Volumetric MRI‐guided high‐intensity focused ultrasound for noninvasive, in vivo determination of tissue thermal conductivity: Initial experience in a pig model

Zhang, Jiming; Mougenot, Charles; Partanen, Ari; Muthupillai, Raja; Hor, P. H.

doi:10.1002/jmri.23878

Cited by 14 publications

(19 citation statements)

References 23 publications

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“…The spatiotemporal temperature evolution in tissue not in the vicinity of large‐vessel flow may be described by the well‐known bio‐heat transfer equation:

ρ_{t} c_{t} \frac{\partial T (\overset{true\to}{r}, t)}{\partial t} = k_{t} \nabla^{2} T (\overset{true\to}{r}, t) - ρ_{b} ω_{b} c_{b} (T (\overset{true\to}{r}, t) ‐ T_{a}) + Q_{m e t} + Q_{e x t}

where

T (\overset{true\to}{r}, t)

is the tissue temperature at time t and location

\overset{true\to}{r}

; ρ t , c t , and k t are tissue density, specific heat, and thermal conductivity, respectively; ρ b , c b , and w b are blood density, specific heat, and perfusion rate, respectively; T a is the arterial blood temperature; Q met is the metabolic rate, and Q ext is the power deposition per unit volume by the external heat source. Dragonu et al proposed that if the spatial distribution of temperature can be modeled as a 3D Gaussian, and the local region that is heated is considered homogenous, then the solution of this bio‐heat transfer equation during the cooling period can be expressed as :

T (\overset{true\to}{r}, t) = T_{0} \frac{σ_{0 x y}^{2}}{σ_{0 x y}^{2} + 2 D t} \sqrt{\frac{σ_{0 z}^{2}}{σ_{0 z}^{2} + 2 D t}} exp [‐ w_{b} t] exp [‐ \frac{x^{2} + y^{2}}{2 σ_{0 x y}^{2} + 4 D t}] exp [‐ \frac{z^{2}}{2 σ_{0 z}^{2} + 4 D t}]

…”

Section: Methodsmentioning

confidence: 99%

Noninvasive, in vivo determination of uterine fibroid thermal conductivity in MRI‐guided high intensity focused ultrasound therapy

Zhang¹,

Fischer²,

Warner

et al. 2014

Magnetic Resonance Imaging

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“…The spatiotemporal temperature evolution in tissue not in the vicinity of large‐vessel flow may be described by the well‐known bio‐heat transfer equation:

ρ_{t} c_{t} \frac{\partial T (\overset{true\to}{r}, t)}{\partial t} = k_{t} \nabla^{2} T (\overset{true\to}{r}, t) - ρ_{b} ω_{b} c_{b} (T (\overset{true\to}{r}, t) ‐ T_{a}) + Q_{m e t} + Q_{e x t}

where

T (\overset{true\to}{r}, t)

is the tissue temperature at time t and location

\overset{true\to}{r}

T (\overset{true\to}{r}, t) = T_{0} \frac{σ_{0 x y}^{2}}{σ_{0 x y}^{2} + 2 D t} \sqrt{\frac{σ_{0 z}^{2}}{σ_{0 z}^{2} + 2 D t}} exp [‐ w_{b} t] exp [‐ \frac{x^{2} + y^{2}}{2 σ_{0 x y}^{2} + 4 D t}] exp [‐ \frac{z^{2}}{2 σ_{0 z}^{2} + 4 D t}]

…”

Section: Methodsmentioning

confidence: 99%

Noninvasive, in vivo determination of uterine fibroid thermal conductivity in MRI‐guided high intensity focused ultrasound therapy

Zhang¹,

Fischer²,

Warner

et al. 2014

Magnetic Resonance Imaging

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“…They applied their technique to several ex vivo tissues and in vivo rabbit thigh muscle, reporting precision errors of less than 10%. Subsequent studies have applied their method in ex vivo perfused porcine kidney (precision of 10% [13]), in vivo porcine kidney (precision of 40–50% [14]), and in vivo porcine thigh muscle (precision of 10% [15]). In those studies, the maximum focal temperature and noise in temperature measurements varied significantly, limiting the value of directly comparing precision values.…”

Section: Introductionmentioning

confidence: 99%

The accuracy and precision of two non-invasive, magnetic resonance-guided focused ultrasound-based thermal diffusivity estimation methods

