Modeling the combined impacts of host plant resistance and biological control on the population dynamics of a major pest of wheat.

Background: Single-tool approaches often fail to provide effective long-term suppression of pest populations, such that combining several tools into an integrated management strategy is critical. Yet studies that harness the power of population models to explore the relative efficacy of various management tools and their combinations remain rare. We constructed a Leslie matrix population model to evaluate the potential of crop resistance, acting alone or in combination with biological control, to reduce populations of the wheat stem sawfly, Cephus cinctus Norton, a major pest of wheat in North America.

Mathematical Modeling of Neurostimulation for Post-traumatic Stress Disorder: A Migration Towards Multiscale Modeling to Assess Neural Response to Transcranial Direct Current Stimulation Treatments.

Post-traumatic stress disorder (PTSD) is a neurological condition which results from a traumatic experience caused by physiological shock or physical harm. Clinical results show success in combating the symptoms of PTSD with a neurostimulation treatment called transcranial Direct Current Stimulation (tDCS). Though effective, the underlying mechanisms of the treatment and its success are not fully comprehended.

Location Specificity of Transcranial Electrical Stimulation on Neuronal Electrodynamics: A Mathematical Model of Ion Channel Gating Dynamics and Ionic Flux Due to Neurostimulation.

Transcranial Electrical Stimulation (TES) continues to demonstrate success as a medical intervention for individuals with neurodegenerative diseases. Despite promising results from these neuromodulation modalities, the cellular level mechanisms by which this neurotherapy operates are not fully comprehended. In particular, the effects of TES on ion channel gating and ion transport are not known.

Multiscale coupling of transcranial direct current stimulation to neuron electrodynamics: modeling the influence of the transcranial electric field on neuronal depolarization.

Transcranial direct current stimulation (tDCS) continues to demonstrate success as a medical intervention for neurodegenerative diseases, psychological conditions, and traumatic brain injury recovery. One aspect of tDCS still not fully comprehended is the influence of the tDCS electric field on neural functionality. To address this issue, we present a mathematical, multiscale model that couples tDCS administration to neuron electrodynamics.