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We study the interplay between analysis on manifolds with singularities and complex analysis and develop new structures of operators based on the Mellin transform and tools for iterating the calculus for higher singularities. We refer to the idea of interpreting boundary value problems (BVPs) in terms of pseudo-differential operators with a principal symbolic hierarchy, taking into account that BVPs are a source of cone and edge operator algebras. The respective cone and edge pseudo-differential algebras in turn are the starting point of higher corner theories. In addition there are deep relationships between corner operators and complex analysis. This will be illustrated by the Mellin symbolic calculus.
The increase in atmospheric methane concentration, which is determined by an imbalance between its sources and sinks, has led to investigations of the methane cycle in various environments. Aquatic environments are of an exceptional interest due to their active involvement in methane cycling worldwide and in particular in areas sensitive to climate change. Furthermore, being connected with each other aquatic environments form networks that can be spread on vast areas involving marine, freshwater and terrestrial ecosystems. Thus, aquatic systems have a high potential to translate local or regional environmental and subsequently ecosystem changes to a bigger scale. Many studies neglect this connectivity and focus on individual aquatic or terrestrial ecosystems.
The current study focuses on environmental controls of the distribution and aerobic oxidation of methane at the example of two aquatic ecosystems. These ecosystems are Arctic fresh water bodies and the Elbe estuary which represent interfaces between freshwater-terrestrial and freshwater-marine environments, respectively.
Arctic water bodies are significant atmospheric sources of methane. At the same time the methane cycle in Arctic water bodies is strongly affected by the surrounding permafrost environment, which is characterized by high amounts of organic carbon. The results of this thesis indicate that the methane concentrations in Arctic lakes and streams substantially vary between each other being regulated by local landscape features (e.g. floodplain area) and the morphology of the water bodies (lakes, streams and river). The highest methane concentrations were detected in the lake outlets and in a floodplain lake complex. In contrast, the methane concentrations measured at different sites of the Lena River did not vary substantially. The lake complexes in comparison to the Lena River, thus, appear as more individual and heterogeneous systems with a pronounced imprint of the surrounding soil environment. Furthermore, connected with each other Arctic aquatic environments have a large potential to transport methane from methane-rich water bodies such as streams and floodplain lakes to aquatic environments relatively poor in methane such as the Lena River.
Estuaries represent hot spots of oceanic methane emissions. Also, estuaries are intermediate zones between methane-rich river water and methane depleted marine water. Substantiated through this thesis at the example of the Elbe estuary, the methane distribution in estuaries, however, cannot entirely be described by the conservative mixing model i.e. gradual decrease from the freshwater end-member to the marine water end-member. In addition to the methane-rich water from the Elbe River mouth substantial methane input occurs from tidal flats, areas of significant interaction between aquatic and terrestrial environments. Thus, this study demonstrates the complex interactions and their consequences for the methane distribution within estuaries. Also it reveals how important it is to investigate estuaries at larger spatial scales.
Methane oxidation (MOX) rates are commonly correlated with methane concentrations. This was shown in previous research studies and was substantiated by the present thesis. In detail, the highest MOX rates in the Arctic water bodies were detected in methane-rich streams and in the floodplain area while in the Elbe estuary the highest MOX rates were observed at the coastal stations. However, in these bordering environments, MOX rates are affected not only via the regulation through methane concentrations. The MOX rates in the Arctic lakes were shown to be also dependent on the abundance and community composition of methane-oxidising bacteria (MOB), that in turn are controlled by local landscape features (regardless of the methane concentrations) and by the transport of MOB between neighbouring environments. In the Elbe estuary, the MOX rates in addition to the methane concentrations are largely affected by the salinity, which is in turn regulated by the mixing of fresh- and marine waters. The magnitude of the salinity impact on MOX rates thereby depends on the MOB community composition and on the rate of the salinity change.
This study extends our knowledge of environmental controls of methane distribution and aerobic methane oxidation in aquatic environments. It also illustrates how important it is to investigate complex ecosystems rather than individual ecosystems to better understand the functioning of whole biomes.
Earthquakes deform Earth's surface, building long-lasting topographic features and contributing to landscape and mountain formation.
