Cerebellar mechanisms for motor learning: Testing predictions from a large-scale computer simulation

The cerebellum is the major brain structure that contributes to our ability to improve movements through learning and experience. We have combined computer simulations with behavioral and lesion studies to investigate how modification of synaptic strength at two different sites within the cerebellum contributes to a simple form of motor learning—Pavlovian conditioning of the eyelid response. These studies are based on the wealth of knowledge about the intrinsic circuitry and physiology of the cerebellum and the straightforward manner in which this circuitry is engaged during eyelid conditioning. Thus, our simulations are constrained by the well-characterized synaptic organization of the cerebellum and further, the activity of cerebellar inputs during simulated eyelid conditioning is based on existing recording data. These simulations have allowed us to make two important predictions regarding the mechanisms underlying cerebellar function, which we have tested and confirmed with behavioral studies. The first prediction describes the mechanisms by which one of the sites of synaptic modification, the granule to Purkinje cell synapses (gr → Pkj) of the cerebellar cortex, could generate two time-dependent properties of eyelid conditioning—response timing and the ISI function. An empirical test of this prediction using small, electrolytic lesions of the cerebellar cortex revealed the pattern of results predicted by the simulations. The second prediction made by the simulations is that modification of synaptic strength at the other site of plasticity, the mossy fiber to deep nuclei synapses (mf → nuc), is under the control of Purkinje cell activity. The analysis predicts that this property should confer mf → nuc synapses with resistance to extinction. Thus, while extinction processes erase plasticity at the first site, residual plasticity at mf → nuc synapses remains. The residual plasticity at the mf → nuc site confers the cerebellum with the capability for rapid relearning long after the learned behavior has been extinguished. We confirmed this prediction using a lesion technique that reversibly disconnected the cerebellar cortex at various stages during extinction and reacquisition of eyelid responses. The results of these studies represent significant progress toward a complete understanding of how the cerebellum contributes to motor learning. ^

Mutual Information for Testing Gene-Environment Interaction

Despite current enthusiasm for investigation of gene-gene interactions and gene-environment interactions, the essential issue of how to define and detect gene-environment interactions remains unresolved. In this report, we define gene-environment interactions as a stochastic dependence in the context of the effects of the genetic and environmental risk factors on the cause of phenotypic variation among individuals. We use mutual information that is widely used in communication and complex system analysis to measure gene-environment interactions. We investigate how gene-environment interactions generate the large difference in the information measure of gene-environment interactions between the general population and a diseased population, which motives us to develop mutual information-based statistics for testing gene-environment interactions. We validated the null distribution and calculated the type 1 error rates for the mutual information-based statistics to test gene-environment interactions using extensive simulation studies. We found that the new test statistics were more powerful than the traditional logistic regression under several disease models. Finally, in order to further evaluate the performance of our new method, we applied the mutual information-based statistics to three real examples. Our results showed that P-values for the mutual information-based statistics were much smaller than that obtained by other approaches including logistic regression models.

Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.

Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.

Interim analysis of clinical trials: Simulation studies of fractional Brownian motion

Interim clinical trial monitoring procedures were motivated by ethical and economic considerations. Classical Brownian motion (Bm) techniques for statistical monitoring of clinical trials were widely used. Conditional power argument and α-spending function based boundary crossing probabilities are popular statistical hypothesis testing procedures under the assumption of Brownian motion. However, it is not rare that the assumptions of Brownian motion are only partially met for trial data. Therefore, I used a more generalized form of stochastic process, called fractional Brownian motion (fBm), to model the test statistics. Fractional Brownian motion does not hold Markov property and future observations depend not only on the present observations but also on the past ones. In this dissertation, we simulated a wide range of fBm data, e.g., H = 0.5 (that is, classical Bm) vs. 0.5< H <1, with treatment effects vs. without treatment effects. Then the performance of conditional power and boundary-crossing based interim analyses were compared by assuming that the data follow Bm or fBm. Our simulation study suggested that the conditional power or boundaries under fBm assumptions are generally higher than those under Bm assumptions when H > 0.5 and also matches better with the empirical results. ^

A simulation study of the effects of small center enrollment in multi -center clinical trials

Multi-center clinical trials are very common in the development of new drugs and devices. One concern in such trials, is the effect of individual investigational sites enrolling small numbers of patients on the overall result. Can the presence of small centers cause an ineffective treatment to appear effective when treatment-by-center interaction is not statistically significant?^ In this research, simulations are used to study the effect that centers enrolling few patients may have on the analysis of clinical trial data. A multi-center clinical trial with 20 sites is simulated to investigate the effect of a new treatment in comparison to a placebo treatment. Twelve of these 20 investigational sites are considered small, each enrolling less than four patients per treatment group. Three clinical trials are simulated with sample sizes of 100, 170 and 300. The simulated data is generated with various characteristics, one in which treatment should be considered effective and another where treatment is not effective. Qualitative interactions are also produced within the small sites to further investigate the effect of small centers under various conditions.^ Standard analysis of variance methods and the "sometimes-pool" testing procedure are applied to the simulated data. One model investigates treatment and center effect and treatment-by-center interaction. Another model investigates treatment effect alone. These analyses are used to determine the power to detect treatment-by-center interactions, and the probability of type I error.^ We find it is difficult to detect treatment-by-center interactions when only a few investigational sites enrolling a limited number of patients participate in the interaction. However, we find no increased risk of type I error in these situations. In a pooled analysis, when the treatment is not effective, the probability of finding a significant treatment effect in the absence of significant treatment-by-center interaction is well within standard limits of type I error. ^