources (i.e., sources which wrap around a rod).

Wave2500™ has the potential to generate new insights and approaches to many problems in ultrasonics. For the first time, the user has the capability to "experiment" to his or her heart's content, without turning on a pulser-receiver or connecting a "BNC" cable. Indeed, the simulations can "run" while the user is word processing a document or analyzing data from an earlier simulation. The computer can work "around the clock" (for example, by using the "Multi-batch feature") computing solutions to problems that are difficult to perform in the laboratory or the field, but the results of the simulations can provide important understanding and knowledge for future experiments or for data already collected.

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Hardware, Software and Memory Requirements

Wave2500™ is designed to run on any PC that has the Windows XP, Vista, 7 or 8 operating systems installed. Minimum hardware requirements are extremely modest (for example 15 megabytes free hard disk space and 128 megabytes memory), although we recommend 1 GB or more memory for handling the larger simulation models. (Detailed information on memory requirements can be found in the 'Algorithm' topic of the Wave2500™ User Guide Section of the Help file.) Minimum graphics requirements are 256 color VGA and a compatible mouse, but of course most systems will have hardware characteristics much higher than these minimums. As noted, Wave2500™ operates best with as much RAM memory as possible, which allows problems of increasingly larger size to be accommodated and avoids the need for virtual (disk) memory to be used. Note also that Wave2500™ supports multiprocessor systems, that allows the program to potentially speed-up the execution of the program. This is most effective for "large" objects; experimentation by the user will determine when multiprocessors can lead to faster execution times. The multiprocessors can be either actual multiproccessor systems, or multicore processors, or both.

Wave2500™ is a "memory-hungry" program; this is simply the nature of the acoustic problem which is being simulated. To aid the user in assessing the memory requirements for a particular simulation model, we can provide the following approximate relationships.

Because of the axisymmetric nature of the problem, the memory requirements can be computed based on the "size" of the 2D cross-section, as follows: The simplest approach for approximating memory needed is to multiply the number of finite difference grid elements, N, by 30; this is the amount of memory required in bytes (plus some additional "fixed" program overhead which can usually be neglected in comparison to the 30 x N quantity). As an example, if an object image cross-section is 3 cm x 4 cm and the pixel resolution ("Pixels/mm") is 10 pixels/mm, the number of pixels in this image will be 300 x 400 = 120,000 pixels. Now if we assume that the finite difference grid elements generated by Wave2500™ are coincident with the number of image pixels (i.e., Grid/Pixel = 1), then the memory required is 30 x N = 30 x 120,000 = 3.4 megabytes.

Another perspective on memory requirements can be gained by determining the memory needed as a function of object (cross-section) size in terms of wavelengths. In the example above, it was assumed the the grid size was coincident with object image pixel size, i.e., both were 0.1 mm square (10 pixels/mm). For the case of a problem in which the minimum wavelength is about 1 mm, this 0.1 mm size for the finite difference grid element should provide a reasonably accurate solution. We may extend this reasoning for a more generic assessment of memory requirements as follows. Assuming that we would like to have a grid element dimension 10 times less than the minimum wavelength, then that implies that 100 x 30 = 3000 bytes for a square object 1 wavelength on a side. If one has a square object which is 10 wavelengths on a side, then using the same relative grid dimensions, Wave2500™ would require about 10,000 x 30 = 293 kilobytes of memory. One may also extend this approximation to any number of (minimum) wavelengths to evaluate memory requirements. Assuming a rectangular object Q wavelengths by R wavelengths in overall dimensions, and again assuming 10 grid elements per wavelength, then the memory required for this model is approximately 30 x 100 x Q x R = 2.93 Q x R kilobytes. It is useful to also point out that the minimum wavelength is inversely proportional to the frequency of the source waveform. Therefore, if a simulation with a 1 MHz source waveform requires 1 megabyte of memory, then changing to a source waveform operating at 2 MHz will generally require four times as much memory, or in this case 4 megabytes, to be used. (This assumes that the same size object is used in both cases.) Thus the user may want to carry out as many of his or her simulations as possible with relatively low frequency sources, in order to reduce computational overhead.

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Wave Equation

The specific viscoelastic wave equation that is simulated in a Wave2500™ simulation is given by:

rho {d^2 ur / dt^2} = (lambda + (phi-2/3 eta) d/dt + 2 mu + 2 eta d/dt) d/dr {(1/r) d/dr(rur)} + (mu + eta d/dt) d^2 ur/dz^2 + (lambda + (phi-2/3 eta) d/dt) + mu + eta d/dt) d^2uz/dzdr

rho {d^2 uz / dt^2} = (lambda + (phi-2/3 eta) d/dt + mu + eta d/dt) (1/r) d/dr {dur/dz)} + (lambda + (phi-2/3 eta) d/dt + 2 mu + 2 eta d/dt) d^2 uz/dz^2 + (mu + eta d/dt)(1/r) d/dr (rduz/dr)

In the above equations, which applies in a cylindrical isotropic elastic region,

rho = material density [kg/m^3],

lambda = first Lame constant [N/m^2],

mu = second Lame constant [N/m^2],

eta = shear viscosity [N-s/m^2],

phi = bulk viscosity [N-s/m^2],

d denotes the partial differential operator,

t = time [s],

and

ur is the radial displacement and uz is the displacement in the z direction, where the z-axis is the cylinder axis. Note that ur and uz are functions of (r,z), and independent of the angle phi around the axis (based on the assumed axisymmetric properties of the object and sources).

Wave2500™ solves the above equation set within each homogeneous grid element of the object, and computes (and displays) the (magnitude of the) displacement vector [ur uz] at the intersection of 4 grid elements at each time step of the simulation.

Wave2500™ does not implement "ray-tracing" or other "non-general" methods in simulating ultrasound measurements. Rather, it is a comprehensive engineering software package designed to compute the full and accurate solution to practically any 3D axisymmetric ultrasonic problem. Wave2500™ simulates data that you would measure on the lab bench or in the field. In addition, it has an easy to use graphical user interface allowing you to begin simulating complex ultrasound problems in a matter of minutes after receiving your Wave2500™ software.

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For features available in Wave2500™, you can look at Wave2500 page. For additional information, you may want to review several of our Wave2500 Examples. In addition you can download the program and obtain a free time limited license for program evaluation by registering with us and logging in. Information on pricing is also available. Please Contact Us to discuss your intended application(s) or for any other additional information you would like to have on Wave2500™.

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