However, seismic waves produced by earthquakes may also destabilize hillslopes, leading to large amounts of soil and bedrock moving downslope. Moreover, static deformation and shaking are suspected to damage the surface bedrock and therefore alter its future properties, affecting hydrological and erosional dynamics. Thus, earthquakes participate both in mountain building and stimulate directly or indirectly their erosion. Moreover, the impact of earthquakes on hillslopes has important implications for the amount of sediment and organic matter delivered to rivers, and ultimately to oceans, during episodic catastrophic seismic crises, the magnitude of life and property losses associated with landsliding, the perturbation and recovery of landscape properties after shaking, and the long term topographic evolution of mountain belts. Several of these aspects have been addressed recently through individual case studies but additional data compilation as well as theoretical or numerical modelling are required to tackle these issues in a more systematic and rigorous manner.
This dissertation combines data compilation of earthquake characteristics, landslide mapping, and seismological data interpretation with physically-based modeling in order to address how earthquakes impact on erosional processes and landscape evolution. Over short time scales (10-100 s) and intermediate length scales (10 km), I have attempted to improve our understanding and ability to predict the amount of landslide debris triggered by seismic shaking in epicentral areas. Over long time scales (1-100 ky) and across a mountain belt (100 km) I have modeled the competition between erosional unloading and building of topography associated with earthquakes. Finally, over intermediate time scales (1-10 y) and at the hillslope scale (0.1-1 km) I have collected geomorphological and seismological data that highlight persistent effects of earthquakes on landscape properties and behaviour.
First, I compiled a database on earthquakes that produced significant landsliding, including an estimate of the total landslide volume and area, and earthquake characteristics such as seismic moment and source depth. A key issue is the accurate conversion of landslide maps into volume estimates. Therefore I also estimated how amalgamation - when mapping errors lead to the bundling of multiple landslide into a single polygon - affects volume estimates from various earthquake-induced landslide inventories and developed an algorithm to automatically detect this artifact. The database was used to test a physically-based prediction of the total landslide area and volume caused by earthquakes, based on seismological scaling relationships and a statistical description of the landscape properties. The model outperforms empirical fits in accuracy, with 25 out of 40 cases well predicted, and allows interpretation of many outliers in physical terms. Apart from seismological complexities neglected by the model I found that exceptional rock strength properties or antecedent conditions may explain most outliers.
Second, I assessed the geomorphic effects of large earthquakes on landscape dynamics by surveying the temporal evolution of precipitation-normalized landslide rate. I found strongly elevated landslide rates following earthquakes that progressively recover over 1 to 4 years, indicating that regolith strength drops and recovers. The relaxation is clearly non-linear for at least one case, and does not seem to correlate with coseismic landslide reactivation, water table level increase or tree root-system recovery. I suggested that shallow bedrock is damaged by the earthquake and then heals on annual timescales. Such variations in ground strength must be translated into shallow subsurface seismic velocities that are increasingly surveyed with ambient seismic noise correlations. With seismic noise autocorrelation I computed the seismic velocity in the epicentral areas of three earthquakes where I constrained a change in landslide rate. We found similar recovery dynamics and timescales, suggesting that seismic noise correlation techniques could be further developed to meaningfully assess ground strength variations for landscape dynamics. These two measurements are also in good agreement with the temporal dynamics of post-seismic surface displacement measured by GPS. This correlation suggests that the surface healing mechanism may be driven by tectonic deformation, and that the surface regolith and fractured bedrock may behave as a granular media that slowly compacts as it is sheared or vibrated.
Last, I compared our model of earthquake-induced landsliding with a standard formulation of surface deformation caused by earthquakes to understand which parameters govern the competition between the building and destruction of topography caused by earthquakes. In contrast with previous studies I found that very large (Mw>8) earthquakes always increase the average topography, whereas only intermediate (Mw ~ 7) earthquakes in steep landscapes may reduce topography. Moreover, I illustrated how the net effect of earthquakes varies with depth or landscape steepness implying a complex and ambivalent role through the life of a mountain belt. Further I showed that faults producing a Gutenberg-Richter distribution of earthquake sizes, will limit topography over a larger range of fault sizes than faults producing repeated earthquakes with a characteristic size.
