Heat conduction in porcine muscle and blood: experiments and time-fractional telegraph equation model

Madhukar, Amit; Park, Yeonsoo; Kim, Woojae; Sunaryanto, Hans Julian; Berlin, Richard B.; Chamorro, Leonardo P.; Bentsman, Joseph; Ostoja–Starzewski, Martin

doi:10.1098/rsif.2019.0726

Cited by 31 publications

(33 citation statements)

References 31 publications

(44 reference statements)

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“…Due to the combination of the coarser temporal and the finer spatiotemporal control in the overall control configuration, the results presented have a broad appeal in other applications involving complex multiscale spatiotemporal dynamics, such as, for example, robotic electrosurgery [41]. In this application, the motion of the cutting probe is strongly coupled to the spatiotemporal electrosurgical impact of the latter on the target tissues, and the near-field probe-tissue interaction process is best described by a complex time-fractional PDE [42]. These features make the technique proposed a good match for this application.…”

Section: Discussionmentioning

confidence: 97%

Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed

et al. 2020

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Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H ∞ design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input model structure, nonlinear in the wavelet basis, but linear in parameters, is used to identify the dominant temporal chemical looping process dynamics. The control inputs and the wavelet model parameters are calculated by optimizing a quadratic cost function using a gradient descent method. The respective identification and tracking error convergence of the proposed self-tuning identification and control schemes, the latter using the unconstrained generalized predictive control structure, is separately ascertained through the Lyapunov stability theorem. The rate constraint on the control signal in the temporal control law is then imposed and the control topology is augmented by an additional control loop with self-tuning deadbeat controller which uses the spatiotemporal wavelet riser dynamics representation. The novelty of this work is three-fold: (1) developing the self-tuning controller design methodology that consists in embedding the real-time tunable temporal highly nonlinear, but linearly parametrizable, multiresolution system representations into the classical rate-constrained generalized predictive quadratic optimal control structure, (2) augmenting the temporal multiresolution loop by a more complex spatiotemporal multiresolution self-tuning deadbeat control loop, and (3) demonstrating the effectiveness of the proposed methodology in producing fast recursive real-time algorithms for controlling highly uncertain nonlinear multiscale processes. The latter is shown through the data from the implemented temporal and augmented spatiotemporal solutions of a difficult chemical looping cold flow tracking control problem.

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Section: Discussionmentioning

confidence: 97%

Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed

et al. 2020

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“…Madhukar et al. 23 presented an experimental observation of time fractional HHC behaviour in porcine muscle and blood, and validated the results with finite difference scheme. Kabiri and Talaee 24 utilized a hyperbolic bioheat model in cylindrical form to investigate thermal analysis based on the microwave ablation in prostate cancer with the help of Eigen value method.…”

Section: Introductionmentioning

confidence: 91%

Two-dimensional hybrid analytical approach for the investigation of thermal aspects in human tissue undergoing regional hyperthermia therapy

Dutta

Kundu

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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The formation of the present work is based on the development of the exact analytical solution of two-dimensional temperature response by employing the hyperbolic heat conduction bioheat model in a single-layered human skin tissue subjected to the regional hyperthermia therapy (RHT) for cancer treatment. The mathematical approach has been utilized as a hybrid form of ‘separation of variables’ and ‘finite integral transform’ method. Three kinds of surface heat fluxes (constant, sinusoidal and cosine) have been employed as an external heat source on the therapeutic surface of the square-shaped skin tissue of 100 mm × 100 mm. An innovative form of initial condition (spatially dependent) has been implemented in the present mathematical formulation as skin tissues are highly non-homogeneous and non-uniform in structure. The present research outcome indicates that cosine heat flux would be a suitable alternative for the sinusoidal heat flux. The impact of the relaxation time lag has been clearly noted in the thermal response with the waveform-like behaviour and it justifies the postulate of hyperbolic heat conduction. The two-dimensional temperature of the skin tissue has been observed in the range of 48.1 ℃–40 ℃ (in decreasing order). Estimated peak temperatures are in the proposed spectrum of hyperthermia therapy for an exposure time of 100 s, and this fact is true in an agreement with the medical protocol of the cancer treatment. The accuracy of the mathematical modelling and in-house computer codes are justified with the published numerical models and the maximum deviation of the thermal response has been noticed in order of 1.5–3%. The two-dimensional surface thermal contours have provided a glimpse of heat flow in the physical domain of skin tissue under different heating conditions and this research output may be beneficial to establish the theoretical standard of the regional hyperthermia treatment for cancer eradication.

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“…For the infinite case, we use Bloch's theorem [19,20], which establishes the dispersion relation of the Bloch wavenumber Q as cos(pQ) = 1 2 Tr(M), where p = d 1 + d 2 is the period of the superlattice, and M = M 2 M 1 is the transfer matrix of the unit cell. In the infinite case, the reflectivity r will be given by Equation (11) but with admittance of the following.…”

Section: Thermal Superlatticementioning

confidence: 99%

“…Several experiments have explored the non-Fourier behavior of heat transport in a variety of systems, such as granular media [3,8], wet sands [9], organic materials [10], blood and porcine muscle [11], and processed meat [12]. Skin bio-thermomechanics and bioheat transfer mechanisms also follow a non-Fourier behavior [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Bragg Mirrors for Thermal Waves

et al. 2021

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We present a numerical calculation of the heat transport in a Bragg mirror configuration made of materials that do not obey Fourier’s law of heat conduction. The Bragg mirror is made of materials that are described by the Cattaneo-Vernotte equation. By analyzing the Cattaneo-Vernotte equation’s solutions, we define the thermal wave surface impedance to design highly reflective thermal Bragg mirrors. Even for mirrors with a few layers, very high reflectance is achieved (>90%). The Bragg mirror configuration is also a system that makes evident the wave-like nature of the solution of the Cattaneo-Vernotte equation by showing frequency pass-bands that are absent if the materials obey the usual Fourier’s law.

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Heat conduction in porcine muscle and blood: experiments and time-fractional telegraph equation model

Cited by 31 publications

References 31 publications

Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed

Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed

Two-dimensional hybrid analytical approach for the investigation of thermal aspects in human tissue undergoing regional hyperthermia therapy

Bragg Mirrors for Thermal Waves

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