Linear and Nonlinear Modeling of Cerebral Flow Autoregulation Using Principal Dynamic Modes

Cerebral Flow Autoregulation (CFA) is the dynamic process by which cerebral blood flow is maintained within physiologically acceptable bounds during fluctuations of cerebral perfusion pressure. The distinction is made with “static” flow autoregulation under steady-state conditions of perfusion pressure, described by the celebrated “autoregulatory curve” with a homeostatic plateau. This paper studies the dynamic CFA during changes in perfusion pressure, which attains critical clinical importance in patients with stroke, traumatic brain injury and neurodegenerative disease with a cerebrovascular component. Mathematical and computational models have been used to advance our quantitative understanding of dynamic CFA and to elucidate the underlying physiological mechanisms by analyzing the relation between beat-to-beat data of mean arterial blood pressure (viewed as input) and mean cerebral blood flow velocity(viewed as output) of a putative CFA system. Although previous studies have shown that the dynamic CFA process is nonlinear, most modeling studies to date have been linear. It has also been shown that blood CO2 tension affects the CFA process. This paper presents a nonlinear modeling methodology that includes the dynamic effects of CO2 tension (or its surrogate, end-tidal CO2) as a second input and quantifies CFA from short data-records of healthy human subjects by use of the modeling concept of Principal Dynamic Modes (PDMs). The PDMs improve the robustness of the obtained nonlinear models and facilitate their physiological interpretation. The results demonstrate the importance of including the CO2 input in the dynamic CFA study and the utility of nonlinear models under hypercapnic or hypocapnic conditions

Modeling convergent ON and OFF pathways in the early visual system

For understanding the computation and function of single neurons in sensory systems, one needs to investigate how sensory stimuli are related to a neuron’s response and which biological mechanisms underlie this relationship. Mathematical models of the stimulus–response relationship have proved very useful in approaching these issues in a systematic, quantitative way. A starting point for many such analyses has been provided by phenomenological “linear–nonlinear” (LN) models, which comprise a linear filter followed by a static nonlinear transformation. The linear filter is often associated with the neuron’s receptive field. However, the structure of the receptive field is generally a result of inputs from many presynaptic neurons, which may form parallel signal processing pathways. In the retina, for example, certain ganglion cells receive excitatory inputs from ON-type as well as OFF-type bipolar cells. Recent experiments have shown that the convergence of these pathways leads to intriguing response characteristics that cannot be captured by a single linear filter. One approach to adjust the LN model to the biological circuit structure is to use multiple parallel filters that capture ON and OFF bipolar inputs. Here, we review these new developments in modeling neuronal responses in the early visual system and provide details about one particular technique for obtaining the required sets of parallel filters from experimental data

Nonlinear multivariate analysis of dynamic cerebral blood flow regulation in humans

The dynamic relationship between cerebral blood flow, arterial blood pressure and arterial CO2 is studied using the Laguerre-Volterra network methodology for modeling multiple-input nonlinear systems. Spontaneous beat-to-beat cerebral blood flow velocity and mean arterial blood pressure fluctuations, as well as breath-to-breath end-tidal CO2 fluctuations are analyzed and the Volterra kernels of the system are obtained. It is found that, while pressure changes explain most of the blood flow velocity variations, the inclusion of end-tidal CO2 fluctuations as an additional input variable can improve the prediction accuracy of the model output considerably. The model includes also nonlinear interactions between pressure and end-tidal CO2 and their impact on cerebral blood flow

General Higgins of the Salvation Army, New South Wales, 27 April 1932, 2 [picture].

Title devised from accompanying information where available.; Part of the: Fairfax archive of glass plate negatives.; Fairfax number: 3334.; Also available online at: http://nla.gov.au/nla.pic-vn6220030; Acquired from Fairfax Media, 2012