Rapidly uplifting coastlines are frequently associated with convergent tectonic boundaries, like subduction zones, which are repeatedly breached by giant megathrust earthquakes. The coastal relief along tectonically active realms is shaped by the effect of sea-level variations and heterogeneous patterns of permanent tectonic deformation, which are accumulated through several cycles of megathrust earthquakes. However, the correlation between earthquake deformation patterns and the sustained long-term segmentation of forearcs, particularly in Chile, remains poorly understood. Furthermore, the methods used to estimate permanent deformation from geomorphic markers, like marine terraces, have remained qualitative and are based on unrepeatable methods. This contrasts with the increasing resolution of digital elevation models, such as Light Detection and Ranging (LiDAR) and high-resolution bathymetric surveys.
Throughout this thesis I study permanent deformation in a holistic manner: from the methods to assess deformation rates, to the processes involved in its accumulation. My research focuses particularly on two aspects: Developing methodologies to assess permanent deformation using marine terraces, and comparing permanent deformation with seismic cycle deformation patterns under different spatial scales along the M8.8 Maule earthquake (2010) rupture zone. Two methods are developed to determine deformation rates from wave-built and wave-cut terraces respectively. I selected an archetypal example of a wave-built terrace at Santa Maria Island studying its stratigraphy and recognizing sequences of reoccupation events tied with eleven radiocarbon sample ages (14C ages). I developed a method to link patterns of reoccupation with sea-level proxies by iterating relative sea level curves for a range of uplift rates. I find the best fit between relative sea-level and the stratigraphic patterns for an uplift rate of 1.5 +- 0.3 m/ka.
A Graphical User Interface named TerraceM® was developed in Matlab®. This novel software tool determines shoreline angles in wave-cut terraces under different geomorphic scenarios. To validate the methods, I select test sites in areas of available high-resolution LiDAR topography along the Maule earthquake rupture zone and in California, USA. The software allows determining the 3D location of the shoreline angle, which is a proxy for the estimation of permanent deformation rates. The method is based on linear interpolations to define the paleo platform and cliff on swath profiles. The shoreline angle is then located by intersecting these interpolations. The
accuracy and precision of TerraceM® was tested by comparing its results with previous assessments, and through an experiment with students in a computer lab setting at the University
of Potsdam.
I combined the methods developed to analyze wave-built and wave-cut terraces to assess regional patterns of permanent deformation along the (2010) Maule earthquake rupture. Wave-built terraces are tied using 12 Infra Red Stimulated luminescence ages (IRSL ages) and shoreline angles in wave-cut terraces are estimated from 170 aligned swath profiles. The comparison of coseismic slip, interseismic coupling, and permanent deformation, leads to three areas of high permanent uplift, terrace warping, and sharp fault offsets. These three areas correlate with regions of high slip and low coupling, as well as with the spatial limit of at least eight historical megathrust ruptures (M8-9.5). I propose that the zones of upwarping at Arauco and Topocalma reflect changes in frictional properties of the megathrust, which result in discrete boundaries for the propagation of mega earthquakes.
To explore the application of geomorphic markers and quantitative morphology in offshore areas I performed a local study of patterns of permanent deformation inferred from hitherto unrecognized drowned shorelines at the Arauco Bay, at the southern part of the (2010) Maule earthquake rupture zone. A multidisciplinary approach, including morphometry, sedimentology, paleontology, 3D morphoscopy, and a landscape Evolution Model is used to recognize, map, and assess local rates and patterns of permanent deformation in submarine environments. Permanent deformation patterns are then reproduced using elastic models to assess deformation rates of an active submarine splay fault defined as Santa Maria Fault System. The best fit suggests a reverse structure with a slip rate of 3.7 m/ka for the last 30 ka. The register of land level changes during the earthquake cycle at Santa Maria Island suggest that most of the deformation may be accrued through splay fault reactivation during mega earthquakes, like the (2010) Maule event. Considering a recurrence time of 150 to 200 years, as determined from historical and geological observations, slip between 0.3 and 0.7 m per event would be required to account for the 3.7 m/ka millennial slip rate. However, if the SMFS slips only every ~1000 years, representing a few megathrust earthquakes, then a slip of ~3.5 m per event would be required to account for the long- term rate. Such event would be equivalent to a magnitude ~6.7 earthquake capable to generate a local tsunami.
