Pragmatism Research Philosophy
Brains are characterized by a vast number of elements [1], ultra-high structural complexity, and massive connectivity, all of which change and evolve in response to experience. Information related to sensors and effectors is processed in a both parallel and recurrent hierarchical fashion. The connectivity between different hierarchical levels is bidirectional, and its specificity and effectiveness are continuously controlled by specific associational and neuromodulatory centers. Typically, any observed brain activity is probabilistic, and its evolution is initial-condition dependent. In mathematical physics, such structures are termed Complex Dynamic Systems (CDS), with the term “complex” not meaning “complicated” [2]. Instead, it implies that the behavior of the whole is “emerging”, and it cannot be reduced to, or predicted from, the activity of the system’s components.
CDS are commonly characterized by sequential epochs of stability, self-organized criticalities, and occasionally so-called catastrophic states, with “catastrophic” denoting a state ranging from an extremely unusual regime to one which may even destroy the system. The phase transitions of CDS, e.g. from stability to self-organized criticality, have been the subject of numerous studies, demonstrating that criticalities may potentially be predicted, as they often emerge inside the transition epoch between stability and catastrophe domains, having characteristic dynamic patterns (e.g. oscillations).
Systems such as earthquakes, volcanic eruptions, weather/climate evolution, social communication, market crashes, or genetics and epidemics have long been studied intensively using this CDS approach, and these studies have undoubtedly advanced our ability to predict “random-looking” evolution paths.
By sharp contrast, the application of CDS in systems neuroscience has been very limited and rather “selective”, mostly encountered in human studies using almost exclusively neuroimaging techniques, such as various forms of functional magnetic resonance imaging (MRI). Yet, neural activity in such cases can only be indirectly estimated, mainly reflecting changes in metabolic energy demands. Such measures cannot differentiate between input/output-specific processing and neuromodulation, between bottom-up and top-down signals, and they may occasionally confuse excitation and inhibition (Logothetis, 2008). Fathoming into the states of excitation-inhibition networks (EIN), that integrate signals from glutamatergic and GABAergic neurons in a complex dynamical manner, can only be best accomplished by combining the electrophysiology-fMRI with measurements of neurotransmitters.
Notably, the brain is an example par excellence of an adaptive CDS, with a capacity to change its environment-brought-forth reorganization under the influence of feedback mechanisms, including generative perception and various types of memory, all providing with resilience in the face of perturbation. This in turn implies that understanding and modelling brain-networks as adaptive CDS, requires concurrent monitoring of different brain-domains, as well as tracking of changes in their effective dynamic connectivity. One such approach is the aforementioned concurrent combination of functional MRI with invasive techniques that can directly assess the brain’s electrical and neurochemical activity, albeit correct interpretation of the signals also requires identification of brain structure-specific hemodynamic responses, which could permit the estimation of neural signals from deconvolved fMRI time series.
A multimodal approach is more necessary than ever for the study of the brain’s function and dysfunction. Such an approach must include further improvements of the MRI technology and its combination with other invasive techniques that directly assess the brain’s electrical activity, but it also requires a profound understanding of the neural basis of the brain encephalic, structure-specific hemodynamic responses, as well as of the models permitting the estimation of neural signals from the fMRI time series. Strikingly classic system identification techniques fall short when dealing with complex ensembles, such as those comprised of neural, glial, and vascular components. More so, when the neurovascular ensemble of some brain structure appears to have strong feedback loops, falling into the category of “non-causal” systems (i.e. Impulse Response Functions with non-zero values in the range of negative lags).
In successfully combined neurophysiology and fMRI experiments, one can not only fathom into the neural origin of the up- and down-modulation patterns by directly recording the activity of single neurons, microcircuits, and columns, but also use the multimodal and multi-scale data for realistically enabling the application of CDS, the latter likely being the only way to accurately describe brain states, their transitions and sequences, and the relationship of the latter to our cognitive capacities.
In the ICPBR we are committed to apply a variety of methods, such as the multi-site Miniscope Imaging of (e.g. Inscopix, M. Schnitzer, Stanford), Microendoscopic Calcium Imaging (MCI), already applied to NHP – enabling recordings of Cellular-Resolution Calcium Dynamics from large populations of neurons simultaneously in more than one cortical site – and Electro-Neuro-Chemical (ENC) methodologies, permitting concurrent measurements of electrical activity and neurotransmitter/neuromodulator concentration changes, which can largely decrease signal ambiguity. The development of an ENC methodology was already started in the MPI-BC, Tübingen and continued in the ICPBR, by Dr. Hamid Noori and Ekaterina Mitricheva (Ph.D. Thesis), a principal investigator and a graduate student respectively. It will now be taken over by a colleague with electrochemistry background.
