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Reply:
======

* R.K.S. Rathore
* R.K. Gupta

We thank Paula Alcaide-Leon and Álex Rovira for their interest in our work.1 In a given a time-series model involving a number of parameters, it is reasonable to expect that a determination of the parameters by using very few time points may result in erroneous estimates due to noise in the data. However, if one uses enough time points, the computations are expected to be relatively error-free; the inclusion of too many time points need not result in any better estimates.

Furthermore, if the model describes the data (ie, it is applicable), the variability in the parameter estimates using variable time points should only be random. A systematic variation in estimated parameter with respect to variable time points is indicative of an inadequacy of the model to describe the data.

The generalized tracer kinetic model (GTKM) given by ![Formula][1]</img>  is a 2-compartment model used by the commenting authors.

To resolve the persistence of uptake, researchers are using a model that assumes unidirectional exchange (ie, from the capillary plasma to the extracellular extravascular space [EES]2⇓–4), which essentially consists of the Patlak model: ![Formula][2]</img>  describing a pure contrast uptake voxel.

The actual situation, however, appears to be best described by the 3-compartment leaky tracer kinetic model (LTKM)5: ![Formula][3]</img>  presented in Rathore et al6,7 and Sahoo et al.8

LTKM reduces to GTKM if the leakage space is absent (λ*tr* = 0); and it reduces to the Patlak model in the absence of a permeable space (*ktr* = 0).

The systematic variability of the tracer kinetic parameters using GTKM and its cessation using LTKM is considered at length in Sahoo et al.5

In short, it not necessary to prolong the observations until the washout phase, and a study of approximately 3 minutes is quite adequate. What is needed is to use the correct model in which the constancy of the parameters is restored to its original state. For further discussion of LTKM, readers may refer to Sahoo et al.5

We used only an in-house-developed code for our computations.

## References

1.  1. Gupta RK, Awasthi R, Garg RK, et al. T1-weighted dynamic contrast-enhanced MR evaluation of different stages of neurocysticercosis and its relationship with serum MMP-9 expression. AJNR Am J Neuroradiol 2012 Nov 22. [Epub ahead of print]
    
    

2.  2. Sourbron SP, Buckley DL. Tracer kinetic modeling in MRI: estimating perfusion and capillary permeability. Phys Med Biol 2012;57:R1–33
    
    [CrossRef](http://www.ajnr.org/lookup/external-ref?access_num=10.1088/0031-9155/57/2/R1&link_type=DOI) 
    
    [PubMed](http://www.ajnr.org/lookup/external-ref?access_num=22173205&link_type=MED&atom=%2Fajnr%2F34%2F5%2FE60.atom) 

3.  3. Li KL, Zhu XP, Checkley DR, et al. Simultaneous mapping of blood volume and endothelial permeability surface area product in gliomas using iterative analysis of first-pass dynamic contrast enhanced MRI data. Br J Radiol 2003;76:39–50
    
    [Abstract/FREE Full Text](http://www.ajnr.org/lookup/ijlink/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6NzoiYmpyYWRpbyI7czo1OiJyZXNpZCI7czo5OiI3Ni85MDEvMzkiO3M6NDoiYXRvbSI7czoxOToiL2FqbnIvMzQvNS9FNjAuYXRvbSI7fXM6ODoiZnJhZ21lbnQiO3M6MDoiIjt9) 

4.  4. Patlak CS, Blasberg RG, Fenstermacher JD. Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. J Cereb Blood Flow Metab 1983;3:1–7
    
    [CrossRef](http://www.ajnr.org/lookup/external-ref?access_num=10.1038/jcbfm.1983.1&link_type=DOI) 
    
    [PubMed](http://www.ajnr.org/lookup/external-ref?access_num=6822610&link_type=MED&atom=%2Fajnr%2F34%2F5%2FE60.atom) 
    
    [Web of Science](http://www.ajnr.org/lookup/external-ref?access_num=A1983QD19900001&link_type=ISI) 

5.  5. Sahoo P, Rathore RK, Awasthi R, et al. Subcompartmentalization of extracellular extravascular space (EES) into permeability and leaky space with local arterial input function (AIF) results in improved discrimination between high- and low-grade glioma using dynamic contrast-enhanced (DCE) MRI. J Magn Reson Imaging 2013 Feb 6. [Epub ahead of print]
    
    

6.  6. Rathore RKS, Sahoo P, Awasthi R, et al. A modified generalized tracer kinetic model for perfusion parameters in DCE-MRI for high grade intracranial mass lesions. In: Proceedings of the Nineteenth Annual Meeting of the International Society of Magnetic Resonance in Medicine, Montreal, Quebec, Canada; May 6–13, 2011
    
    

7.  7. Rathore RKS, Gupta RK, Sahoo P, et al. DCE-MRI using a three compartment leaky tracer kinetic model (LTKM) for whole body applications. In: Proceedings of the Twentieth Annual Meeting of the International Society of Magnetic Resonance in Medicine, Melbourne, Australia; May 5–11, 2012
    
    

8.  8. Sahoo P, Awasthi R, Rathore RKS, et al. Effects of AIF selection and pharmacokinetic model selection on discrimination of chronic infective from chronic inflammatory knee arthritis using DCE-MRI. In: Proceedings of the Twentieth Annual Meeting of the International Society of Magnetic Resonance in Medicine. Melbourne, Australia; May 5–11, 2012
    
    

*   © 2013 by American Journal of Neuroradiology

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