Abstract
This chapter brings enigmatic connectivity of the cerebellar dentate nucleus (DN) and the cerebellar forward model hypothesis together to demonstrate the cerebrocerebellum as loci of Kalman filters. We start with a brief history of the cerebellar internal model hypothesis. Next we present two lines of new evidence for the forward model hypothesis. First, we show physiological evidence that the cerebellar outputs from DN are predictive for the inputs to the cerebrocerebellum. Second, we introduce an enigmatic MF collateral to DN and demonstrate it is an essential key to the Kalman filter model. We further discuss how the Kalman filter model for the motor cerebrocerebellum could be generalized to non-motor parts as a unifying principle for the diverse functions of the cerebrocerebellum. We conclude that the Kalman filter model also explains how parallel modules in the cerebrocerebellar communication loops are coordinated in a cascadic manner, providing a partial explanation for unity of mind.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Albus, J. S. (1971). A theory of cerebellar function. Mathematical Biosciences, 10, 25–61.
Allen, G. I., & Tukahara, N. (1974). Cerebrocerebellar communication systems. Physiological Reviews, 54, 957–1006.
Alstermark, B., & Ekerot, C. F. (2013). The lateral reticular nucleus: a precerebellar centre providing the cerebellum with overview and integration ofmotor functions at systems level. A new hypothesis. Journal of Physiology, 591, 5453–5458.
Bastian, A. J. (2006). Learning to predict the future: The cerebellum adapts feedforward movement control. Current Opinion in Neurobiology, 16, 645–649.
Bastian, J., & Zakon, H. H. (2005). Plasticity of sense organs and brain. In T. H. Bullock, C. D. Hopkins, A. N. Popper, & R. R. Fay (Eds.), Electroception (pp. 195–228). Springer.
Brodal, P., & Bijaalie, J. G. (2003). Organization of the pontine nuclei. Neuroscience Research, 13, 83–118.
Bruckmoser, P., Hepp, M. C., & Wiesendanger, M. (1969). Cortical influence on the lateral reticular nucleus of the cat. Brain Research, 15, 556–558.
Droulez, J., & Cornílleau-Pérèz, V. (1993). Application of the coherence scheme to the multisensory fusion problem. In A. Berthoz (Ed.), Multisensory control of movement (pp. 485–501). Oxford University Press.
Ebner, T. J., & Pasalar, S. (2008). Cerebellum predicts the future motor state. Cerebellum, 7, 583–588.
Eccles, J. C., Ito, M., & Szentágothai, J. (1967). The cerebellum as a neuronal machine. Springer-Verlag.
Flash, T., & Hogan, N. (1985). The coordination of arm movements: an experimentally confirmed mathematical model. Journal of Neuroscience., 5, 1688–1703.
Gerrits, N. M., & Voogd, J. (1987). The projection of the nucleus reticularis tegmenti pontis and adjacent regions of the pontine nuclei to the centralcerebellar nuclei in the cat. Journal of Comparative Neurology, 258, 52–69.
Haggard, P., & Wing, A. (1995). Coordinate responses following mechanical perturbations of the arm during prehension. Experimental Brain Research, 102, 483–494.
Harris, C. M., & Wolpert, D. M. (1998). Signal dependent noise determines motor planning. Nature, 394, 780–784.
Heidary, H., & Tomasch, J. (1969). Neuron numbers and perikaryon areas in the human cerebellar nuclei. Acta Anatomica (Basel), 74, 290–296.
Hoppensteadt, F. C., & Izhikevich, E. M. (1997). Weakly connected neural networks. Springer-Verlag. (Page 23).
Ishikawa, T., Tomatsu, S., Tsunoda, Y., Lee, J., Hoffman, D. S., & Kakei, S. (2014). Releasing dentate nucleus cells from Purkinje cell inhibition generates output from the cerebrocerebellum. PLoS One, 9, e108774. https://doi.org/10.1371/journal.pone.0108774
Ishikawa, T., Tomatsu, S., Izawa, J., & Kakei, S. (2016). The cerebro-cerebellum: Could it be loci of forward models? Neuroscience Research, 104, 72–79.
Ito, M. (1970). Neurophysiological aspects of the cerebellar motor control system. International Journal of Neurology, 7, 162–176.
Ito, M. (1984). The cerebellum and neural control. New York: Raven Press.
Ito, M. (2008). Control of mental activities by internal models in the cerebellum. Nature Reviews. Neuroscience, 9, 304–313.
