The Tofts model in frequency domain: Fast and robust determination of pharmacokinetic maps for dynamic contrast enhancement MRI

Nithin N. Vajuvalli, Dharmendra Kumar K. Chikkemenahally, Krupa N. Nayak, Manoj G. Bhosale, Sairam Geethanath

Research output: Contribution to journalArticlepeer-review


Dynamic contrast enhancement magnetic resonance imaging (DCE-MRI) is a well-established method for non-invasive detection and therapeutic monitoring of pathologies through administration of intravenous contrast agent. Quantification of pharmacokinetic (PK) maps can be achieved through application of compartmental models relevant to the pathophysiology of the tissue under interrogation. The determination of PK parameters involves fitting of time-concentration data to these models. In this work, the Tofts model in frequency domain (TM-FD) is applied to a weakly vascularized tissue such as the breast. It is derived as a convolution-free model from the conventional Tofts model in the time domain (TM-TD). This reduces the dimensionality of the curve-fitting problem from two to one. The approaches of TM-FD and TM-TD were applied to two kinds of in silico phantoms and six in vivo breast DCE data sets with and without the addition of noise. The results showed that computational time taken to estimate PK maps using TM-FD was 16-25% less than with TM-TD. Normalized root mean square error (NRMSE) calculation and Pearson correlation analyses were performed to validate robustness and accuracy of the TM-FD and TM-TD approaches. These compared with ground truth values in the case of phantom studies for four different temporal resolutions. Results showed that NRMSE values for TM-FD were significantly lower than those of TM-TD as validated by a paired t-test along with reduced computational time. This approach therefore enables online evaluation of PK maps by radiologists in a clinical setting, aiding in the evaluation of 3D and/or increased coverage of the tissue of interest.

Original languageEnglish (US)
Pages (from-to)8462-8475
Number of pages14
JournalPhysics in medicine and biology
Issue number24
StatePublished - Nov 15 2016
Externally publishedYes


  • breast
  • magnetic resonance imaging (MRI)
  • perfusion imaging
  • pharmacokinetic modeling
  • quantification and estimation

ASJC Scopus subject areas

  • Radiological and Ultrasound Technology
  • Radiology Nuclear Medicine and imaging


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