Quantitative Analysis of Kilohertz-Frequency Neurostimulation

Mainstream electrical stimulation therapies, e.g., spinal cord stimulation (SCS) and deep brain stimulation, use pulse trains that are delivered at rates no higher than 200 Hz. In recent years, stimulation of nerve fibers using kilohertz-frequency (KHF) signals has received increased attention due to the potential to penetrate deeper in the tissue and to the ability to block conduction of action potentials. As well, there are a growing number of clinical applications that use KHF waveforms, including transcutaneous electrical stimulation (TES) for overactive bladder and SCS for chronic pain. However, there is a lack of fundamental understanding of the mechanisms of action of KHF stimulation. The goal of this research was to analyze quantitatively KHF neurostimulation.

We implemented a multilayer volume conductor model of TES including dispersion and capacitive effects, and we validated the model with in vitro measurements in a phantom constructed from dispersive materials. We quantified the effects of frequency on the distribution of potentials and fiber excitation. We also quantified the effects of a novel transdermal amplitude modulated signal (TAMS) consisting of a non-zero offset sinusoidal carrier modulated by a square-pulse train. The model revealed that high-frequency signals generated larger potentials at depth than did low frequencies, but this did not translate into lower stimulation thresholds. Both TAMS and conventional rectangular pulses activated more superficial fibers in addition to the deeper, target fibers, and at no frequency did we observe an inversion of the strength-distance relationship. In addition, we performed in vivo experiments and applied direct stimulation to the sciatic nerve of cats and rats. We measured electromyogram and compound action potential activity evoked by pulses, TAMS and modified versions of TAMS in which we varied the amplitude of the carrier. Nerve fiber activation using TAMS showed no difference with respect to activation with conventional pulse for carrier frequencies of 20 kHz and higher, regardless the size of the carrier. Therefore, TAMS with carrier frequencies >20 kHz does not offer any advantage over conventional pulses, even with larger amplitudes of the carrier, and this has implications for design of waveforms for efficient and effective TES.

We developed a double cable model of a dorsal column (DC) fiber to quantify the responses of DC fibers to a novel KHF-SCS signal. We validated the model using in vivo recordings of the strength-duration relationship and the recovery cycle of single DC fibers. We coupled the fiber model to a model of SCS in human and applied the KHF-SCS signal to quantify thresholds for activation and conduction block for different fiber diameters at different locations in the DCs. Activation and block thresholds increased sharply as the fibers were placed deeper in the DCs, and decreased for larger diameter fibers. Activation thresholds were > 5 mA in all cases and up to five times higher than for conventional (~ 50 Hz) SCS. For fibers exhibiting persistent activation, the degree of synchronization of the firing activity to the KHF-SCS signal, as quantified using the vector strength, was low for a broad amplitude range, and the dissimilarity between the activities in pairs of fibers, as quantified using the spike time distance, was high and decreased for more closely positioned fibers. Conduction block thresholds were higher than 30 mA for all fiber diameters at any depth and well above the amplitudes used clinically (0.5 – 5 mA). KHF-SCS appears to activate few, large, superficial fibers, and the activated fibers fire asynchronously to the stimulation signal and to other activated fibers.

The outcomes of this work contribute to the understanding of KHF neurostimulation by establishing the importance of the tissue filtering properties on the distribution of potentials, assessing quantitatively the impact of KHF stimulation on nerve fiber excitation, and developing and validating a detailed model of a DC fiber to characterize the effects of KHF stimulation on DC axons. The results have implications for design of waveforms for efficient and effective nerve fiber stimulation in the peripheral and central nervous system.

Predicting Forest Responses to Changing Environmental Conditions

Forests change with changes in their environment based on the physiological responses of individual trees. These short-term reactions have cumulative impacts on long-term demographic performance. For a tree in a forest community, success depends on biomass growth to capture above- and belowground resources and reproductive output to establish future generations. Here we examine aspects of how forests respond to changes in moisture and light availability and how these responses are related to tree demography and physiology.

First we address the long-term pattern of tree decline before death and its connection with drought. Increasing drought stress and chronic morbidity could have pervasive impacts on forest composition in many regions. We use long-term, whole-stand inventory data from southeastern U.S. forests to show that trees exposed to drought experience multiyear declines in growth prior to mortality. Following a severe, multiyear drought, 72% of trees that did not recover their pre-drought growth rates died within 10 years. This pattern was mediated by local moisture availability. As an index of morbidity prior to death, we calculated the difference in cumulative growth after drought relative to surviving conspecifics. The strength of drought-induced morbidity varied among species and was correlated with species drought tolerance.