Izhikevich, E. M. (2007). Dynamical Systems in Neuroscience – The geometry of excitability and bursting. The MIT Press.
Kakei, S., Hoffman, D. S., & Strick, P. L. (1999). Muscle and movement representations in the primary motor cortex. Science, 285, 2136–2139.
Kakei, S., Hoffman, D. S., & Strick, P. L. (2001). Direction of action is represented in the ventral premotor cortex. Nature Neuroscience, 4, 1020–1025.
Kakei, S., Lee, J., Mitoma, H., Tanaka, H., Manto, M., & Hampe, C. S. (2019). Contribution of the cerebellum to predictive motor control and its evaluation in ataxic patients. Frontiers in Human Neuroscience, 13, 216. https://doi.org/10.3389/fnhum.2019.00216
Kalman, R. E., & Bucy, R. S. (1961). New results in linear filtering and prediction. ASME Journal of Basic Engineering, 83, 95–108.
Kelly, R. M., & Strick, P. L. (2003). Cerebellar loops with motor cortex and prefrontal cortex of a nonhuman primate. The Journal of Neuroscience, 23, 8432–8444.
Kirk, D. E. (1970). Optimal control theory: An introduction. Prentice-Hall.
Larsell, O. (1967). The comparative anatomy and histology of the cerebellum. University of Minnesota Press.
Lee, J., Kagamihara, Y., Tomatsu, S., & Kakei, S. (2012). The functional role of the cerebellum in visually guided tracking movement. Cerebellum, 11, 426–433.
Marr, D. (1969). A theory of cerebellar cortex. The Journal of Physiology, 202, 437–470.
Matsuyama, K., & Drew, T. (1997). Organization of the projections from the pericruciate cortex to the pontomedullary brainstem of the cat: a studyusing the anterograde tracer Phaseolus vulgaris-leucoagglutinin. Journal of Comparative Neurology, 389, 617–641.
Miall, R. C., Weir, D. J., Wolpert, D. M., & Stein, J. (1993). Is the cerebellum a smith predictor? Journal of Motor Behavior, 25, 203–216.
Miall, R. C., Christensen, L. O. D., Cain, O., & Stanley, J. (2007). Disruption of state estimation in the human lateral cerebellum. PLoS Biology, 5, e316.
Mitoma, H., Adhikari, K., Aeschlimann, D., Chattopadhyay, P., Hadjivassiliou, M., Hampe, C. S., Honnorat, J., Joubert, B., Kakei, S., Lee, J., Manto, M., Matsunaga, A., Mizusawa, H., Nanri, K., Shanmugarajah, P., Yoneda, M., & Yuki, N. (2016). Consensus paper: Neuroimmune mechanisms of cerebellar ataxias. Cerebellum, 15, 213–232.
Na, J., Sugihara, I., & Shinoda, Y. (2019). The entire trajectories of single pontocerebellar axons and their lobular and longitudinal terminal distribution patterns in multiple aldolase C-positive compartments of the rat cerebellar cortex. The Journal of Comparative Neurology, 527, 2488–2511.
Paulin, M. (1989). A Kalman filter theory of the cerebellum. In M. A. Arbib & S. Amari (Eds.), Dynamic interactions in neural networks: Models and data (pp. 239–259). Springer.
Paulin, M. (1997). Neural representations of moving systems. In J. D. Schmahmann (Ed.), The cerebellum and cognition (pp. 515–533). Academic Press.
Sanger, T. D., Yamashita, O., & Kawato, M. (2019). Expansion coding and computation in the cerebellum: 50 years after the Marr-Albus codon theory. Journal of Physiology, 598, 913–928.
Schmahmann, J. D., & Pandya, D. N. (1989). Anatomical investigation of projections to the basis pontis from posterior parietal association cortices in rhesus monkey. The Journal of Comparative Neurology, 289, 53–73.
Schmahmann, J. D., & Pandya, D. N. (1991). Projections to the basis pontis from the superior temporal sulcus and superior temporal region in the rhesus monkey. The Journal of Comparative Neurology, 308, 224–248.
Schmahmann, J. D., & Pandya, D. N. (1993). Prelunate, occipitotemporal, and parahippocampal projections to the basis pontis in rhesus monkey. The Journal of Comparative Neurology, 337, 94–112.
Schmahmann, J. D., & Pandya, D. N. (1997). Anatomic organization of the basilar pontine projections from prefrontal cortices in rhesus monkey. The Journal of Neuroscience, 17, 438–458.
