Traumatic brain injury (TBI) is a major health care concern that currently lacks any effective treatment. Despite promising outcomes from many preclinical studies, clinical evaluations have failed to identify effective pharmacological therapies, suggesting that the translational potential of preclinical models may require improvement. Rodents continue to be the most widely used species for preclinical TBI research. As most human TBIs result from impact to an intact skull, closed head injury (CHI) models are highly relevant, however, traditional CHI models suffer from extensive experimental variability that may be due to poor control over biomechanical inputs. Here we describe a novel CHI model called CHIMERA (Closed-Head Impact Model of Engineered Rotational Acceleration) that fully integrates biomechanical, behavioral, and neuropathological analyses. CHIMERA is distinct from existing neurotrauma model systems in that it uses a completely non-surgical procedure to precisely deliver impacts of prescribed dynamic characteristics to a closed skull while enabling kinematic analysis of unconstrained head movement. In this study, we characterized head kinematics as well as functional, neuropathological, and biochemical outcomes up to 14d following repeated TBI (rTBI) in adult C57BL/6 mice using CHIMERA.
Head kinematic analysis showed excellent repeatability over two closed head impacts separated at 24h. Injured mice showed significantly prolonged loss of righting reflex and displayed neurological, motor, and cognitive deficits along with anxiety-like behavior. Repeated TBI led to diffuse axonal injury with extensive microgliosis in white matter from 2-14d post-rTBI. Injured mouse brains also showed significantly increased levels of TNF-α and IL-1β and increased endogenous tau phosphorylation.
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Quantitative analysis of silver stain images. Silver stained images were quantified by calculating the % of region of interest (ROI) in the white matter tract area that was stained with silver. Bars indicate mean SD percent of ROI showing positive signal in sham and rTBI-induced animals in (A) olfactory nerve layer, (B) corpus callosum and (C) optic tract. Data were analyzed using two-way ANOVA followed by a Tukey post-hoc test. Cohort size: olfactory nerve layer: Sham (2d: N = 4, 7d: N = 5, 14d: N = 6); rTBI (2d: N = 8, 7d and 14 d: N = 5); corpus callosum: Sham (2d and 7d: N = 5, 14d: N = 6); rTBI (2d: N = 16, 7d: N = 5, and 14 d: N = 6); optic tract: Sham (2d: N = 5, and 7d: N = 4, 14d: N = 6); rTBI (2d: N = 17, 7d and 14d: N = 5). For all graphs, * indicates a significant rTBI effect within a particular time point and # indicates a significant time effect within rTBI group. **: p p p p p
Quantitative analysis of microglial response to rTBI. Bar graphs in the left column (A-D) indicate mean SD fractal dimension for microglial morphology in (A) olfactory nerve layer, (B) corpus callosum, (C) brachium of superior colliculus, and (D) optic tract. Bar graphs in the right column (E-H) show mean SD number of Iba-1 positive cells per mm2 in the same white matter regions. Data were analyzed by two-way ANOVA followed by a Tukey post-hoc test. Numbers inside the bars indicate sample size. For all graphs, * indicates a significant rTBI effect within a particular time point while # indicates a significant time effect within rTBI group. *: p p p p p p
The pneumatic impactor system includes an accumulator air tank, pressure regulator, digital pressure gauge, two-way solenoid valve, and trigger button. The pressure regulator and digital pressure gauge allow precise adjustment of air pressure to 0.1 psi (0.69 kPa), enabling accurate delivery of piston velocity and impact energy. Impact is induced with a 50 g free-floating chrome-coated steel piston whose trajectory is constrained to linear motion by a steel barrel. The piston barrel has an array of holes drilled near the muzzle end to vent air and equalize the pressure as the piston moves past them towards the impact site. The piston is accelerated by a controlled pulse of compressed air along the length of the barrel until it clears the venting holes.
The CHIMERA impactor was calibrated by measuring the exit velocity of the piston at various air pressures (0.5, 1, 1.5, 2, 3, 5, 7, and 10 psi) to determine the relationship between air pressure and piston velocity. Three measurements were taken at each pressure value. Each impact event was recorded by a high-speed video camera at 10,000 fps and tracked by video motion analysis software (TEMA Motion, Image Systems AB, Sweden). A 2nd order polynomial curve was used to fit the data. The r2 value was 0.9996 (Figure 9D). Using this curve, the desired impact velocity or energy can be independently interpolated. By choosing the appropriate air pressure, impacts of input energy ranging from 0.01 J to 1 J can be precisely generated.
