Brain Displacement at Spencer Technologies

Spencer see gains in their ability to design and test algorithms in an efficient fashion, using Jacket software,
which will make for lower development costs

Power M-mode Doppler (PMD) is a medical ultrasound modality for observing motion along an axis emanating from an ultrasound probe. Although Doppler ultrasound is generally used to detect blood flow, it can also be used to detect tissue micropulsations. Such tissue pulsations originate from low velocity blood perfusion which is cyclical and synchronous with each heart beat. Investigators have reported sensitivity to motion at the sub-micron level. At Spencer Technologies, they were interested in understanding these brain tissue pulsations in order to characterize bleeding or ischemia (lack of blood flow).

In this work, Spencer describes how the Jacket software facilitates the development of fast algorithms which enable them to observe brain displacement across depth with sampling density that far surpasses previous benchmarks. Jacket accomplishes this by offloading MATLAB computations that would normally occur on the CPU to a more powerful graphic processing units (GPUs).

Method: A Transducer (Figure 1) is used to emit and detect high frequency sound waves. A high voltage transmit pulse is applied to the piezoelectric crystal inside the transducer to generate a short-bust of ultrasonic energy. As this ultrasonic pulse propagates in tissue, it encounters interfaces between different tissue structures. At these junctions, some of the energy in the ultrasonic pulse is reflected (as an echo), some of it is absorbed and some of it continues to propagate deeper into tissue. The relative magnitudes of each of these wave components is a function of the degree of acoustic impedance mismatch between tissues. Tissues regions with similar compositions have a low degree of mismatch; thus allowing more of the ultrasonic pulse to penetrate deeper and vice versa.

At Spencer Technologies they use 2 MHz ultrasound for studying the brain. This frequency is low enough to penetrate the skull in most people yet it is high enough to provide easily detected echoes from blood flow and tissue. The wavelength (&lambda) at 2 MHz is about 0.8 mm, which is more than an order of magnitude larger than the tissue motions they can detect. The fact that they are detecting phase changes over time enables them to detect tissue motion at the micron level with this wavelength. A phase change of &pi results in a displacement through the Doppler sample volume of &lambda /4, or about 0.2 mm. Angular measurements with resolutions of &pi /1000 can easily be accomplished which result in displacement resolutions of less than a micron.

The system used for this application operates with a 2MHz carrier frequency and an 8 cycle transmit burst emitted at a pulse-repetition frequency of 6.25 KHz. The transmit burst size results in an axial resolution (aka "sample volume") of about 3 mm. Axial resolution should not be confused with the angular resolution for displacement calculation discussed in the previous paragraph. As the ultrasound pulse propagates into tissue, it tracks the motion of scatterers. It is important that the sample volume size not be mismatched with the size of independently moving tissue elements, otherwise multiple moving tissue elements might result in a net displacement of zero by this technique. Also, large tissue excursions in a small sample volume will produce uncertainty due to decorrelation of scatterers within the sample volume from one pulse to another.

The Doppler shift signal for each pulse repetition period is obtained by:

  • (1) amplifying the received echoes and digitizing them at 32 MSamp/s with a 16 bit A/D converter, and
  • (2) demodulating and decimating in an off-the-shelf DSP card (TigerSHARC® engine).

Each pulse period thereby starts as 5120 echo samples and is transformed into 320 demodulated IQ values that are evenly spaced at 0.4 mm intervals i.e. &lambda / 2 of the carrier. These 320 IQ values are then re-sampled into 64 IQ samples which stratify a range in depth from 10 - 100 mm in 1.5 mm intervals. In this fashion, complex Doppler shift signal is sampled at 6250 kSamp/s at each gate depth.

Local brain motion for each of the 64 gates is calculated in MATLAB via Jacket using an NVIDIA GTX 280 graphics card using Jacket's gsingle datatype. Displacement is derived from the unwrapped instantaneous phase of the IQ signal calculated using equation (1). Equation (2) captures the relationship between phase and displacement.

IQ signal calcuated using this mathematical equation
Mathematical equation for relationship between phase and
              displacement of brain

The 16 gates shown in Figure 1 span a range from 10 to 100 mm (away from the probe) in 4mm intervals. These are a subset of the 64 sample gates that were actually used to calculate the displacement time series whose timing values are noted below. All of the displacement waveforms in Figure 1 share a common x-axis which represents time in seconds. The Y-axis shows the magnitude of the local displacements in microns for each curve. These brain displacement plots have a strong heart-cycle presence. The curves also show displacement values as low as 20 microns for total excursions measured between end diastole and a time shortly after peak systole (Note that the heart relaxes during diastole and pumps during systole). With each heart cycle the brain generally displaces in one direction beginning at onset of systole and moves back in the opposite direction starting near the end of systole. Looking across all depths for any given time shows both positive and negative displacement values with varying magnitudes, indicating heterogeneity of tissue positions with respect to source of incoming blood flow.

The GTX 280 GPU used in this study has 240 processing cores with 1GB of on-chip Ram and has the capability of doing 1000 Giga-Floating-Point calculation a second (GFLOPS). For this application, Spencer divided the data into 64 Doppler gates by 2.5 second data matrices which result in an input matrix of 64 x 80640 complex data values. Displacement is calculated (using equation 1 & 2) both in the CPU using MATLAB® and the GPU using Jacket for comparison. The timing measurements reported were averaged over 50 trials.

  • On average, the GPU is able to calculate displacement in 51.50 ms while the CPU takes 621.5 ms to do the same.
  • With its highly parallel architecture, the GPU is able to outperform the CPU by a factor of 12.

When they tease apart the GPU timing measurements further they observe that on average memory transfers between the CPU and the GPU take up 41 ms (80% of the total time) while the actual calculations take a mere 10.5 ms (20% of the total time).

Spencer's initial experience with Jacket software and GPU technology was very positive. They anticipate that it will form a foundation for calculation performance that far exceeds DSP state of the art of the last decade. This feature is essential for processing of tissue micropulsations as a function of depth in real time, which is a basic objective of their work. Spencer further see gains in ability to design and test algorithms in an efficient fashion, using Jacket software, which will make for lower development costs.

Brain signals image

Brain displacement over time along the ultrasound beam. The upper left hand corner shows the Marc 600 head frame holding a transducer (a) securely placed on the temporal acoustic window into the brain. The transducer (a) is also shown adjacent to the MRI image of the brain with overlaid depiction of paths of major anterior arteries branching from the circle of Willis that are adjacent to the path of the ultrasound beam. The arteries shown include the right middle cerebral artery (RMCA), the right anterior cerebral artery (RACA), the left anterior cerebral artery (LACA) and the left middle cerebral artery (LMCA). The right hand side of the figure shows displacement waveforms (in µ m y-axis) vs. time (in s x-axis) for Doppler gates placed from 10 to 100 mm (in 6 mm increments) away from the probe.

The Spencer Technologies' product development team that conducted this study included Asanka Dewaraja MS, Travis Rothlisberger, Bob Giansiracusa MS, Steven Swdenburg, Gene Saxon MS, and Mark Moehring, PhD

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