Schmahmann, J. D., Rosene, D. L., & Pandya, D. N. (2004). Motor projections to the basis pontis in rhesus monkey. The Journal of Comparative Neurology, 478, 248–268.
Stein, R. B., Oguztoreli, M. N., & Capaday, C. (1994). What is optimized in muscular movements? In Stengel R. F. Optimal Control and Estimation. New York: Dover
Stengel, R. F. (1994). Optimal control and estimation. Dover.
Sugahara, F., Pascual-Anaya, J., Oisi, Y., Kuraku, S., Aota, S., Adachi, N., Takagi, W., Hirai, T., Sato, N., Murakami, Y., & Kuratani, S. (2016). Evidence from cyclostomes for complex regionalization of the ancestral vertebrate brain. Nature, 531, 97–100.
Tanaka, H., Ishikawa, T., & Kakei, S. (2019). Neural evidence of the cerebellum as a state predictor. Cerebellum, 18, 349–371. https://doi.org/10.1007/s12311-018-0996-4
Tanaka, H., Ishikawa, T., Lee, J., & Kakei, S. (2020). The cerebro-cerebellum as a locus of forward model; a review. Frontiers in Systems Neuroscience, 14, 19.
Thach, W. T. (1975). Timing of activity in cerebellar dentate nucleus and cerebral motor cortex during prompt volitional movement. Brain Research, 88, 233–241.
Thach, W. T. (1978). Correlation of neural discharge with pattern and force of muscular activity, joint position, and direction of intended next movement in motor cortex and cerebellum. Journal of Neurophysiology, 41, 654–676.
Thier, P., & Markanday, A. (2019). Role of the vermal cerebellum in visually guided eye movements and visual motion perception. Annual Review of Vision Science, 5, 247–268.
Todorov, E. (2004). Optimality principles in sensorimotor control. Nature Neuroscience, 7, 907–915.
Tomasch, J. (1969). The numerical capacity of the human cortico-pontocerebellar system. Brain Research, 13, 476–484.
Tomatsu, S., Ishikawa, T., Tsunoda, Y., Lee, J., Hoffman, D. S., & Kakei, S. (2016). Information processing in the hemisphere of the cerebellar cortex for control of wrist movement. Journal of Neurophysiology, 115, 255–270.
Uno, Y., Kawato, M., & Suzuki, R. (1989). Formation and control of optimal trajectory in human multijoint arm movement: Minimum torque-change model. Biological Cybernetics, 61, 89–101.
Wilson, H. R., & Cowan, J. D. (1973). A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, 13, 55–80.
Wolpert, D. M., & Miall, R. C. (1996). Forward models for physiological motor control. Neural Networks, 9, 1265–1279.
Wu, H., Sugihara, I., & Shinoda, Y. (1999). Projection patterns of single mossy fibers originating from the lateral reticular nucleus in the rat cerebellar cortex and nuclei. The Journal of Comparative Neurology, 411, 97–118.
Acknowledgments
We thank Profs. Hiroshi Mitoma and Koji Ito for their valuable comments and discussions.
Support
This work was supported by Grants-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology in Japan (MEXT) (http://www.mext.go.jp/) (no. 26120003, no. 14580784, no. 15016008, no. 16015212, no. 20033029, and no. 21500319 to SK; no. 25430007, no. 26120005, and no. 16 K12476 to HT; no. 21700229 and no. 24650304 to JL; and no. 24650224 to TI), the Japan Science and Technology Agency (A-STEP) to SK (http://www.jst.go.jp/), the Japan Science and Technology Agency (PRESTO: Intelligent Cooperation and Control) (SK), NBRP “Japanese Monkeys” through the National BioResource Project of MEXT, the JSPS Programs (Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers, and Embodied-Brain Systems Science) (HT), and the Hitachi-Kurata and the Tateishi Science Foundations (HT). This research was also supported by AMED under grant number 16ek0109048h0003 to SK. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Kakei, S., Tanaka, H., Ishikawa, T., Tomatsu, S., Lee, J. (2021). The Input-Output Organization of the Cerebrocerebellum as Kalman Filter. In: Mizusawa, H., Kakei, S. (eds) Cerebellum as a CNS Hub. Contemporary Clinical Neuroscience. Springer, Cham. https://doi.org/10.1007/978-3-030-75817-2_19
Download citation
DOI: https://doi.org/10.1007/978-3-030-75817-2_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-75816-5
Online ISBN: 978-3-030-75817-2
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)