Telegrapher's equation with variable propagation speeds

All derivations of the one-dimensional telegraphers equation, based on the persistent random walk model, assume a constant speed of signal propagation. We generalize here the model to allow for a variable propagation speed and study several limiting cases in detail. We also show the connections of this model with anomalous diffusion behavior and with inertial dichotomous processes.

Statistics of depth probed by cw measurement of photons in a turbid medium

Photon migration in a turbid medium has been modeled in many different ways. The motivation for such modeling is based on technology that can be used to probe potentially diagnostic optical properties of biological tissue. Surprisingly, one of the more effective models is also one of the simplest. It is based on statistical properties of a nearest-neighbor lattice random walk. Here we develop a theory allowing one to calculate the number of visits by a photon to a given depth, if it is eventually detected at an absorbing surface. This mimics cw measurements made on biological tissue and is directed towards characterizing the depth reached by photons injected at the surface. Our development of the theory uses formalism based on the theory of a continuous-time random walk (CTRW). Formally exact results are given in the Fourier-Laplace domain, which, in turn, are used to generate approximations for parameters of physical interest.

Non independent continuous-time random walks

The usual development of the continuous-time random walk (CTRW) assumes that jumps and time intervals are a two-dimensional set of independent and identically distributed random variables. In this paper, we address the theoretical setting of nonindependent CTRWs where consecutive jumps and/or time intervals are correlated. An exact solution to the problem is obtained for the special but relevant case in which the correlation solely depends on the signs of consecutive jumps. Even in this simple case, some interesting features arise, such as transitions from unimodal to bimodal distributions due to correlation. We also develop the necessary analytical techniques and approximations to handle more general situations that can appear in practice.

Parrondo-like behavior in continuous-time random walks with memory

The continuous-time random walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this paper we will show how the random combination of two different unbiased CTRWs can give rise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought of as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same as that of the Parrondo paradox in game theory.

Assessment of physical activity with a pedometer and its relationship with VO2max among adolescents in Switzerland.

OBJECTIVES: In the absence of a gold standard, the assessment of physical activity in children remains difficult. To record physical activity with a pedometer and to examine to what extent it is correlated with VO2max. METHODS: Survey on physical activity and fitness; 233 Swiss adolescents aged 11 to 15 carried a pedometer (Pedoboy) during seven consecutive days. VO2max was estimated through an endurance shuttle run test. RESULTS: The physical activity recorded by the pedometer did not vary from one day to the other (p > 0.05). The physical activity was higher among boys than among girls (p < 0.001) and higher among younger adolescents (6th versus 8th grade; p < 0.001). The correlation between physical activity and estimated VO2max was 0.30 (p < 0.01). CONCLUSIONS: The use of a pedometer to assess physical activity over one entire week is feasible among adolescents. The record provided by the pedometer gives an objective measure of the usual physical activity and, as such, is relatively well correlated with aerobic capacity.

Association between foot growth and musculoskeletal loading in children with Prader-Willi syndrome before and during growth hormone treatment

OBJECTIVE: To explore how foot growth relates to musculoskeletal loading in children with Prader-Willi syndrome (PWS). STUDY DESIGN: In 37 children with PWS, foot length (FL) before and after 6 years of growth hormone therapy (GHT) was retrospectively evaluated with parental and sibling's FL, height, and factors reflecting musculoskeletal loading, such as weight for height (WfH), lean body mass (LBM; dual energy X-ray absorptiometry, deuterium labeled water), physical activity (accellerometry), and walk age. Because of the typically biphasic evolution of body mass and the late walk age in PWS, 2 age groups were separated (group 1, >2.5 years; group 2, < or =2.5 years). RESULTS: Children with PWS normalized height, but not FL after 6 years of GHT. Parental FL correlation with PWS's FL was lower than with sibling's FL. In group 1, FL positively correlated with WfH, LBM, and physical activity. In group 2, FL negatively correlated with age at onset of independent ambulation. Foot catch-up growth with GHT was slower in group 2 compared with group 1. CONCLUSION: In PWS, FL is positively associated with musculoskeletal loading. Small feet in children with PWS before and during long-term GHT may be more than just another dysmorphic feature, but may possibly reflect decreased musculoskeletal loading influencing foot growth and genetic and endocrine factors.