Dillon

Payne

Christensen

et al. 2014

International Journal of Hyperthermia

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Purpose The use of correct tissue thermal diffusivity values is necessary for making accurate thermal modeling predictions during magnetic resonance-guided focused ultrasound (MRgFUS) treatment planning. This study evaluates the accuracy and precision of two non-invasive thermal diffusivity estimation methods, a Gaussian Temperature method published by Cheng and Plewes in 2002 and a Gaussian specific absorption rate (SAR) method published by Dillon et al in 2012. Materials and Methods Both methods utilize MRgFUS temperature data obtained during cooling following a short (<25s) heating pulse. The Gaussian SAR method can also use temperatures obtained during heating. Experiments were performed at low heating levels (ΔT~10°C) in ex vivo pork muscle and in vivo rabbit back muscle. The non-invasive MRgFUS thermal diffusivity estimates were compared with measurements from two standard invasive methods. Results Both non-invasive methods accurately estimate thermal diffusivity when using MR-temperature cooling data (overall ex vivo error<6%, in vivo<12%). Including heating data in the Gaussian SAR method further reduces errors (ex vivo error<2%, in vivo<3%). The significantly lower standard deviation values (p<0.03) of the Gaussian SAR method indicate that it has better precision than the Gaussian Temperature method. Conclusions With repeated sonications, either MR-based method could provide accurate thermal diffusivity values for MRgFUS therapies. Fitting to more data simultaneously likely makes the Gaussian SAR method less susceptible to noise, and using heating data helps it converge more consistently to the FUS fitting parameters and thermal diffusivity. These effects lead to the improved precision of the Gaussian SAR method.

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“…In the past, applying (1) for analytical estimation of ultrasound and thermal properties has required eliminating the time integral through the assumption of instantaneous heating (Parker 1983, Cheng and Plewes 2002, Anand and Kaczkowski 2008, 2009, Dragonu et al 2009, Cornelis et al 2011, Zhang et al 2013, 2015) or simplifying the integrand for evaluation by neglecting perfusion (Cline et al 1994, Dillon et al 2012, 2013, 2014) and/or utilizing only the center-line, on-axis solution (Parker 1985, Kress and Roemer 1987, Cline et al 1994, Dillon et al 2012). To our knowledge, the full analytical solution of (1) cannot be directly evaluated.…”

Section: Theorymentioning

confidence: 99%

“…In recent years, MRTI has been used in estimation techniques for determining a variety of ultrasound (Salomir et al 2000, Dragonu et al 2009, Dillon et al 2012, 2013, Appanaboyina et al 2013, Alon et al 2013), thermal (Cline et al 1994, Salomir et al 2000, Cheng and Plewes 2002, Huttunen et al 2006, Sumi and Yanagimura 2007, Dragonu et al 2009, Cornelis et al 2011, Zhang et al 2013, Appanaboyina et al 2013, Alon et al 2013, Dillon et al 2013, 2014, Zhang et al 2013, 2015), and perfusion properties (Cheng and Plewes 2002, Huttunen et al 2006, Dragonu et al 2009, Cornelis et al 2011, Appanaboyina et al 2013, Alon et al 2013, Dillon et al 2015). …”

Section: Introductionmentioning

confidence: 99%

Analytical estimation of ultrasound properties, thermal diffusivity, and perfusion using magnetic resonance-guided focused ultrasound temperature data

2016

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For thermal modeling to play a significant role in treatment planning, monitoring, and control of magnetic resonance-guided focused ultrasound (MRgFUS) thermal therapies, accurate knowledge of ultrasound and thermal properties is essential. This study develops a new analytical solution for the temperature change observed in MRgFUS which can be used with experimental MR temperature data to provide estimates of the ultrasound initial heating rate, Gaussian beam variance, tissue thermal diffusivity, and Pennes perfusion parameter. Simulations demonstrate that this technique provides accurate and robust property estimates that are independent of the beam size, thermal diffusivity, and perfusion levels in the presence of realistic MR noise. The technique is also demonstrated in vivo using MRgFUS heating data in rabbit back muscle. Errors in property estimates are kept less than 5% by applying a third order Taylor series approximation of the perfusion term and ensuring the ratio of the fitting time (the duration of experimental data utilized for optimization) to the perfusion time constant remains less than one.

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Volumetric MRI‐guided high‐intensity focused ultrasound for noninvasive, in vivo determination of tissue thermal conductivity: Initial experience in a pig model

Cited by 14 publications

References 23 publications

Noninvasive, in vivo determination of uterine fibroid thermal conductivity in MRI‐guided high intensity focused ultrasound therapy

Noninvasive, in vivo determination of uterine fibroid thermal conductivity in MRI‐guided high intensity focused ultrasound therapy

The accuracy and precision of two non-invasive, magnetic resonance-guided focused ultrasound-based thermal diffusivity estimation methods

Analytical estimation of ultrasound properties, thermal diffusivity, and perfusion using magnetic resonance-guided focused ultrasound temperature data

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