Fourier domain closed-form formulas for estimation of kinetic parameters in reversible multi-compartment models

BioMedical Engineering OnLine

Grant T Gullberg²  Dan J Kadrmas¹  Gengsheng L Zeng¹ 

[1]Utah Center for Advanced Imaging Research, Department of Radiology, University of Utah, 729 Arapeen Drive, Salt Lake City, Utah, 84108, USA

[2]Department of Radiotracer Development & Imaging Technology, Lawrence Berkeley National Laboratory, One Cyclotron Road, Mailstop: 55R0121, Berkeley, CA 94720, USA

关键词: Fourier transform;    Compartment modeling;    Nuclear medicine imaging;    Least-squares estimation;    Dynamic imaging;    Kinetic parameter estimation;   

Others  :  798009
DOI  :  10.1186/1475-925X-11-70

 received in 2012-06-16, accepted in 2012-09-06,  发布年份 2012

【 摘 要 】

Background

Compared with static imaging, dynamic emission computed tomographic imaging with compartment modeling can quantify in vivo physiologic processes, providing useful information about molecular disease processes. Dynamic imaging involves estimation of kinetic rate parameters. For multi-compartment models, kinetic parameter estimation can be computationally demanding and problematic with local minima.

Methods

This paper offers a new perspective to the compartment model fitting problem where Fourier linear system theory is applied to derive closed-form formulas for estimating kinetic parameters for the two-compartment model. The proposed Fourier domain estimation method provides a unique solution, and offers very different noise response as compared to traditional non-linear chi-squared minimization techniques.

Results

The unique feature of the proposed Fourier domain method is that only low frequency components are used for kinetic parameter estimation, where the DC (i.e., the zero frequency) component in the data is treated as the most important information, and high frequency components that tend to be corrupted by statistical noise are discarded. Computer simulations show that the proposed method is robust without having to specify the initial condition. The resultant solution can be fine tuned using the traditional iterative method.

Conclusions

The proposed Fourier-domain estimation method has closed-form formulas. The proposed Fourier-domain curve-fitting method does not require an initial condition, it minimizes a quadratic objective function and a closed-form solution can be obtained. The noise is easier to control, simply by discarding the high frequency components, and emphasizing the DC component.

【 授权许可】

   
2012 Zeng et al.; licensee BioMed Central Ltd.

【 图 表 】

Figure 1.

Figure 2.

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