For histological analyses, mice were anesthetized with an intraperitoneal injection of 150 mg/kg ketamine (Zoetis) and 20 mg/kg xylazine (Bayer) at 2, 7, or 14d after the second TBI, and brains were collected from perfused animals as described [46], except that 4% paraformaldehyde rather than neutral buffered formalin was used to post-fix hemisected brain tissue for histology. For biochemical analyses, brains were harvested as above at 6 h, 12 h, 2d, 7d, and 14d post-rTBI, longitudinally hemisected and rapidly frozen over dry ice and stored at -80C until analysis.
This work was supported by an operating grant from the Canadian Institutes of Health Research to CLW (MOP 123461). DRN was supported by an Alzheimer Society Research Program (ASRP) Doctoral Award (Alzheimer Society of Canada, -Society-Research-Program). WHC is supported by an ASRP Doctoral Award and Comissao Technica de Atribuicao de Bolsas para Estudos Pos-Graduados Macao. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. We are indebted to Dr. Peter Davies (Albert Einstein College of Medicine) for the kind gifts of tau antibodies.
Linear, delayed, sliding mode, high gain, Tau, homogeneity-based, extended and cubic observers are among several observer structures used for state estimation of linear and nonlinear systems. A linear observer structure is described in the following sections.
When the observer gain L \displaystyle L is high, the linear Luenberger observer converges to the system states very quickly. However, high observer gain leads to a peaking phenomenon in which initial estimator error can be prohibitively large (i.e., impractical or unsafe to use).[1] As a consequence, nonlinear high-gain observer methods are available that converge quickly without the peaking phenomenon. For example, sliding mode control can be used to design an observer that brings one estimated state's error to zero in finite time even in the presence of measurement error; the other states have error that behaves similarly to the error in a Luenberger observer after peaking has subsided. Sliding mode observers also have attractive noise resilience properties that are similar to a Kalman filter.[2][3]Another approach is to apply multi observer, that significantly improves transients and reduces observer overshoot. Multi-observer can be adapted to every system where high-gain observer is applicable.[4]
High gain, sliding mode and extended observers are the most common observers for nonlinear systems. To illustrate the application of sliding mode observers for nonlinear systems, first consider the no-input non-linear system:
One suggestion by Krener and Isidori[5] and Krener and Respondek[6] can be applied in a situation when there exists a linearizing transformation (i.e., a diffeomorphism, like the one used in feedback linearization) z = Φ ( x ) \displaystyle z=\Phi (x) such that in new variables the system equations read
Ciccarella, Dalla Mora, and Germani[9] obtained more advanced and general results, removing the need for a nonlinear transform and proving global asymptotic convergence of the estimated state to the true state using only simple assumptions on regularity.
As suggested by Drakunov,[10] a sliding mode observer can also be designed for a class of non-linear systems. Such an observer can be written in terms of original variable estimate x ^ \displaystyle \hat x and has the form
In this article, we present Biologically Annotated Neural Networks (BANNs), a nonlinear probabilistic framework for association mapping in genome-wide association (GWA) studies. BANNs are feedforward models with partially connected architectures that are based on biological annotations. This setup yields a fully interpretable neural network where the input layer encodes SNP-level effects, and the hidden layer models the aggregated effects among SNP-sets. We treat the weights and connections of the network as random variables with prior distributions that reflect how genetic effects manifest at different genomic scales. The BANNs software uses variational inference to provide posterior summaries which allow researchers to simultaneously perform (i) mapping with SNPs and (ii) enrichment analyses with SNP-sets on complex traits. Through simulations, we show that our method improves upon state-of-the-art association mapping and enrichment approaches across a wide range of genetic architectures. We then further illustrate the benefits of BANNs by analyzing real GWA data assayed in approximately 2,000 heterogenous stock of mice from the Wellcome Trust Centre for Human Genetics and approximately 7,000 individuals from the Framingham Heart Study. Lastly, using a random subset of individuals of European ancestry from the UK Biobank, we show that BANNs is able to replicate known associations in high and low-density lipoprotein cholesterol content. 2ff7e9595c
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