The results of this thesis provide novel and fundamental information regarding the amount of permanent deformation accrued in the crust, and the mechanisms responsible for this accumulation at millennial time-scales along the M8.8 Maule earthquake (2010) rupture zone. Furthermore, the results of this thesis highlight the application of quantitative geomorphology and the use of repeatable methods to determine permanent deformation, improve the accuracy of marine terrace assessments, and estimates of vertical deformation rates in tectonically active coastal areas. This is vital information for adequate coastal-hazard assessments and to anticipate realistic earthquake and tsunami scenarios.
In the past, floods were basically managed by flood control mechanisms. The focus was set on the reduction of flood hazard. The potential consequences were of minor interest. Nowadays river flooding is increasingly seen from the risk perspective, including possible consequences. Moreover, the large-scale picture of flood risk became increasingly important for disaster management planning, national risk developments and the (re-) insurance industry. Therefore, it is widely accepted that risk-orientated flood management ap-proaches at the basin-scale are needed. However, large-scale flood risk assessment methods for areas of several 10,000 km² are still in early stages. Traditional flood risk assessments are performed reach wise, assuming constant probabilities for the entire reach or basin. This might be helpful on a local basis, but where large-scale patterns are important this approach is of limited use. Assuming a T-year flood (e.g. 100 years) for the entire river network is unrealistic and would lead to an overestimation of flood risk at the large scale. Due to the lack of damage data, additionally, the probability of peak discharge or rainfall is usually used as proxy for damage probability to derive flood risk. With a continuous and long term simulation of the entire flood risk chain, the spatial variability of probabilities could be consider and flood risk could be directly derived from damage data in a consistent way.
The objective of this study is the development and application of a full flood risk chain, appropriate for the large scale and based on long term and continuous simulation. The novel approach of ‘derived flood risk based on continuous simulations’ is introduced, where the synthetic discharge time series is used as input into flood impact models and flood risk is directly derived from the resulting synthetic damage time series.
The bottleneck at this scale is the hydrodynamic simu-lation. To find suitable hydrodynamic approaches for the large-scale a benchmark study with simplified 2D hydrodynamic models was performed. A raster-based approach with inertia formulation and a relatively high resolution of 100 m in combination with a fast 1D channel routing model was chosen.
To investigate the suitability of the continuous simulation of a full flood risk chain for the large scale, all model parts were integrated into a new framework, the Regional Flood Model (RFM). RFM consists of the hydrological model SWIM, a 1D hydrodynamic river network model, a 2D raster based inundation model and the flood loss model FELMOps+r. Subsequently, the model chain was applied to the Elbe catchment, one of the largest catchments in Germany. For the proof-of-concept, a continuous simulation was per-formed for the period of 1990-2003. Results were evaluated / validated as far as possible with available observed data in this period. Although each model part introduced its own uncertainties, results and runtime were generally found to be adequate for the purpose of continuous simulation at the large catchment scale.
Finally, RFM was applied to a meso-scale catchment in the east of Germany to firstly perform a flood risk assessment with the novel approach of ‘derived flood risk assessment based on continuous simulations’. Therefore, RFM was driven by long term synthetic meteorological input data generated by a weather generator. Thereby, a virtual time series of climate data of 100 x 100 years was generated and served as input to RFM providing subsequent 100 x 100 years of spatially consistent river discharge series, inundation patterns and damage values. On this basis, flood risk curves and expected annual damage could be derived directly from damage data, providing a large-scale picture of flood risk. In contrast to traditional flood risk analysis, where homogenous return periods are assumed for the entire basin, the presented approach provides a coherent large-scale picture of flood risk. The spatial variability of occurrence probability is respected. Additionally, data and methods are consistent. Catchment and floodplain processes are repre-sented in a holistic way. Antecedent catchment conditions are implicitly taken into account, as well as physical processes like storage effects, flood attenuation or channel–floodplain interactions and related damage influencing effects. Finally, the simulation of a virtual period of 100 x 100 years and consequently large data set on flood loss events enabled the calculation of flood risk directly from damage distributions. Problems associated with the transfer of probabilities in rainfall or peak runoff to probabilities in damage, as often used in traditional approaches, are bypassed.
RFM and the ‘derived flood risk approach based on continuous simulations’ has the potential to provide flood risk statements for national planning, re-insurance aspects or other questions where spatially consistent, large-scale assessments are required.
