Thomas Wulf

Spinal lordosis optimizes the requirements for a stable erect posture

BackgroundLordosis is the bending of the lumbar spine that gives the vertebral column of humans its characteristic ventrally convex curvature. Infants develop lordosis around the time when they acquire bipedal locomotion. Even macaques develop a lordosis when they are trained to walk bipedally. The aim of this study was to investigate why humans and some animals develop a lumbar lordosis while learning to walk bipedally.ResultsWe developed a musculoskeletal model of the lumbar spine, that includes an asymmetric, dorsally shifted location of the spinal column in the body, realistic moment arms, and physiological cross-sectional areas (PCSA) of the muscles as well as realistic force-length and force-velocity relationships. The model was used to analyze the stability of an upright body posture. According to our results, lordosis reduces the local joint torques necessary for an equilibrium of the vertebral column during an erect posture. At the same time lordosis increases the demands on the global muscles to provide stability.ConclusionsWe conclude that the development of a spinal lordosis is a compromise between the stability requirements of an erect posture and the necessity of torque equilibria at each spinal segment.

Phasic bursting pattern of postural responses may reflect internal dynamics: Simulation of trunk reflexes with a neural oscillator model

Postural responses are usually investigated as reflexes. Several trials are averaged, and trial-to-trial variations are interpreted as noise. Several studies providing single-trial data plots revealed oscillations that may be cancelled out in averaged time series. Variations between single trials may also be interpreted as a consequence of changed dynamic properties of the neural circuitries. Therefore, we propose a Matsuoka oscillator model to describe single-trial postural responses to external perturbations. The applicability of the model was demonstrated by a comparison between simulations and experimental electromyographic (EMG) data. Vertical force perturbations of durations 0.4 s and 0.2 s were applied via a handle to 10 subjects. Handle force was used as model input, and EMG data from the external oblique muscles was compared with simulation output. Model coefficients were optimized by a least-squares algorithm. The optimization produced a good similarity between simulation and experimental data with determination coefficients of r(2)=0.7 and greater. Furthermore, as a model validation, the model coefficients were used to predict other perturbation trials with similarities between predictions and respective EMG data of about r(2)=0.45, which was in the range of trial-to-trial EMG variability. The observed oscillations are assumed to originate from the central nervous system with changes in the neural circuitries between trials. Hence, the oscillations in single trial responses which are usually regarded as noise might be generated by the dynamics of a neural oscillator.

Disorder induced regular dynamics in oscillating lattices.

We explore the impact of weak disorder on the dynamics of classical particles in a periodically oscillating lattice. It is demonstrated that the disorder induces a hopping process from diffusive to regular motion; i.e., we observe the counterintuitive phenomenon that disorder leads to regular behavior. If the disorder is localized in a finite-sized part of the lattice, the described hopping causes initially diffusive particles to even accumulate in regular structures of the corresponding phase space. A hallmark of this accumulation is the emergence of pronounced peaks in the velocity distribution of particles that should be detectable in state of the art experiments, e.g., with cold atoms in optical lattices.

[Is there a correlation between back pain and stability of the lumbar spine in pregnancy? A model-based hypothesis].

During pregnancy approximately 50% of women suffer from low back pain (LBP), which significantly affects their everyday life. The pain could result in chronic insomnia, limit the pregnant women in their ability to work and produce a reduction of their physical activity. The etiology of the pain is still critically discussed and not entirely understood. In the literature different explanations for LBP are given and one of the most common reasons is the anatomical changes of the female body during pregnancy; for instance, there is an increase in the sagittal moments because of the enlarged uterus and fetus and the occurrence of hyperlordosis.The aim of this study was to describe how the anatomical changes in pregnant women affect the stability and the moments acting on the lumbar spine with the help of a simplified musculoskeletal model.A two-dimensional musculoskeletal model of the lumbar spine in the sagittal plane consisting of five lumbar vertebrae was developed. The model included five centres of rotation and three antagonistic pairs of paraspinal muscles. The concept of altered acting torques during pregnancy was explored by varying the geometrical arrangements. The situations non-pregnant, pregnant and pregnant with hyperlordosis were considered for the model-based approach. These simulations were done dependent on the stability of the erect posture and local countertorques of every lumbar segment.In spite of the simplicity of the model and the musculoskeletal arrangement it was possible to maintain equilibrium of the erect posture at every lumbar spinal segment with one minimum physiological cross-sectional area of all paraspinal muscles. The stability of the musculoskeletal system depends on the muscular activity of the paraspinal muscles and diminishing the muscular activity causes unstable lumbar segments.The relationship between the non-pregnant and the pregnant simulations demonstrated a considerable increase of acting segmental countertorques. Simulating an increased lordosis for the pregnant situation in the sagittal plane substantially reduced these acting countertorques and therefore the demand on the segmental muscles.It is assumed that hyperlordosis is a physiological adaptation to the anatomical changes during pregnancy to minimize the segmental countertorques and therefore the demand on the segmental muscles.Further, it can be expected that an enhanced muscle activity caused by selective activity of lumbar muscles increases the stability of the lumbar spine and may improve the situation with LBP during pregnancy.

