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VOP Compression Algorithms

Patient safety is an important factor in MRI. The RF power transmitted to excite the spins in the human body can heat up and potentially damage the tissues. To prevent this, the specific absorption rate (SAR) in W/kg is limited by guidelines and MR systems need to make sure to stay below the specified maximum values for whole body and 10g-averages at all times.

While SAR supervision of single channel systems is fairly easy as the SAR is just a linear function of the input power, the situation is more complicated in multi-channel transmit systems. Here, the SAR is a function of the complex excitation vector, containing the signal of all channels in amplitude and phase.

As the SAR in the human body cannot be measured, sophisticated simulations with exact coil models and high resolution human body models are performed. These simulations provide SAR matrices (S-matrices) which can be used to calculate the SAR by a simple vector-matrix-vector multiplication with the excitation vector. Unfortunately, there is an S-matrix for each 10g-averaging volume in the body which results in millions vector-matrix-vector multiplications to calculate the SAR. Since the excitation vector can change within a few µs, an online SAR supervision on an MRI has to do these calculations very quickly. Fortunately, it is possible to use compression algorithms which can trade the number of matrices for this calculation for an overestimation of the SAR [1-5]. This smaller set of matrices are called virtual observation point (VOPs).

Our recent investigations have shown that even with the best available compression algorithms, the computational burden for an SAR supervision increases with the number of channels to the power of more than 4 [6], making this computational burden the most difficult obstacle for increasing the number of RF channels in an MRI system.

Current and future work in this area includes:

  • Investigating the field strength dependence of the number of VOPs
  • Improving the speed of the SAR compression
  • Finding improved post-processing algorithms of VOPs



  1. Eichfelder, G. and M. Gebhardt (2011). "Local specific absorption rate control for parallel transmission by virtual observation points." Magn Reson Med 66(5): 1468-1476.
  2. Lee, J., et al. (2012). "Local SAR in parallel transmission pulse design." Magn Reson Med 67(6): 1566-1578.
  3. Orzada, S., et al. (2021). "Local SAR compression with overestimation control to reduce maximum relative SAR overestimation and improve multi-channel RF array performance." MAGMA 34(1): 153-163.
  4. Orzada, S., et al. (2021). "Local SAR compression algorithm with improved compression, speed, and flexibility." Magn Reson Med 86(1): 561-568.
  5. Orzada, S., et al. (2021). "Post-processing algorithms for specific absorption rate compression." Magn Reson Med 86(5): 2853-2861.
  6. Orzada, S., et al. (2023). "An investigation into the dependence of virtual observation point-based specific absorption rate calculation complexity on number of channels." Magn Reson Med 89(1): 469-476.

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