Linear random knots and their scaling behavior

We present here a nonbiased probabilistic method that allows us to consistently analyze knottedness of linear random walks with up to several hundred noncorrelated steps. The method consists of analyzing the spectrum of knots formed by multiple closures of the same open walk through random points on a sphere enclosing the walk. Knottedness of individual "frozen" configurations of linear chains is therefore defined by a characteristic spectrum of realizable knots. We show that in the great majority of cases this method clearly defines the dominant knot type of a walk, i.e., the strongest component of the spectrum. In such cases, direct end-to-end closure creates a knot that usually coincides with the knot type that dominates the random closure spectrum. Interestingly, in a very small proportion of linear random walks, the knot type is not clearly defined. Such walks can be considered as residing in a border zone of the configuration space of two or more knot types. We also characterize the scaling behavior of linear random knots.

A new method to estimate the infilling of alluvial sediment of glacial valleys using a sloping local base level

A new method is used to estimate the volumes of sediments of glacial valleys. This method is based on the concept of sloping local base level and requires only a digital terrain model and the limits of the alluvial valleys as input data. The bedrock surface of the glacial valley is estimated by a progressive excavation of the digital elevation model (DEM) of the filled valley area. This is performed using an iterative routine that replaces the altitude of a point of the DEM by the mean value of its neighbors minus a fixed value. The result is a curved surface, quadratic in 2D. The bedrock surface of the Rhone Valley in Switzerland was estimated by this method using the free digital terrain model Shuttle Radar Topography Mission (SRTM) (~92 m resolution). The results obtained are in good agreement with the previous estimations based on seismic profiles and gravimetric modeling, with the exceptions of some particular locations. The results from the present method and those from the seismic interpretation are slightly different from the results of the gravimetric data. This discrepancy may result from the presence of large buried landslides in the bottom of the Rhone Valley.

Programming of marginal zone B-cell fate by basic Kruppel-like factor (BKLF/KLF3).

Splenic marginal zone (MZ) B cells are a lineage distinct from follicular and peritoneal B1 B cells. They are located next to the marginal sinus where blood is released. Here they pick up antigens and shuttle the load onto follicular dendritic cells inside the follicle. On activation, MZ B cells rapidly differentiate into plasmablasts secreting antibodies, thereby mediating humoral immune responses against blood-borne type 2 T-independent antigens. As Krüppel-like factors are implicated in cell differentiation/function in various tissues, we studied the function of basic Krüppel-like factor (BKLF/KLF3) in B cells. Whereas B-cell development in the bone marrow of KLF3-transgenic mice was unaffected, MZ B-cell numbers in spleen were increased considerably. As revealed in chimeric mice, this occurred cell autonomously, increasing both MZ and peritoneal B1 B-cell subsets. Comparing KLF3-transgenic and nontransgenic follicular B cells by RNA-microarray revealed that KLF3 regulates a subset of genes that was similarly up-regulated/down-regulated on normal MZ B-cell differentiation. Indeed, KLF3 expression overcame the lack of MZ B cells caused by different genetic alterations, such as CD19-deficiency or blockade of B-cell activating factor-receptor signaling, indicating that KLF3 may complement alternative nuclear factor-κB signaling. Thus, KLF3 is a driving force toward MZ B-cell maturation.

