We have developed a new class of magnetic resonance imaging contrast agents with large proton relaxation enhancements and high molecular relaxivities. The reagents are built from the polyamidoamine form of Starburst dendrimers in which free amines have been conjugated to the chelator 2-(4-isothiocyanatobenzyl)-6-methyl-diethylenetriaminepentaacetic acid. The dendrimer gadolinium poly-chelates have enhancement factors, i.e., the ratio of the relaxivity per Gd(III) ion to that of Gd(III)-diethylenetriaminepentaacetic acid, of up to 6. These factors are more than twice those observed for analogous metal-chelate conjugates formed with serum albumins, polylysine, or dextran. One of the dendrimer-metal chelate conjugates has 170 gadolinium ions bound, which greatly exceeds the number bound to other macromolecular agents reported in the literature, and has a molecular relaxivity of 5,800 (mM.s)-1, at 25 MHz, 20 degrees C, and pH of 7.4. We observed that these dendrimer-based agents enhance conventional MR images and 3D time of flight MR angiograms, and that those with molecular weights of 8,508 and 139,000 g/mole have enhancement half lives of 40 +/- 10 and 200 +/- 100 min, much longer than the 24 +/- 4 min measured for Gd(III)-diethylenetriaminepentaacetic acid. Our results suggest that this new and powerful class of contrast agents have the potential for diverse and extensive application in MR imaging.

1800" to 2000'C. The sarnples stayed at that temperature for 10 to 20 m n before belng quenched by the cuttng off of power to the furnace. The quench rate was measured to be -500'C per second The samples were subsequently decompressed at a rate of 2 to 3 GPaihour. 17. NMR spectra descrlbed here were collected with a Varan Unity spectrometer operating at 9 L T was a MAS probe from Doty Scentfic (Coumba, SC), wlth 3.5-mm rotors commonly splnning at 9.3 kHz (unless otherwise specifed). To make 27AI analyss as straightforward as possible, a small tip angle ( i n I 6 ) was used in all cases. ' "a and "Al NMR was done w t h the use of delay tmes on the order of 1 s, wlth a spectral band width of 2 MHz. For2"S1 NMR. a smaller spectral band width was used because of the mited chemical shft range in Si; however much longer delay tlmes were used (70 s) because o i the possibility of havng long relaxaton tlmesfor Si speces even w t h a small paramagnetic dopant (Gd20,) [A. Abragam. Principles of Nuclear Magnetism (Oxford Unv. Press, New York, 1961)). We subtracted a 27Al background from the probe by colectng data on an empty rotor under condtions identical to those under whlch the glass samples were run. There was no probe background ~n the 23Na and 23S1 spectra; however, the Si3N, rotors gave a characteristc resonance at -L8.8 ppm relative to tetramethyl silane at 0 ppm with spinnlng sdebands in the sllcon NMR Thls was used as an internal chemical shift cabratlon for '%i NMR. To reference the chemcal sh~ft of ' % l a and "AI, a liquid sample of 1 M NaC (0 ppm) and 1 M ACI, (0 ppm) was run before each spectrum, respectvely. 18. We prepared the ?9S~enriched Ab5,NTS5, by fusing sto~chometr~c amounts of 92%-abeed 29Si0, glass (Cambridge Isotope Laboratory. Andover, MA) with sodium carbonate (Na,CO,), alumnum oxlde (A120s). and 0.1 weght percent gadolnium oxide (Gd20,) at 1200'C for 2 hours. Glass was formed upon removal of the Pt crucble containing the mixed iqud components from the furnace. We did not chemically analyze the sample because of the expense of labeled material and the proven nature of the synthesis process. Gd20s was added to shorten the spin-lattlce relaation time of SI. This sample. along wlth unlabeled glass made under the same conditions, was then sealed In Pt capsules for use in the hlgh-pressure multl-anvl quenchng descrlbed in (76).

a b s t r a c tFractional (non-integer order) calculus can provide a concise model for the description of the dynamic events that occur in biological tissues. Such a description is important for gaining an understanding of the underlying multiscale processes that occur when, for example, tissues are electrically stimulated or mechanically stressed. The mathematics of fractional calculus has been applied successfully in physics, chemistry, and materials science to describe dielectrics, electrodes and viscoelastic materials over extended ranges of time and frequency. In heat and mass transfer, for example, the half-order fractional integral is the natural mathematical connection between thermal or material gradients and the diffusion of heat or ions. Since the material properties of tissue arise from the nanoscale and microscale architecture of subcellular, cellular, and extracellular networks, the challenge for the bioengineer is to develop new dynamic models that predict macroscale behavior from microscale observations and measurements. In this paper we describe three areas of bioengineering research (bioelectrodes, biomechanics, bioimaging) where fractional calculus is being applied to build these new mathematical models.

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The brain's attentional system identifies and selects information that is task-relevant while ignoring information that is task-irrelevant. In two experiments using functional magnetic resonance imaging, we examined the effects of varying task-relevant information compared to task-irrelevant information. In the first experiment, we compared patterns of activation as attentional demands were increased for two Stroop tasks that differed in the task-relevant information, but not the task-irrelevant information: a color-word task and a spatial-word task. Distinct subdivisions of dorsolateral prefrontal cortex and the precuneus became activated for each task, indicating differential sensitivity of these regions to task-relevant information (e.g., spatial information vs. color). In the second experiment, we compared patterns of activation with increased attentional demands for two Stroop tasks that differed in task-irrelevant information, but not task-relevant information: a color-word task and color-object task. Little differentiation in activation for dorsolateral prefrontal and precuneus regions was observed, indicating a relative insensitivity of these regions to task-irrelevant information. However, we observed a differentiation in the pattern of activity for posterior regions. There were unique areas of activation in parietal regions for the color-word task and in occipitotemporal regions for the color-object task. No increase in activation was observed in regions responsible for processing the perceptual attribute of color. The results of this second experiment indicate that attentional selection in tasks such as the Stroop task, which contain multiple potential sources of relevant information (e.g., the word vs. its ink color), acts more by modulating the processing of task-irrelevant information than by modulating processing of task-relevant information.

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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.