Flood generation at the scale of large river basins is triggered by the interaction of the hydrological pre-conditions and the meteorological event conditions at different spatial and temporal scales. This interaction controls diverse flood generating processes and results in floods varying in magnitude and extent, duration as well as socio-economic consequences. For a process-based understanding of the underlying cause-effect relationships, systematic approaches are required. These approaches have to cover the complete causal flood chain, including the flood triggering meteorological event in combination with the hydrological (pre-)conditions in the catchment, runoff generation, flood routing, possible floodplain inundation and finally flood losses.
In this thesis, a comprehensive probabilistic process-based understanding of the causes and effects of floods is advanced. The spatial and temporal dynamics of flood events as well as the geophysical processes involved in the causal flood chain are revealed and the systematic interconnections within the flood chain are deciphered by means of the classification of their associated causes and effects. This is achieved by investigating the role of the hydrological pre-conditions and the meteorological event conditions with respect to flood occurrence, flood processes and flood characteristics as well as their interconnections at the river basin scale.
Broadening the knowledge about flood triggers, which up to now has been limited to linking large-scale meteorological conditions to flood occurrence, the influence of large-scale pre-event hydrological conditions on flood initiation is investigated. Using the Elbe River basin as an example, a classification of soil moisture, a key variable of pre-event conditions, is developed and a probabilistic link between patterns of soil moisture and flood occurrence is established. The soil moisture classification is applied to continuously simulated soil moisture data which is generated using the semi-distributed conceptual rainfall-runoff model SWIM. Applying successively a principal component analysis and a cluster analysis, days of similar soil moisture patterns are identified in the period November 1951 to October 2003.
The investigation of flood triggers is complemented by including meteorological conditions described by a common weather pattern classification that represents the main modes of atmospheric state variability. The newly developed soil moisture classification thereby provides the basis to study the combined impact of hydrological pre-conditions and large-scale meteorological event conditions on flood occurrence at the river basin scale.
A process-based understanding of flood generation and its associated probabilities is attained by classifying observed flood events into process-based flood types such as snowmelt floods or long-rain floods. Subsequently, the flood types are linked to the soil moisture and weather patterns. Further understanding of the processes is gained by modeling of the complete causal flood chain, incorporating a rainfall-runoff model, a 1D/2D hydrodynamic model and a flood loss model. A reshuffling approach based on weather patterns and the month of their occurrence is developed to generate synthetic data fields of meteorological conditions, which drive the model chain, in order to increase the flood sample size. From the large number of simulated flood events, the impact of hydro-meteorological conditions on various flood characteristics is detected through the analysis of conditional cumulative distribution functions and regression trees.
The results show the existence of catchment-scale soil moisture patterns, which comprise of large-scale seasonal wetting and drying components as well as of smaller-scale variations related to spatially heterogeneous catchment processes. Soil moisture patterns frequently occurring before the onset of floods are identified. In winter, floods are initiated by catchment-wide high soil moisture, whereas in summer the flood-initiating soil moisture patterns are diverse and the soil moisture conditions are less stable in time. The combined study of both soil moisture and weather patterns shows that the flood favoring hydro-meteorological patterns as well as their interactions vary seasonally. In the analysis period, 18 % of the weather patterns only result in a flood in the case of preceding soil saturation. The classification of 82 past events into flood types reveals seasonally varying flood processes that can be linked to hydro-meteorological patterns. For instance, the highest flood potential for long-rain floods is associated with a weather pattern that is often detected in the presence of so-called ‘Vb’ cyclones. Rain-on-snow and snowmelt floods are associated with westerly and north-westerly wind directions. The flood characteristics vary among the flood types and can be reproduced by the applied model chain. In total, 5970 events are simulated. They reproduce the observed event characteristics between September 1957 and August 2002 and provide information on flood losses. A regression tree analysis relates the flood processes of the simulated events to the hydro-meteorological (pre-)event conditions and highlights the fact that flood magnitude is primarily controlled by the meteorological event, whereas flood extent is primarily controlled by the soil moisture conditions.
Describing flood occurrence, processes and characteristics as a function of hydro-meteorological patterns, this thesis is part of a paradigm shift towards a process-based understanding of floods. The results highlight that soil moisture patterns as well as weather patterns are not only beneficial to a probabilistic conception of flood initiation but also provide information on the involved flood processes and the resulting flood characteristics.