Avulsion fracture of peroneus longus tendon at the first metatarsal insertion: a case report : P16

Introduction: Isolated avulsion fracture at the plantar lateral base of the first metatarsal (M1) is very rare. Case report: A 35 year old overweight woman sustained an eversion strain of her right foot. Despite pain along M1 she was able to continue walking for three days before presenting to her family doctor. Swelling on the plantar aspect of the foot was noticed, there was also pain at eversion of the foot and extension of the ankle. Plain X-ray showed no abnormalities. A MRI showed minimal bone bruise at the basis of M1 and a partial rupture of the peroneus longus tendon at its insertion. The patient was allowed to walk with partial weight bearing with a soft ankle brace. After 6 months she presented at our hospital because of persistent pain. There was still a painful insertion of the peroneus longus but active plantarflexion of M1 was possible. Plain X-rays were poorly contributive except for a discrete flattening of the longitunal arch. CT-scan showed a non displaced fracture at the M1-basis. A protocol with partial weight-bearing in a short-leg cast and partial weight-bearing orthosis each for 6 weeks was unsuccessfully attempted. Therefore, an excision of the non healed bone fragment at the basis of M1 and a first tarsometatarsal joint arthrodesis were performed. Postoperatively the patient wore a partial weight-bearing short leg cast for 6 weeks followed by a weight-bearing short leg cast for 6 weeks with favourable outcome. Discussion: Initial internal fixation has been reported to lead to good results [1, 2]. In our case the conservative treatment failed and leaded to non union. At that time we considered as too risky (overweight) to excise the fragment and reattach the peroneus longus tendon. Therefore, we excised the fragment and fused the first tarsometatarsal joint. This procedure allowed, at least partially, to compensate for the function of the peroneus longus tendon. 1 Murakami T, et al. Avulsion fracture of the peroneus longus at the first metatarsal insertion: a case report. Br J Sports Med. 2004. 2 Kwak HY, and Bae SW. Isolated avulsion fracture at the plantar lateral base of the first metatarsal: a case report. Foot Ankle Int 2000.

Subclinical hypothyroidism and functional mobility in older adults.

BACKGROUND: Health risks associated with subclinical hypothyroidism in older adults are unclear. Our objective was to compare the functional mobility of people aged 70 to 79 years by thyroid function categorized by thyrotropin (TSH) level as euthyroid (>or=0.4 to <4.5 mIU/L), mild subclinical hypothyroid (>or=4.5 to <7.0 mIU/L), or moderate subclinical hypothyroid (>or=7.0 to <or=20.0 mIU/L with a normal free thyroxine level) cross-sectionally and over 2 years. METHODS: A total of 2290 community-dwelling residents participating in the year 2 clinic visit (July 1998-June 1999) of the Health, Aging, and Body Composition (Health ABC) Study, who had measured TSH level, had the capacity to walk 20 m unaided, and were not taking thyroid medication or had TSH levels consistent with hyperthyroidism or hypothyroidism. Main outcome measures included self-reported and performance-based measures of mobility (usual and rapid gait speed and endurance walking ability) assessed at study baseline (year 2) and 2 years later. RESULTS: In age- and sex-adjusted analyses, the mild subclinical hypothyroid group (vs the euthyroid group) demonstrated better mobility (faster mean usual and rapid gait speed [1.20 vs 1.15 m/s and 1.65 vs 1.56 m/s, respectively; P < .001] and had a higher percentage of those with good cardiorespiratory fitness and reported walking ease [39.2% vs 28.0% and 44.7% vs 36.5%, respectively; P < .001]). After 2 years, persons with mild subclinical hypothyroidism experienced a similar decline as the euthyroid group but maintained their mobility advantage. Persons with moderate subclinical hypothyroidism had similar mobility and mobility decline as the euthyroid group. CONCLUSION: Generally, well-functioning 70- to 79-year-old individuals with subclinical hypothyroidism do not demonstrate increased risk of mobility problems, and those with mild elevations in TSH level show a slight functional advantage.

Role of glutamate in neuron-glia metabolic coupling.

