Hardware, Software and Memory Requirements

Wave2500® is designed to run on any PC that has the Windows 2000, XP or Vista 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, Wave2000 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.

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.

Features in Wave2500:

• Batch processing (making "unattended simulations" possible)
• Multiprocessor capability (making large-scale simulations less time consuming) Ability to insert user-defined objects
• Ability to set delays on annular source or receiver arrays for focussing
• User selectable transducer apodizations, including Hamming, Hanning and Gaussian weighting functions (among others)
• Infinite (absorbing) boundary conditions, allowing the simulation of "infinite media"
• Extensive material libraries, including a wide range of solids and liquids
• Wave simulation "playback" including "single stepping" through simulation
• "Data Export" facility, making saving of simulation measurements even easier
• Ability to define sources with "void" backings, making it easier to simulate sources located within an object
• Descriptive error and information messages