Currently, there are a few techniques available that would allow measurements of neurochemical changes in vivo and can help to determine spontaneous and stimulus-induced temporal changes of transmitter concentrations associated with neural activity within a region of interest (ROI). In vivo microdialysis sampling is probably the most prominent of such techniques but the method has significant limitations, given our sampling requirements. Although it is possible to estimate the neural origin of the measured transmitters, the concentration of the obtained dialysate due to the difference in time scales (withdrawal-time of dialysate is measured in minutes) cannot accurately show the concentration of the substance in situ.
An alternative to such methods would be electrochemical biosensors, ultimately used by Noori and Mitricheva in their preliminary experiments. This method works either based on the principle of voltammetry or amperometry, whereby the second is optimal when our signal amplification systems were made for processing electrical currents (for in-magnet-recordings). Peroxidase-based amperometric sensors were used, with a probe diameter smaller than 300 micrometers and time-scale in seconds. The multisite electrodes had both electrical and electrochemical sites. This initial work provided the very first recordings using combined electrophysiological-electrochemical measurements, as well as active electromagnetic-interference-compensation for gradient-noise. Glutamate and GABA were measured concurrently with the modulations of mean extracellular field potential. The initial measurements demonstrated that the methodology, allows indeed simultaneous recording of electrophysiological activity, glutamate, GABA within one voxel and suggests different scenarios of how changes in glutamate and GABA concentrations relate to BOLD and neural activity.
In the ICPBR such multimodal data will be first employed for system identification. Initial steps will follow the black-box approach, referring to a number of modelling techniques that use only input-output data to build a model of the system. Such models will be also used for estimates of basic parameters, such as delays, zeros and poles characterizing impulse response functions. With a second critical step, the signals will be also used for estimating AutoRegressive (AR) models with eXogenous variables (ARX) or Moving Average (ARMAX), as well as Multi-Input/Output polynomial models. Multiple Input Variables and one Output variable (MISO) will be the very important step for gaining some deeper insights into the NVC. Specifically, if the time-series of one single fMRI voxel is considered to be the local output of the neurovascular system, input is surely not the multi-unit spiking or the LFP of one recording site. Even for single-tip recordings, the input to the NVC is likely a weighted average of scaled band-limited-power (BLP) signals combined with the neurochemical signals reflecting neurotransmitter and neuromodulator concentration-changes. Various methods will be used to estimate optimal polynomials including weight estimates and considering the aforementioned non-causality cases. Successful estimates will be immensely important for finally convolving or deconvolving signals prior to detection and identification of events or significant inter-channel moving coherence changes, as well as for accurate descriptions of Multi-Structure-Activity (MSA).
Detailed description of our ICPBR research can be found in the Director’s Page. The last two sections offer a very brief description of the brain properties that show how much CDS is needed for addressing system-questions.
[1] The Contents of a Neural Voxel
The local hemodynamic response reflects the total synaptic activity of a region rather than the function-specific responses of individual pyramidal cells. It is therefore likely to depend on regional neuronal and synaptic density, as well as on local vascularization. When attempting to interpret the fMRI signal by modeling, or when comparing the results of human neuroimaging to those obtained in monkey physiology experiments, it is perhaps useful to take the following numbers into consideration.
In humans, there are about 90,000-100,000 neurons under 1 mm2 of cortical surface (and A. Schüz, personal communication). This number is remarkably constant for all structurally and functionally distinct areas, including the somatosensory, temporal, parietal, frontal, and motor cortical areas. Interestingly, it is also constant across many species, including mouse, rat, cat, monkey and human. The only exception to this rule is the primary visual cortex of certain primates, including monkey and man, which has approximately 2.5 times as many neurons. Cortical thickness varies from area to area and from species to species; for example, from mouse to man cortex becomes approximately 3 times thicker. It follows that neuronal density varies in inverse proportion to cortical thickness, while the length of neuronal processes and synaptic density remain relatively constant. Likewise, unchanged is the ratio of excitatory to inhibitory synapses, while the number of synapses and the axonal length per neuron increases with increasing cortical thickness (Schuz & Demianenko, 1995).
On the average, neural density is 20,000 to 30,000neurons/mm3 (Braendgaard et al., 1990; Haug, 1987; Shariff, 1953). In the primary visual cortex (the thinnest cortex in the primate) neural density is 3 to 4 times higher, while motor cortex has the lowest density, with about 10,000 neurons per mm3. The density of synapses in humans, on the other hand, ranges from 0.4-1 x 109/mm3 (Huttenlocher, 1979; Huttenlocher & de, 1987; Huttenlocher et al., 1982). Depending on the thickness of the cortex, which can range from 2 to 4 mm, the number of synapses beneath 1 mm2 surface will be around 109 (0.8-4x109). The processes are typically several kilometers/ mm3 (axon length 4 km/mm3 and dendrite length 0.4 km/ mm3) (Braitenberg, 1998; Braitenberg & Schuez, 1998).
