Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation

Fedele, Francesco; Laible, Jeffrey P.; Eppstein, Margaret J.

doi:10.1016/s0021-9991(03)00150-5

Cited by 61 publications

(50 citation statements)

References 38 publications

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“…The first-order Fréchet derivative of (or ) with respect to the fluorophore concentration at the EKF total concentration estimate at the th step is given by [31], [35], [36] (34)…”

Section: B Estimation Of Pharmacokinetic-rate Images By Extended Kalmentioning

confidence: 99%

“…where we define as the solution of (6) and (10), as the solution of (7) and (11), as the Green's function of (7) and (11), and as the solution of (6) and (10) where in (6) is replaced by given the EKF estimates of the fluorophore concentrations at different compartments at the th step [35]. In (34), the first integral results from the right-hand side of (7), while the second and third integrals originate from the dependence of and TABLE I EKF ALGORITHM FOR THE SIMULTANEOUS ESTIMATION OF FLUOROPHORE CONCENTRATION, PHARMACOKINETIC-RATE, AND VOLUME FRACTION IMAGES , respectively, on the unknown fluorophore absorption coefficient.…”

Section: B Estimation Of Pharmacokinetic-rate Images By Extended Kalmentioning

confidence: 99%

See 1 more Smart Citation

Direct Reconstruction of Pharmacokinetic Rate Images of Indocyanine Green in Fluorescence Molecular Tomography

Alacam¹,

Yazıcı

Intes³

et al. 2006

Biomedical Optics

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Abstract-In this paper, we present a new method to form pharmacokinetic-rate images of optical fluorophores directly from near infra-red (NIR) boundary measurements. We first derive a mapping from spatially resolved pharmacokinetic rates to NIR boundary measurements by combining compartmental modeling with a diffusion based NIR photon propagation model. We express this mapping as a state-space equation. Next, we introduce a spatio-temporal prior model for the pharmacokinetic-rate images and combine it with the state-space equation. We address the image formation problem using the extended Kalman filtering framework. We analyze the computational complexity of the resulting algorithms and evaluate their performance in numerical simulations. An important feature of our approach is that the reconstruction of fluorescence concentrations and compartmental modeling are combined into a single step 1) to take advantage of the inherent temporal correlations in dynamic NIR measurements, and 2) to incorporate spatio-temporal a priori information on pharmacokinetic-rate images. Simulation results show that the resulting algorithms are more robust and lead to higher signal-to-noise ratio as compared to existing approaches where the reconstruction of concentrations and compartmental modeling are treated separately. Additionally, we reconstructed pharmacokinetic-rate images using in vivo data obtained from three patients with breast tumors. The reconstruction results show that the pharmacokinetic rates of indocyanine green are higher inside the tumor region as compared to the surrounding tissue.

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“…The first-order Fréchet derivative of (or ) with respect to the fluorophore concentration at the EKF total concentration estimate at the th step is given by [31], [35], [36] (34)…”

Section: B Estimation Of Pharmacokinetic-rate Images By Extended Kalmentioning

confidence: 99%

Section: B Estimation Of Pharmacokinetic-rate Images By Extended Kalmentioning

confidence: 99%

Direct Reconstruction of Pharmacokinetic Rate Images of Indocyanine Green in Fluorescence Molecular Tomography

Alacam¹,

Yazıcı

Intes³

et al. 2006

Biomedical Optics

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show abstract

“…The fluorophore is elevated to an excited state and then decays to the ground state while releasing the energy. This creates fluorescence, which can be separated from the excitation light via interference filters [4]. The fluorescent photon has a longer wavelength than that of the excitation photon, resulting in a color shift.…”

Section: Introductionmentioning

confidence: 99%

Image reconstruction of fluorescent molecular tomography based on the simplified matrix system

2013

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Fluorescent molecular tomographic image reconstruction usually involves repeatedly solving large-scale matrix equations, which are computationally expensive. In this paper, a method is proposed to reduce the scale of the matrix system. The Jacobian matrix is simplified by deleting the columns or the rows whose values are smaller than a threshold. Furthermore, the measurement data are divided into two groups and are used for iteration of image reconstruction in turn. The simplified system is then solved in the wavelet domain to further accelerate the process of solving the inverse problem. Simulation results demonstrate that the proposed method can significantly speed up the reconstruction process.

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“…The coupled diffusion equations for the case of fluorescence-enhanced imaging in the frequency domain are [104] [ ]…”

Section: Light Propagation In Biological Tissuesmentioning

confidence: 99%

“…[104] The Kalman filter is a linear state Bayesian estimator that is used in process control in order to estimate a state recursively, using the previous observations. The filter yields estimates of true measurement values and the corresponding calculated values by the following process: (i) predict a value, (ii) estimate the uncertainty of the predicted value, (iii) compute a weighted average of the predicted value and the measured value.…”

Section: Approximate Extended Kalman Filter (Aekf) Based Reconstructimentioning

confidence: 99%

Clinical Translation of a Novel Hand-held Optical Imager for Breast Cancer Diagnosis

Erickson¹

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Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation

Cited by 61 publications

References 38 publications

Direct Reconstruction of Pharmacokinetic Rate Images of Indocyanine Green in Fluorescence Molecular Tomography

Direct Reconstruction of Pharmacokinetic Rate Images of Indocyanine Green in Fluorescence Molecular Tomography

Image reconstruction of fluorescent molecular tomography based on the simplified matrix system

Clinical Translation of a Novel Hand-held Optical Imager for Breast Cancer Diagnosis

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