Modeling normal and altered human erythrocyte shapes by a new parametric equation: Application to the calculation of induced transmembrane potentials

Martín, Sara Guillén; Sebastián, J.L.; Álvarez, Gabriel

doi:10.1002/bem.20234

Cited by 17 publications

(23 citation statements)

References 39 publications

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“…This was relevant to the experimental NMR-based studies then being done. Muñoz San Martín et al (2006) were interested only in a numerical solution of the Laplace equation so could relax the requirement for the boundary being the coordinate surface on an orthogonal coordinate system.…”

Section: Discocyte Modelsmentioning

confidence: 99%

“…Here, we derive the Cartesian form of the set of parametric equations given by Muñoz San Martín et al (2006) to generate both discocytic and stomatocytic RBCs. The parametric equations that use Jacobi elliptic functions are…”

Section: Cartesian Representationmentioning

confidence: 99%

“…The simplest one uses a surface of revolution described by an oval of Cassini (Vayo, 1983); however, the shape is specified by only two parameters, the diameter and thickness of the cell, and clearly deviates systematically from experimental reality. Among the more complex models of discocytes are those based on three parameters: the cell diameter, the maximum and minimum thickness of the cell, and a useful form is one described by parametric equations using Jacobi elliptic functions and integrals (Kuchel and Fackerell, 1999;Sebastián et al, 2005;Muñoz San Martín et al, 2006). These models have been used experimentally for the calculation of dielectric spectra (di Biasio et al, 2009), the effects of RF fields on cells (Muñoz San Martín et al, 2003;Muñoz et al, 2004), and in simulating nuclear magnetic resonance (NMR)-detected diffusiondiffraction signals (Regan and Kuchel, 2003).…”

Section: Introductionmentioning

confidence: 99%

“…There is current interest in modelling these abnormally shaped RBCs to understand the membrane characteristics that control the transformation from discocytes to either of the alternative shapes (Waugh, 1996;Iglič, 1997;Lim et al, 2002;Mukhopadhyay et al, 2002;Kuzman et al, 2004). The discocyte model of Muñoz San Martín et al (2006) includes an additional parameter that enables the description of the stomatocyte-shaped RBCs, including morphological transitions ("morphing") between the two shapes. Our interest in modelling RBCs is for simulations of the signal intensity from NMR-detected measurements of water diffusing in RBCs of different shapes.…”

Section: Introductionmentioning

confidence: 99%

“…Our interest in modelling RBCs is for simulations of the signal intensity from NMR-detected measurements of water diffusing in RBCs of different shapes. These simulations are most readily implemented using an expression for the boundary of the cell in Cartesian form, therefore, we also derived the Cartesian form of the parametric equations of Muñoz San Martín et al (2006).…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Models of Naturally “Morphed” Human Erythrocytes: Stomatocytes and Echinocytes

Larkin

Kuchel

2010

Bull. Math. Biol.

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We present two mathematical models that describe human red blood cells (RBCs) with morphologies that are attained naturally under certain patho-physiological conditions, namely stomatocytes and echinocytes. Muñoz San Martín et al. (Bioelectromagnetics 27:521-527, 2006) recently presented models of these shapes based on our previous set of parametric equations (Kuchel and Fackerell, Bull. Math. Biol. 61:209-220, 1999) that involve Jacobi elliptic functions and integrals. Thus, both discocytes and stomatocytes are described. Here, we derived the Cartesian forms of these new equations; and, in addition, present a realistic model of a Type III echinocyte, using prolate spheroids 'decorating' a central sphere at the vertices of an internal dodecahedron. The RBC models based on Cartesian equations have been used for representing the shape changes (morphological transformations or "morphing") that occur in RBCs under various experimental conditions; specifically, when the shape changes have been monitored by nuclear magnetic resonance (NMR) micro-imaging.

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Section: Discocyte Modelsmentioning

confidence: 99%

Section: Cartesian Representationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Mathematical Models of Naturally “Morphed” Human Erythrocytes: Stomatocytes and Echinocytes

Larkin

Kuchel

2010

Bull. Math. Biol.

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Quantitative assessment of dielectric parameters for membrane lipid bi‐layers from RF permittivity measurements

Merla¹,

Liberti²,

Apollonio³

et al. 2009

Bioelectromagnetics

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In this article, we propose and validate theoretical and experimental methods to quantitatively assess the Debye dielectric model of membrane lipid bi-layers. This consists of two steps: permittivity measurements of biological solutions (liposomes), and estimation of the model parameters by inverse application of the Effective Medium Theory. The measurements are conducted in the frequency domain between 100 MHz and 2 GHz using a modified coaxial connector, at the temperatures of 27 and 30 degrees C. Estimations have been performed using a three-layered model based on the Maxwell-Wagner formulation. Debye parameters (mean value +/- standard error) found from fitting experimental data are: epsilon(s) = 11.69 +/- 0.09, epsilon(infinity) = 4.00 +/- 0.07, f(relax) = 179.85 +/- 6.20 MHz and epsilon(s) = (1.1 +/- 0.1) x 10(-7) S/m. This model can be used in microdosimetric studies aiming to precisely determine the E-field distribution in a biological target down to the single cell level. In this context the use of an accurate membrane dielectric model, valid through a wide frequency range, is particularly appropriate.

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Estimation of cellular‐interstitial water exchange in dynamic contrast enhanced MRI using two flip angles

Zhang

Kim

2019

NMR in Biomedicine

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Purpose To investigate the feasibility of using multiple flip angles in dynamic contrast enhanced (DCE) MRI to reduce the uncertainty in estimation of intracellular water lifetime (τi). Methods Numerical simulation studies were conducted to assess the uncertainty in estimation of τi using dynamic contrast enhanced MRI with one or two flip angles. In vivo experiments with a murine brain tumor model were conducted at 7T using two flip angles. The in vivo data were used to compare τi estimation using the single‐flip‐angle (SFA) protocol with that using the double‐flip‐angle (DFA) protocol. Data analysis was conducted using the two‐compartment exchange model combined with the three‐site‐two‐exchange model for water exchange. Results In the numerical simulation studies with a range of contrast kinetic parameters and signal‐to‐noise ratio = 20, the median bias of τi estimation decreased from 72 ms with SFA to 65 ms with DFA, and the corresponding median inter‐quartile range reduced from 523 ms to 156 ms. In the in vivo studies, τi estimation with SFA was not successful in most voxels in the tumors, as the estimated τi values reached the upper limit of the parameter range (2 s). In contrast, the estimated τi values with DFA were mostly between 0.2 and 1.5 s and homogeneously distributed spatially across the tumor. The τi estimation with DFA was less sensitive to arterial input function scaling but more sensitive to pre‐contrast T1 than the other contrast kinetic parameters. Conclusion This study results demonstrate the feasibility of using multiple flip angles to encode the post‐contrast time‐intensity curve with different weighting of water exchange effect to reduce the uncertainty in τi estimation.

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Modeling normal and altered human erythrocyte shapes by a new parametric equation: Application to the calculation of induced transmembrane potentials

Cited by 17 publications

References 39 publications

Mathematical Models of Naturally “Morphed” Human Erythrocytes: Stomatocytes and Echinocytes

Mathematical Models of Naturally “Morphed” Human Erythrocytes: Stomatocytes and Echinocytes

Quantitative assessment of dielectric parameters for membrane lipid bi‐layers from RF permittivity measurements

Estimation of cellular‐interstitial water exchange in dynamic contrast enhanced MRI using two flip angles

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