The coupling between synaptic activity and glucose utilization (neurometabolic coupling) is a central physiologic principle of brain function that has provided the basis for 2-deoxyglucose-based functional imaging with positron emission tomography. Approximately 10 y ago we provided experimental evidence that indicated a central role of glutamate signaling on astrocytes in neurometabolic coupling. The basic mechanism in neurometabolic coupling is the glutamate-stimulated aerobic glycolysis in astrocytes, such that the sodium-coupled reuptake of glutamate by astrocytes and the ensuing activation of the Na(+)-K(+) ATPase triggers glucose uptake and its glycolytic processing, which results in the release of lactate from astrocytes. Lactate can then contribute to the activity-dependent fueling of the neuronal energy demands associated with synaptic transmission. Analyses of this coupling have been extended in vivo and have defined the methods of coupling for inhibitory neurotransmission as well as its spatial extent in relation to the propagation of metabolic signals within the astrocytic syncytium. On the basis of a large body of experimental evidence, we proposed an operational model, "the astrocyte-neuron lactate shuttle." A series of results obtained by independent laboratories have provided further support for this model. This body of evidence provides a molecular and cellular basis for interpreting data that are obtained with functional brain imaging studies.

Rock Island Centennial Bridge, Final Report on Construction of the Mississippi River Bridge Between Rock Island, Illinois and Davenport, Iowa, 1945

The Rock Island Centennial Bridge spanning the Mississippi River between Rock Island, Illinois and Davenport, Iowa was opened to traffic on July 12, 1940. It is a thoroughly modern, four-lane highway bridge, adequate in every respect for present day high speed passenger and transport traffic. The structure is ideally situated to provide rapid transit between the business districts of Rock Island and Davenport and serves not only the local or shuttle traffic in the Tri-City Area, but also heavy through motor travel on U.S. Highways 67 and 150. The Centennial Bridge is notable in several respects. The main spans are box girder rib tied arches, a type rather unusual in America and permitting simplicity in design with pleasing appearance. The Centennial Bridge is the only bridge across the Mississippi providing for four lanes of traffic with separation of traffic in each direction. It is a toll bridge operating alongside a free bridge and has the lowest rates of toll of any toll bridge on the Mississippi River. It was financed entirely by the City of Rock Island with no obligation on the taxpayers; there was no federal or state participation in the financing. But perhaps the most outstanding feature of the new bridge is its great need. A few remarks on the communities served by the new structure, the services rendered, and some statistics on cross-river traffic in the Tri-City Area will emphasize the reasons for constructing the Centennial Bridge.

Contribution à l'étude neuroanatomique de systèmes enzymatiques impliqués dans le métabolisme énergétique cérébral