Besteht ein Zusammenhang zwischen Rückenschmerz und der Stabilität der lumbalen Wirbelsäule in der Schwangerschaft

During pregnancy approximately 50% of women suffer from low back pain (LBP), which significantly affects their everyday life. The pain could result in chronic insomnia, limit the pregnant women in their ability to work and produce a reduction of their physical activity. The etiology of the pain is still critically discussed and not entirely understood. In the literature different explanations for LBP are given and one of the most common reasons is the anatomical changes of the female body during pregnancy; for instance, there is an increase in the sagittal moments because of the enlarged uterus and fetus and the occurrence of hyperlordosis.The aim of this study was to describe how the anatomical changes in pregnant women affect the stability and the moments acting on the lumbar spine with the help of a simplified musculoskeletal model.A two-dimensional musculoskeletal model of the lumbar spine in the sagittal plane consisting of five lumbar vertebrae was developed. The model included five centres of rotation and three antagonistic pairs of paraspinal muscles. The concept of altered acting torques during pregnancy was explored by varying the geometrical arrangements. The situations non-pregnant, pregnant and pregnant with hyperlordosis were considered for the model-based approach. These simulations were done dependent on the stability of the erect posture and local countertorques of every lumbar segment.In spite of the simplicity of the model and the musculoskeletal arrangement it was possible to maintain equilibrium of the erect posture at every lumbar spinal segment with one minimum physiological cross-sectional area of all paraspinal muscles. The stability of the musculoskeletal system depends on the muscular activity of the paraspinal muscles and diminishing the muscular activity causes unstable lumbar segments.The relationship between the non-pregnant and the pregnant simulations demonstrated a considerable increase of acting segmental countertorques. Simulating an increased lordosis for the pregnant situation in the sagittal plane substantially reduced these acting countertorques and therefore the demand on the segmental muscles.It is assumed that hyperlordosis is a physiological adaptation to the anatomical changes during pregnancy to minimize the segmental countertorques and therefore the demand on the segmental muscles.Further, it can be expected that an enhanced muscle activity caused by selective activity of lumbar muscles increases the stability of the lumbar spine and may improve the situation with LBP during pregnancy.

Analysis of interface conversion processes of ballistic and diffusive motion in driven superlattices.

We explore the nonequilibrium dynamics of noninteracting classical particles in a one-dimensional driven superlattice which is composed of domains exposed to different time-dependent forces. It is shown how the combination of directed transport and conversion processes from diffusive to ballistic motion causes strong correlations between velocity and phase for particles passing through a superlattice. A detailed understanding of the underlying mechanism allows us to tune the resulting velocity distributions at distinguished points in the superlattice by means of local variations of the applied driving force. As an intriguing application we present a scheme how initially diffusive particles can be transformed into a monoenergetic pulsed particle beam whose parameters such as its energy can be varied.

Dynamics of a thin liquid film with surface rigidity and spontaneous curvature.

The effect of rigid surfaces on the dynamics of thin liquid films that are amenable to the lubrication approximation is considered. It is shown that the Helfrich energy of the layer gives rise to additional terms in the time-evolution equations of the liquid film. The dynamics is found to depend on the absolute value of the spontaneous curvature, irrespective of its sign. Due to the additional terms, the effective surface-tension can be negative and an instability at intermediate wavelengths is observed. Furthermore, the dependence of the shape of a droplet on the bending rigidity as well as on the spontaneous curvature is discussed.

Freezing, accelerating, and slowing directed currents in real time with superimposed driven lattices.

We provide a generic scheme offering real-time control of directed particle transport using superimposed driven lattices. This scheme allows one to accelerate, slow, and freeze the transport on demand by switching one of the lattices subsequently on and off. The underlying physical mechanism hinges on a systematic opening and closing of channels between transporting and nontransporting phase space structures upon switching and exploits cantori structures which generate memory effects in the population of these structures. Our results should allow for real-time control of cold thermal atomic ensembles in optical lattices but might also be useful as a design principle for targeted delivery of molecules or colloids in optical devices.

Chaotic and ballistic dynamics in time-driven quasiperiodic lattices.

We investigate the nonequilibrium dynamics of classical particles in a driven quasiperiodic lattice based on the Fibonacci sequence. An intricate transient dynamics of extraordinarily long ballistic flights at distinct velocities is found. We argue how these transients are caused and can be understood by a hierarchy of block decompositions of the quasiperiodic lattice. A comparison to the cases of periodic and fully randomized lattices is performed.

Diffusion and transport in locally disordered driven lattices.

We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density distribution which even increases towards larger positions is shown, thus yielding a highly non-Gaussian particle density evolution. As the key underlying mechanism, we identify the conversion between different components of the unperturbed systems mixed phase space which is induced by the disorder. Based on the introduction of individual conversion rates between chaotic and regular components, a theoretical model is developed which correctly predicts the scaling of the particle density. The effect of disorder on the transport properties is studied where a significant enhancement of the transport for cases of localized disorder is shown, thereby contrasting strongly the merely weak modification of the transport for global disorder.