Richard L Magin | PubMed Health

PubMed2006

Magnetic resonance microscopy for monitoring osteogenesis in tissue-engineered construct in vitro.

Magnetic resonance microscopy (MRM) is used to monitor osteogenesis in tissue-engineered constructs. Measurements of the developing tissue's MR relaxation times (T(1) and T(2)), apparent diffusion coefficient (ADC) and elastic shear modulus were conducted over a 4-week growth period using an 11.74 T Bruker spectrometer with an imaging probe adapted for MR elastography (MRE). Both the relaxation times and the ADC show a statistically significant decrease after only one week of tissue development while the tissue stiffness increases progressively during the first two weeks of in vitro growth. The measured MR parameters are correlated with histologically monitored osteogenic tissue development. This study shows that MRM can provide quantitative data with which to characterize the growth and development of tissue-engineered bone.

Alkaline Phosphatase↗

PubMed2006

Nondestructive evaluation of osteogenic differentiation in tissue-engineered constructs.

Conventional measurements of osteogenesis in tissue-engineered constructs are destructive to living cells and incapable to provide three-dimensional information. In the present study, noninvasive magnetic resonance (MR) microscopy was used to evaluate osteogenic differentiation in vitro in human mesenchymal stem cell-based tissue-engineered constructs. The constructs were prepared by seeding the cells (10(6)cells/ml) on 4 x 4 x 4 mm gelatin sponge cubes and subsequently exposing them to osteogenic differentiation or basic medium. During the 4-week experiment, alkaline phosphatase (ALP) activity and calcium content of differentiated constructs were significantly increased compared to the basic medium controls. The T1, T2, and apparent diffusion coefficient (ADC) of differentiated constructs were significantly lower than those of the control group at each time point (p < 0.05). The MR parameters of constructs were significantly correlated to their ALP activities (r to T1, T2, and ADC = -0.57, -0.78, and -0.81, respectively) and calcium content (r to T1, T2, and ADC = 0.48, 0.90, and 0.92, respectively) measured by biochemical techniques. MR microscopy can be a promising tool for noninvasive assessment of osteogenic differentiation and to provide three-dimensional information about tissue-engineered constructs.

Alkaline Phosphatase↗

PubMed2005

Microscopic magnetic resonance elastography (microMRE).

Magnetic resonance elastography (MRE) was extended to the microscopic scale to image low-frequency acoustic shear waves (typically less than 1 kHz) in soft gels and soft biological tissues with high spatial resolution (34 micromx34 micromx500 microm). Microscopic MRE (microMRE) was applied to agarose gel phantoms, frog oocytes, and tissue-engineered adipogenic and osteogenic constructs. Analysis of the low-amplitude shear wave pattern in the samples allowed the material stiffness and viscous loss properties (complex shear stiffness) to be identified with high spatial resolution. microMRE experiments were conducted at 11.74 T in a 56-mm vertical bore magnet with a 10 mm diameterx75 mm length cylindrical space available for the elastography imaging system. The acoustic signals were generated at 550-585 Hz using a piezoelectric transducer and high capacitive loading amplifier. Shear wave motion was applied in synchrony with the MR pulse sequence. The field of view (FOV) ranged from 4 to 14 mm for a typical slice thickness of 0.5 mm. Increasing the agarose gel concentration resulted in an increase in shear elasticity and shear viscosity. Shear wave motion propagated through the frog oocyte nucleus, enabling the measurement of its shear stiffness, and in vitro shear wave images displayed contrast between adipogenic and osteogenic tissue-engineered constructs. Further development of microMRE should enable its use in characterizing stiffer materials (e.g., polymers, composites, articular cartilage) and assessing with high resolution the mechanical properties of developing tissues.

Adipose Tissue↗

PubMed2004

Fractional calculus in bioengineering.

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub-threshold nerve propagation. By expanding the range of mathematical operations to include fractional calculus, we can develop new and potentially useful functional relationships for modeling complex biological systems in a direct and rigorous manner.

Action Potentials↗

PubMed2004

Fractional calculus in bioengineering, part 2.

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub-threshold nerve propagation. By expanding the range of mathematical operations to include fractional calculus, we can develop new and potentially useful functional relationships for modeling complex biological systems in a direct and rigorous manner. In Part 1 of this review (Crit Rev Biomed Eng 2004; 32(1):1-104), the fundamental properties of fractional calculus were introduced. The reader should refer to that material, particularly the sections on special functions and fractional order differential equations, for background.

Action Potentials↗

PubMed2004

Fractional calculus in bioengineering, part 3.

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub-threshold nerve propagation. By expanding the range of mathematical operations to include fractional calculus, we can develop new and potentially useful functional relationships for modeling complex biological systems in a direct and rigorous manner. In Part 2 of this review (Crit Rev Biomed Eng 2004; 32(1):105-193), fractional calculus was applied to problems in nerve stimulation, dielectric relaxation, and viscoelastic materials by extending the governing differential equations to include fractional order terms. In this third and final installment, we consider distributed systems that represent shear stress in fluids, heat transfer in uniform one-dimensional media, and subthreshold nerve depolarization. Classic electrochemical analysis and impedance spectroscopy are also reviewed from the perspective of fractional calculus, and selected examples from recent studies in neuroscience, bioelectricity, and tissue biomechanics are analyzed to illustrate the vitality of the field.

Axons↗

PubMedDate not supplied

The effect of pulsed ultrasound on mandibular distraction.

This study evaluated the effect of pulsed ultrasound on tissue repair and bone growth during mandibular osteodistraction. Twenty-one rabbits were divided into three groups of 7. The distraction started 72 h after surgically severing both sides of the mandible and proceeded at a rate of 1.5 mm/12 h for 5 days. Group I received pulsed ultrasound (nominally 200 micros pulse of 1.5 MHz at a 1.1 kHz pulse repetition frequency, 30 mW/cm2) for 20 min on both sides of the mandible every other day (alternating sides). Group 2 received the same pulsed ultrasound treatment on one side of the mandible every day for 20 min. Group 3 did not receive any ultrasound treatment. Bone formation at the distraction site was assessed by photodensitometry on head radiographs, a vibratory coherence test across the distraction site, a postmortem three-point bending mechanical stiffness test, and a postmortem histological examination. Statistical analyses performed using analysis of variance revealed that pulsed ultrasound enhanced bone formation at the distraction site with a high level of significance when assessed by the increase in new bone photodensity (p = 0.001), vibratory coherence (p = 0.001), mechanical stiffness (p = 0.003), and qualitative histological studies, especially when the pulsed ultrasound treatment was directly applied daily.

Animals↗