RESUME Il a longtemps été admis que le glucose était le principal, sinon le seul substrat du métabolisme énergétique cérébral. Néanmoins, des études récentes indiquent que dans des situations particulières, d'autres substrats peuvent être employés. C'est le cas des monocarboxylates (lactate et pyruvate principalement). Bien que la barrière hématoencéphalique soit peu perméable à ces molécules, elles deviennent néanmoins des substrats possibles si elles sont produites localement. Les deux systèmes enzymatiques pivots des voies glycolytiques et oxydatives sont la lactate déshydrogénase (LDH, EC 1.1.1.27) qui catalyse l'interconversion du pyruvate et du lactate et le complexe pyruvate déshydrogénase qui catalyse la conversion irréversible du pyruvate en acétyl-CoA qui entre dans la respiration mitochondriale. Nous avons étudié la localisation, tant régionale que cellulaire, des isoformes LDH-1, LDH-5 et PDHEla dans le cerveau du chat et dé l'homme au moyen de diverses techniques histologiques. Dans un premier temps, des investigations par hybridation in situ au moyen d'oligosondes marquées au 33P sur de coupes de cerveau de chat ont permis de montrer une différence de l'expression des enzymes à vocation oxydative (LDH-1 et PDHA1, le gène codant pour la protéine PDHEIa) par rapport à LDH-5, isoforme qui catalyse préférentiellement la formation de lactate. LDH-1 et PDHA 1 ont des distributions similaires et sont enrichies dans de nombreuses structures cérébrales, comme l'hippocampe, de nombreux noyaux thalamiques et des structures pontiques. Le cortex cérébral exhibe également une expression importante de LDH-1 et PDH. LDH-5 a par contre une expression largement plus diffuse à travers le cerveau, bien que l'on trouve néanmoins un enrichissement plus important dans l'hippocampe. Ces résultats sont en accord avec les observations que nous avons précédemment publiées chez le rongeur pour LDH-1 et LDH-5 (Laughton et collaborateurs, 2000). Des analyses par PCR en temps réel ont confirmé que dans certaines régions, LDH-1 est exprimée de façon nettement plus importante que LDH-5. Dans un deuxième temps, nous avons appliqué sur des coupes histologiques d'hippocampe et de cortex occipital humain post-mortem des anticorps monoclonaux spécifiques de l'isoforme LDH-5 et la sous-unité PDHela du complexe pyruvate déshydrogénase. Là aussi, les immunoréactions révèlent une ségrégation régionale mais aussi cellulaire des deux enzymes. Dans les deux régions étudiées, LDH-5 est localisée exclusivement dans les astrocytes. Dans le cortex occipital, la matière blanche et également la couche I corticale sont immunopositives pour LDH-5. Dans l'hippocampe, le CA4 et l'alveus exhibe l'immunomarquage le plus intense pour LDH-5. Seuls des neurones (à de rares exceptions quelques astrocytes) sont immunopositifs à l'anticorps monoclonal dirigé contre PDHela. La couche IV du cortex occipital présente la plus forte immunoréaction. Dans l'hippocampe, une immunoréactivité est observée dans le stratum granulosum et à travers la région CA1 jusqu'à la région CA3. L'ensemble de ces résultats montre une hétérogénéité métabolique dans le cerveau et étaye l'hypothèse "astrocyte-neurone lactate shuttle" (ANL5) (Bittar et collaborateurs, 1996; Magistretti et Pellerin, 1999) qui propose que les astrocytes fournissent aux neurones activés du lactate comme substrat alternatif de leur métabolisme énergétique. ABSTRACT For a long time now, glucose has been thought to be the main, if not the sole substrate for brain energy metabolism. Recent data nevertheless suggest that other molecules, such as monocarboxylates (lactate and pyruvate mainly) could be suitable substrates. Although monocarboxylates poorly cross the blood brain barrier (BBB), such substrates could replace glucose if produced locally. The two key enzymatic systems required for the use and production of these substats are lactate dehydrogenase (LDH; EC 1.1.1.27) that catalyses the interconversion of lactate and pyruvate and the pyruvate dehydrogenase complex that irreversibly funnels pyruvate towards the mitochondrial TCA cycle and oxydative phosphorylation. Our study consisted in localizing these different systems with various histochemical procedures in the cat brain and two regions, i.e. hippocampus and primary visual cortex, of the human brain. First, by means of in situ hybridization with 33P labeled oligoprobes, we have demonstrated that the more oxidative enzymes (LDH-1 and PDHA1, the gene coding for PDHEla) are highly expressed in a variety of feline brain structures. These structures include the hippocampus, various thalamic nuclei and the pons. The cerebral cortex exhibits also a high LDH-1 and PDHAl expression. On the other hand, LDH-5 expression is poorer and more diffuse, although the hippocampus does seem to have a higher expression. These fmdings are consistent with our previous observation of the expression of LDH1 and LDH-5 in the rodent brain (Laughton et al, 2000). Real-time PCR (TagMan tm) revealed that, in various regions, LDH-1 is effectively more highly expressed than LDH-5. In a second set of experiments, monoclonal antibodies to LDH-5 and PDHeIa were applied to cryostat sections of post-mortem human hippocampus and occipital cortex. These procedures revealed not only that the two enzymes have different regional distributions, but also distinct cellular localisation. LDH-5 immunoreactivity is solely observed in astrocytes. In the occipital cortex, the white matter and layer I are immunopositive. In the hippocampus, the alveus and CA4 show LDH-5 immunoréactivity. PDHeIa has been detected, with few exceptions, only in neurons. Layer IV of the occipital cortex was most immmunoreactive. In the hippocampus, PDHela immunoreactivity is noticed in the stratum granulosum and through CA 1 to CA3 areas. The overall observations made in this study show that there is a metabolic heterogeneity in the brain and our findings support the hypothesis of an astrocyte-neuron lactate shuttle (ANLS)(Bittar et al., 1996; Magistretti & Pellerin, 1999) where astrocytes export to active neurons lactate to fuel their energy demands.