Prevalence of Achilles tendinopathy increases with age, leading to a weaker tendon with predisposition to rupture. Previous studies, investigating Achilles tendon (AT) properties, are restricted to standardized isometric conditions. Knowledge regarding the influence of age and pa-thology on AT response under functional tasks remains limited. Therefore, the aim of the thesis was to investigate the influence of age and pathology on AT properties during a single-leg vertical jump.
Healthy children, asymptomatic adults and patients with Achilles tendinopathy participated. Ultrasonography was used to assess AT-length, AT-cross-sectional area and AT-elongation. The reliability of the methodology used was evaluated both Intra- and inter-rater at rest and at maximal isometric plantar-flexion contraction and was further implemented to investigate tendon properties during functional task. During the functional task a single-leg vertical jump on a force plate was performed while simultaneously AT elongation and vertical ground reaction forces were recorded. AT compliance [mm/N] (elongation/force) and AT strain [%] (elongation/length) were calculated. Differences between groups were evaluated with respect to age (children vs. adults) and pathology (asymptomatic adults vs. patients).
Good to excellent reliability with low levels of variability was achieved in the assessment of AT properties. During the jumps AT elongation was found to be statistical significant higher in children. However, no statistical significant difference was found for force among the groups. AT compliance and strain were found to be statistical significant higher only in children. No significant differences were found between asymptomatic adults and patients with tendinopathy.
The methodology used to assess AT properties is reliable, allowing its implementation into further investigations. Higher AT-compliance in children might be considered as a protective factor against load-related injuries. During functional task, when higher forces are acting on the AT, tendinopathy does not result in a weaker tendon.
During the last decade, high intensity interval training (HIIT) has been used as an alternative to endurance (END) exercise, since it requires less time to produce similar physiological adaptations. Previous literature has focused on HIIT changes in aerobic metabolism and cardiorespiratory fitness, however, there are currently no studies focusing on its neuromuscular adaptations.
Therefore, this thesis aimed to compare the neuromuscular adaptations of both HIIT and END after a two-week training intervention, by using a novel technology called high-density surface electromyography (HDEMG) motor unit decomposition. This project consisted in two experiments, where healthy young men were recruited (aged between 18 to 35 years). In experiment one, the reliability of HDEMG motor unit variables (mean discharge rate, peak-to-peak amplitude, conduction velocity and discharge rate variability) was tested (Study 1), a new method to track the same motor units longitudinally was proposed (Study 2), and the level of low (<5Hz) and high (>5Hz) frequency motor unit coherence between vastus medialis (VM) and lateralis (VL) knee extensor muscles was measured (Study 4). In experiment two, a two-week HIIT and END intervention was conducted where cardiorespiratory fitness parameters (e.g. peak oxygen uptake) and motor unit variables from the VM and VL muscles were assessed pre and post intervention (Study 3).
The results showed that HDEMG is reliable to monitor changes in motor unit activity and also allows the tracking of the same motor units across different testing sessions. As expected, both HIIT and END improved cardiorespiratory fitness parameters similarly. However, the neuromuscular adaptations of both types of training differed after the intervention, with HIIT showing a significant increase in knee extensor muscle strength that was accompanied by increased VM and VL motor unit discharge rates and HDEMG amplitude at the highest force levels [(50 and 70% of the maximum voluntary contraction force (MVC)], while END training induced a marked increase in time to task failure at lower force levels (30% MVC), without any influence on HDEMG amplitude and discharge rates. Additionally, the results showed that VM and VL muscles share most of their synaptic input since they present a large amount of low and high frequency motor unit coherence, which can explain the findings of the training intervention where both muscles showed similar changes in HDEMG amplitude and discharge rates.
Taken together, the findings of the current thesis show that despite similar improvements in cardiopulmonary fitness, HIIT and END induced opposite adjustments in motor unit behavior. These results suggest that HIIT and END show specific neuromuscular adaptations, possibly related to their differences in exercise load intensity and training volume.
