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Related Concept Videos

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A derivative quantifies how a function changes in response to variations in its input. It provides a localized rate of change, representing the slope of the tangent line to the function at any given point. When this process is applied systematically across the entire domain of the function, it yields a new function—the derivative function—which encodes the rate of change at every point. This concept is central to calculus and essential for understanding the behavior of dynamic...
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The motion of a Ferris wheel rotating at a constant speed provides an intuitive model for understanding trigonometric functions and their derivatives. As a rider moves along the circular path, the vertical height above the ground changes smoothly and periodically over time. This vertical motion can be accurately represented by a sine function, reflecting the repeating pattern of ascent and descent inherent to circular motion.Height and Rate of ChangeIf the rider’s height is modeled by a...
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Logarithmic and Exponential RelationshipA logarithmic function is the inverse of an exponential function. If y = logb x then, it can be rewritten as by = x. This relationship allows for implicit differentiation, making logarithmic functions useful in calculus. Logarithmic scales are widely used to represent data that span multiple orders of magnitude, such as earthquake magnitudes (Richter scale) and sound intensity (decibels).Differentiation of Logarithmic FunctionsTo differentiate y = logb x,...
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Derivatives quantify the rate of change of a function and can be interpreted geometrically as the slope of a straight line or the slope of a tangent line to a curve at a given point. In the context of a roller coaster, the derivative of the function describing the track’s horizontal position provides a mathematical description of how steep the path is at any location along the ride.Constant and Linear PathsA horizontal segment of a roller coaster can be modeled by a constant function,...
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Related Experiment Video

Updated: Jan 30, 2026

Three-dimensional Quantification of Dendritic Spines from Pyramidal Neurons Derived from Human Induced Pluripotent Stem Cells
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Functional Cortical Axon Tracts Generated from Human Stem Cell-Derived Neurons.

H Isaac Chen1,2, Dennis Jgamadze1, James Lim1

  • 11 Department of Neurosurgery, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania.

Tissue Engineering. Part A
|January 17, 2019
PubMed
Summary

Researchers grew functional human cortical axon tracts from pluripotent stem cells. This axon stretch growth method could enable future cerebral axon transplantation for brain injury repair.

Keywords:
axonscortical neuron differentiationneuronal networkstem cellstissue engineering

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Area of Science:

  • Neuroscience
  • Regenerative Medicine
  • Stem Cell Biology

Background:

  • Axon regeneration is limited in adult mammalian brains, leading to permanent deficits after white matter damage.
  • Current treatments for neurological deficits lack effective strategies for axon repair.
  • Novel approaches are needed to restore neural connections after brain injury.

Purpose of the Study:

  • To detail a human substrate for axon repair via transplantation.
  • To investigate the generation of functional cortical axon tracts from human pluripotent stem cells.
  • To establish a potential patient-specific protocol for cerebral axon transplantation.

Main Methods:

  • Utilizing the technique of axon stretch growth.
  • Generating axon tracts from human pluripotent stem cells.
  • Culturing and assessing the functionality of generated axon tracts.

Main Results:

  • Functional cortical axon tracts were successfully generated from human pluripotent stem cells.
  • Axon tracts were grown at impressive rates of up to 1 mm/day.
  • The generated tracts represent a viable human substrate for transplantation strategies.

Conclusions:

  • Axon stretch growth provides a novel method for generating human cortical axon tracts.
  • This approach offers a promising foundation for patient-specific cerebral axon transplantation.
  • The findings pave the way for potential treatments for permanent neurological deficits caused by white matter damage.