Next, we investigate differences among tree species in reproductive output relative to biomass growth with changes in light availability. Previous studies reach conflicting conclusions about the constraints on reproductive allocation relative to growth and how they vary through time, across species, and between environments. We test the hypothesis that canopy exposure to light, a critical resource, limits reproductive allocation by comparing long-term relationships between reproduction and growth for trees from 21 species in forests throughout the southeastern U.S. We found that species had divergent responses to light availability, with shade-intolerant species experiencing an alleviation of trade-offs between growth and reproduction at high light. Shade-tolerant species showed no changes in reproductive output across light environments.

Given that the above patterns depend on the maintenance of transpiration, we next developed an approach for predicting whole-tree water use from sap flux observations. Accurately scaling these observations to tree- or stand-levels requires accounting for variation in sap flux between wood types and with depth into the tree. We compared different models with sap flux data to test the hypotheses that radial sap flux profiles differ by wood type and tree size. We show that radial variation in sap flux is dependent on wood type but independent of tree size for a range of temperate trees. The best-fitting model predicted out-of-sample sap flux observations and independent estimates of sapwood area with small errors, suggesting robustness in new settings. We outline a method for predicting whole-tree water use with this model and include computer code for simple implementation in other studies.

Finally, we estimated tree water balances during drought with a statistical time-series analysis. Moisture limitation in forest stands comes predominantly from water use by the trees themselves, a drought-stand feedback. We show that drought impacts on tree fitness and forest composition can be predicted by tracking the moisture reservoir available to each tree in a mass balance. We apply this model to multiple seasonal droughts in a temperate forest with measurements of tree water use to demonstrate how species and size differences modulate moisture availability across landscapes. As trees deplete their soil moisture reservoir during droughts, a transpiration deficit develops, leading to reduced biomass growth and reproductive output.

This dissertation draws connections between the physiological condition of individual trees and their behavior in crowded, diverse, and continually-changing forest stands. The analyses take advantage of growing data sets on both the physiology and demography of trees as well as novel statistical techniques that allow us to link these observations to realistic quantitative models. The results can be used to scale up tree measurements to entire stands and address questions about the future composition of forests and the land’s balance of water and carbon.

Influence of Increased Human Presence in the Mills River Basin on Water Availability and Drought

Periods of drought and low streamflow can have profound impacts on both human and natural systems. People depend on a reliable source of water for numerous reasons including potable water supply and to produce economic value through agriculture or energy production. Aquatic ecosystems depend on water in addition to the economic benefits they provide to society through ecosystem services. Given that periods of low streamflow may become more extreme and frequent in the future, it is important to study the factors that control water availability during these times. In the absence of precipitation the slower hydrological response of groundwater systems will play an amplified role in water supply. Understanding the variability of the fraction of streamflow contribution from baseflow or groundwater during periods of drought provides insight into what future water availability may look like and how it can best be managed. The Mills River Basin in North Carolina is chosen as a case-study to test this understanding. First, obtaining a physically meaningful estimation of baseflow from USGS streamflow data via computerized hydrograph analysis techniques is carried out. Then applying a method of time series analysis including wavelet analysis can highlight signals of non-stationarity and evaluate the changes in variance required to better understand the natural variability of baseflow and low flows. In addition to natural variability, human influence must be taken into account in order to accurately assess how the combined system reacts to periods of low flow. Defining a combined demand that consists of both natural and human demand allows us to be more rigorous in assessing the level of sustainable use of a shared resource, in this case water. The analysis of baseflow variability can differ based on regional location and local hydrogeology, but it was found that baseflow varies from multiyear scales such as those associated with ENSO (3.5, 7 years) up to multi decadal time scales, but with most of the contributing variance coming from decadal or multiyear scales. It was also found that the behavior of baseflow and subsequently water availability depends a great deal on overall precipitation, the tracks of hurricanes or tropical storms and associated climate indices, as well as physiography and hydrogeology. Evaluating and utilizing the Duke Combined Hydrology Model (DCHM), reasonably accurate estimates of streamflow during periods of low flow were obtained in part due to the model’s ability to capture subsurface processes. Being able to accurately simulate streamflow levels and subsurface interactions during periods of drought can be very valuable to water suppliers, decision makers, and ultimately impact citizens. Knowledge of future droughts and periods of low flow in addition to tracking customer demand will allow for better management practices on the part of water suppliers such as knowing when they should withdraw more water during a surplus so that the level of stress on the system is minimized when there is not ample water supply.