Background: Low back pain (LBP) is one of the world wide leading causes of limited activity and disability. Impaired motor control has been found to be one of the possible factors related to the development or persistence of LBP. In particularly, motor control strategies seemed to be altered in situations requiring reactive responses of the trunk counteracting sudden external forces. However, muscular responses were mostly assessed in (quasi) static testing situations under simplified laboratory conditions. Comprehensive investigations in motor control strategies during dynamic everyday situations are lacking. The present research project aimed to investigate muscular compensation strategies following unexpected gait perturbations in people with and without LBP. A novel treadmill stumbling protocol was tested for its validity and reliability to provoke muscular reflex responses at the trunk and the lower extremities (study 1). Thereafter, motor control strategies in response to sudden perturbations were compared between people with LBP and asymptomatic controls (CTRL) (study 2). In accordance with more recent concepts of motor adaptation to pain, it was hypothesized that pain may have profound consequences on motor control strategies in LBP. Therefore, it was investigated whether differences in compensation strategies were either consisting of changes local to the painful area at the trunk, or also being present in remote areas such as at the lower extremities.
Methods: All investigations were performed on a custom build split-belt treadmill simulating trip-like events by unexpected rapid deceleration impulses (amplitude: 2 m/s; duration: 100 ms; 200 ms after heel contact) at 1m/s baseline velocity. A total number of 5 (study 1) and 15 (study 2) right sided perturbations were applied during walking trials. Muscular activities were assessed by surface electromyography (EMG), recorded at 12 trunk muscles and 10 (study 1) respectively 5 (study 2) leg muscles. EMG latencies of muscle onset [ms] were retrieved by a semi-automatic detection method. EMG amplitudes (root mean square (RMS)) were assessed within 200 ms post perturbation, normalized to full strides prior to any perturbation [RMS%]. Latency and amplitude investigations were performed for each muscle individually, as well as for pooled data of muscles grouped by location. Characteristic pain intensity scores (CPIS; 0-100 points, von Korff) based on mean intensity ratings reported for current, worst and average pain over the last three months were used to allocate participants into LBP (≥30 points) or CTRL (≤10 points). Test-retest reproducibility between measurements was determined by a compilation of measures of reliability. Differences in muscular activities between LBP and CTRL were analysed descriptively for individual muscles; differences based on grouped muscles were statistically tested by using a multivariate analysis of variance (MANOVA, α =0.05).
Results: Thirteen individuals were included into the analysis of study 1. EMG latencies revealed reflex muscle activities following the perturbation (mean: 89 ms). Respective EMG amplitudes were on average 5-fold of those assessed in unperturbed strides, though being characterized by a high inter-subject variability. Test-retest reliability of muscle latencies showed a high reproducibility, both for muscles at the trunk and legs. In contrast, reproducibility of amplitudes was only weak to moderate for individual muscles, but increased when being assessed as a location specific outcome summary of grouped muscles. Seventy-six individuals were eligible for data analysis in study 2. Group allocation according to CPIS resulted in n=25 for LBP and n=29 for CTRL. Descriptive analysis of activity onsets revealed longer delays for all muscles within LBP compared to CTRL (trunk muscles: mean 10 ms; leg muscles: mean 3 ms). Onset latencies of grouped muscles revealed statistically significant differences between LBP and CTRL for right (p=0.009) and left (p=0.007) abdominal muscle groups. EMG amplitude analysis showed a high variability in activation levels between individuals, independent of group assignment or location. Statistical testing of grouped muscles indicated no significant difference in amplitudes between LBP and CTRL.
Discussion: The present research project could show that perturbed treadmill walking is suitable to provoke comprehensive reflex responses at the trunk and lower extremities, both in terms of sudden onsets and amplitudes of reflex activity. Moreover, it could demonstrate that sudden loadings under dynamic conditions provoke an altered reflex timing of muscles surrounding the trunk in people with LBP compared to CTRL. In line with previous investigations, compensation strategies seemed to be deployed in a task specific manner, with differences between LBP and CTRL being evident predominately at ventral sides. No muscular alterations exceeding the trunk could be found when being assessed under the automated task of locomotion. While rehabilitation programs tailored towards LBP are still under debate, it is tempting to urge the implementation of dynamic sudden loading incidents of the trunk to enhance motor control and thereby to improve spinal protection. Moreover, in respect to the consistently observed task specificity of muscular compensation strategies, such a rehabilitation program should be rich in variety.