What are then the contents of a neuroimaging voxel? In cognitive neuroscience, most fMRI studies to date have used low magnetic fields (1.5-3T) and poor spatial resolution (50-80 µL (mm³)). An examination of the 300 top-cited cognitive fMRI studies shows that 69% of these studies were done in conventional clinical scanners (1.5T), 29% in 2T/3T scanners, and the rest in high-field scanners (>4T). Typically, in-plane resolution is 9-16mm2, with slice thicknesses in the range of 5-7mm. The average voxel size prior to any pre-processing of the data was thus 55 µL (or 55mm3). Often the effective size is 2-3 times larger due to the spatial filtering that most investigators apply to improve the functional SNR. On the basis of the data briefly presented above, a typical unfiltered fMRI voxel contains 5.5 million neurons, 2.2-5.5 x 1010 synapses, 22 km of dendrites and 220 km of axons. These numbers suggest that we must exercise extreme caution when drawing analogies between fMRI and intracortical animal or human (patient) electrophysiology, all the more so because while the actual neurotransmission may be instantiated in the activity of a subset of neurons within a given voxel, the diffuse junctional or non-junctional neuromodulation may affect its entirety.
[2] A Brief Introduction into the Complex Dynamic Systems
Cloud-streets (top left) are convective rolls of rising warm air and sinking cool air. The principle of their formation is similar to that observed in the well-known Rayleigh – Bénard convection cells in boiling fluids. The question with formations such as the “could streets” is: How do the tiny water molecules know how to arrange their concerted movements? Here over very many kilometers?
Systems like convection cells, rolls and sand ripples are non-adaptive, and relatively easier to describe and model. Things get really difficult though with biological complex systems such as the flocking birds, the swarm behavior of fish and anthills (bottom right).
No single ant, fish or bird is in charge; no top-down control exists; yet their behavior is organized and exhibits a kind of group intelligence. The precise and quantitative description of the self-organization process in such systems is currently practically impossible. Systems like genome and the brain are obviously “complex dynamic systems”, and the brain the best example of complexity. As mentioned above, it consists of a huge number of elements, almost “incomprehensible” connectivity, clustering, nested self-organization, and (unfortunately) network-evolution that is initial-condition dependent! Modular organization in such a structure is repeated across a hierarchy of spatial scales, including neurons, minicolumns, cortical columns, functional brain regions, large-scale networks and so on.
Yet, the vast majorities of brain studies ignore this complexity and address questions at one spatiotemporal scale at a time. Brain activity is commonly observed at least at three main space-time scales. At the microscopic scale are the action potentials of single neurons measured in milliseconds and microns. At the macroscopic scale are the domains of high metabolic demand that are imaged in seconds and millimeters (mm) by a variety of techniques for measuring the spatial patterns of cerebral blood flow. In between at the mesoscopic scale of millimeters (mm) and tenths of a second are the patterns of the massed dendritic potentials seen in electroencephalographic (EEG) recordings from waking and sleeping brains.
Almost all studies in the field of systems neuroscience have been and largely continue to be dealing with recordings of microscopic activity in animal experiments or macroscopic activity in humans. Combination of largely different scales has been rare, largely because of a huge number of technical problem when trying to conduct concurrent physiological and imaging recordings. Primary ICPBR aim is to strongly support the systems approach synoptically described above.
Literature
Braendgaard, H., Evans, S. M., Howard, C. V., & Gundersen, H. J. (1990). The total number of neurons in the human neocortex unbiasedly estimated using optical disectors. Journal of Microscopy, 157(Pt 3), 285-304.
Braitenberg, V. (1998). Selection, the impersonal engineer. Artificial Life, 4(4), 309-310.
Braitenberg, V., & Schuez, A. (1998). Cortex: Statistics and Geometry of Neuronal Connectivity (Vol. 2nd). Springer.
Haug, H. (1987). Brain sizes, surfaces, and neuronal sizes of the cortex cerebri: a stereological investigation of man and his variability and a comparison with some mammals (primates, whales, marsupials, insectivores, and one elephant). American Journal of Anatomy, 180(2), 126-142.
Huttenlocher, P. R. (1979). Synaptic density in human frontal cortex - developmental changes and effects of aging. Brain Research, 163(2), 195-205.
Huttenlocher, P. R., & de, C. (1987). The development of synapses in striate cortex of man. Human Neurobiology, 6(1), 1-9.
Huttenlocher, P. R., de, C., Garey, L. J., van der, L. H., & Van der Loos, H. (1982). Synaptogenesis in human visual cortex--evidence for synapse elimination during normal development. Neuroscience Letters, 33(3), 247-252.
Logothetis, N. K. (2008). What we can do and what we cannot do with fMRI [Review]. Nature, 453(7197), 869-878. https://doi.org/10.1038/nature06976
Schuz, A., & Demianenko, G. P. (1995). Constancy and variability in cortical structure. A study on synapses and dendritic spines in hedgehog and monkey. Journal fur Hirnforschung., 36(1), 113-122.
Shariff, G. A. (1953). Cell counts in the primate cerebral cortex. Journal of Comparative Neurology, 98(3), 381-400.