BACKGROUND: The etiology of low back pain (LBP), one of the most prevalent and costly diseases of our time, is accepted to be multi-causal, placing functional factors in the focus of research. Thereby, pain models suggest a centrally controlled strategy of trunk stiffening in LBP. However, supporting biomechanical evidence is mostly limited to static measurements during maximum voluntary contractions (MVC), probably influenced by psychological factors in LBP. Alternatively, repeated findings indicate that the neuromuscular efficiency (NME), characterized by the strength-to-activation relationship (SAR), of lower back muscles is impaired in LBP. Therefore, a dynamic SAR protocol, consisting of normalized trunk muscle activation recordings during submaximal loads (SMVC) seems to be relevant. This thesis aimed to investigate the influence of LBP on the NME and activation pattern of trunk muscles during dynamic trunk extensions.
METHODS: The SAR protocol consisted of an initial MVC reference trial (MVC1), followed by SMVCs at 20, 40, 60 and 80% of MVC1 load. An isokinetic trunk dynamometer (Con-Trex TP, ROM: 45° flexion to 10° extension, velocity: 45°/s) and a trunk surface EMG setup (myon, up to 12 leads) was used. Extension torque output [Nm] and muscular activation [V] were assessed in all trials. Finally, another MVC trial was performed (MVC2) for reliability analysis. For SAR evaluation the SMVC trial values were normalized [%MVC1] and compared inter- and intra-individually.
The methodical validity of the approach was tested in an isometric SAR single-case pilot study (S1a: N = 2, female LBP patient vs. healthy male). In addition, the validity of the MVC reference method was verified by comparing different contraction modes (S1b: N = 17, healthy individuals). Next, the isokinetic protocol was validated in terms of content for its applicability to display known physiological differences between sexes in a cross-sectional study (S2: each n = 25 healthy males/females). Finally, the influence of acute pain on NME was investigated longitudinally by comparing N = 8 acute LBP patients with the retest after remission of pain (S3). The SAR analysis focused on normalized agonistic extensor activation and abdominal and synergistic extensor co-activation (t-tests, ANOVA, α = .05) as well as on reliability of MVC1/2 outcomes.
RESULTS: During the methodological validation of the protocol (S1a), the isometric SAR was found to be descriptively different between individuals. Whereas torque output was highest during eccentric MVC, no relevant difference in peak EMG activation was found between contraction modes (S1b). The isokinetic SAR sex comparison (S2), though showing no significant overall effects, revealed higher normalized extensor activation at moderate submaximal loads in females (13 ± 4%), primarily caused by pronounced thoracic activation. Similarly, co-activation analysis resulted in significantly higher antagonistic activation at moderate loads compared to males (33 ± 9%). During intra-individual analysis of SAR in LBP patients (S3), a significant effect of pain status on the SAR has been identified, manifesting as increased normalized EMG activation of extensors during acute LBP (11 ± 8%) particularly at high load. Abdominal co-activation tended to be elevated (27 ± 11%) just as the thoracic extensor parts seemed to take over proportions of lumbar activation. All together, the M. erector spinae behaviour during the SAR protocol was rather linear with the tendency to rise exponentially during high loads. For the level of normalized EMG activation during SMVCs, a clear increasing trend from healthy males to females over to non-acute and acute LBP patients was discovered. This was associated by elevated antagonistic activation and a shift of synergistic towards lumbar extensor activation. The MVC data revealed overall good reliability, with clearly higher variability during acute LBP.
DISCUSSION: The present thesis demonstrates that the NME of lower back muscles is impaired in LBP patients, especially during an acute pain episode. A new dynamic protocol has been developed that makes it possible to display the underlying SAR using normalized trunk muscle EMG during submaximal isokinetic loads. The protocol shows promise as a biomechanical tool for diagnostic analysis of NME in LBP patients and monitoring of rehabilitation progress. Furthermore, reliability not of maximum strength but rather of peak EMG of MVC measurements seems to be decreased in LBP patients. Meanwhile, the findings of this thesis largely substantiate the assumptions made by the recently presented ‘motor adaptation to pain’ model, suggesting a pain-related intra- and intermuscular activation redistribution affecting movement and stiffness of the trunk. Further research is needed to distinguish the grade of NME impairment between LBP subgroups.