New mathematical models describe diffusion and metabolism dynamics in 3D tissues, stem cell-derived organoids

December 21, 2015, Institute of Neural Regeneration & Tissue Engineering
Models for 3-D neural tissue constructs are shown, which will provide new tools and insights into tissue development, disease modeling, and regenerative medicine. Credit: Richard McMurtrey / Institute of Neural Regeneration & Tissue Engineering

New research has shed light on the complex interactions of stem cell function and molecular diffusion in neural tissue, which may explain many phenomena from stem cell differentiation to the formation of the cortex of the brain. While researching new methods of reconstructing 3D neural tissue and neural pathways in the brain and spinal cord, Dr. Richard McMurtrey devised new mathematical approaches for understanding the concentration of nutrients within the 3D tissue constructs and how this could affect tissue growth.

Stem cells have very unique behaviors and responses to specific concentrations of many molecular factors, meaning that it is important to understand the complex dynamics of nutrient signaling, diffusion, and metabolism in 3D tissues. Many 3D tissues have been constructed with the hope of replicating "mini-organs" from a patient's own , including "mini-brains" or cerebral organoids that can be used to study neurological diseases or which may one day be directly transplanted into damaged tissues of a patient. The ability to guide and direct stem cell development and function to the desired effect in the organoids is therefore an essential aspect of this research.

"I first stumbled upon these ideas when trying to figure out how to obtain exact nutrient concentrations in some 3D tissues I had designed that were composed of ," said Dr. McMurtrey. "The mathematics involved has always fascinated me, but I was surprised that answering my questions was a lot more difficult than I thought it would be. I felt like I kept going down a rabbit hole trying to find solutions, and eventually I figured out the mathematics that could answer my questions. I think these ideas really help us understand the role of diffusion in brain function and neural development better than ever before. But of course there is also much more to still learn."

During human development, stem cells near the center of the developing brain will migrate outwardly and form the neurons in the cortex on the outer rim of the brain, the region where thoughts are formed and processed. The mathematical work described in the paper describes growth limitations imposed by diffusion and metabolism and also suggests an underlying physical basis for the phenomenon of neural migration to a dense external cortical layer. Once the neurons are programmed to migrate to the outer surface, the cortex can then become more convoluted or wrinkled to create more extensive neural networks.

One of the unique aspects of these physical models involved implementing features of cell metabolism in the equations, and the work enables any researcher to adapt the models to their specific cell types as well as to their specific tissue shape and architecture. Even though the mathematics involved in deriving these equations is complex, one of the advantages of these models is that researchers only need to have a working knowledge of algebra to use them. The modeling of many physical phenomena generally requires specialized skills in computational programming, but this work sought to provide what are called analytic or explicit solutions, which simply allow the parameters to be inserted into the formulas and the solutions to be determined.

Dr. McMurtrey's research currently focuses on reconstructing brain and spinal cord structures and pathways using synthetic 3-dimensional made with stem cells, biomaterials, and nanotechnology, and he hopes to use the models to design enhanced artificial tissue implants that could be used clinically to repair sites of tissue damage. These engineered tissue constructs can also be used for studying models of development and disease under controlled conditions or for conditioning cells to enhance survival after implantation into the body. "Many physicists and mathematicians have studied medicine, like Fick or Helmholtz, or wondered in awe at the complex function of the brain, like Einstein or Feynman," Dr. McMurtrey stated. "I wanted to be a physicist growing up, but I happened to end up in medicine, though I still marvel at the underlying physics that can both govern a vast universe and yet also make all neural function possible. I think we will see that, just as with all other systems in the universe, we cannot fully understand a system as complex as the brain until we understand the mathematics governing many fundamental components of that system, whether that is the complexity of neural networks, the dynamics of cell signaling and gene expression networks, the Hodgkin-Huxley-like electrical activity of neuronal membranes, or the biomechanics of developing tissues. Ultimately I believe that physics and engineering have a lot to contribute to solving problems in the human body that the medical field as of yet cannot solve."

Explore further: Reconstructing 3D neural tissue with biocompatible nanofiber scaffolds and hydrogels

More information: Richard J. McMurtrey. Analytic Models of Oxygen and Nutrient Diffusion, Metabolism Dynamics, and Architecture Optimization in Three-Dimensional Tissue Constructs with Applications and Insights in Cerebral Organoids, Tissue Engineering Part C: Methods (2015). DOI: 10.1089/ten.TEC.2015.0375

RichardJ McMurtrey. Novel advancements in three-dimensional neural tissue engineering and regenerative medicine, Neural Regeneration Research (2015). DOI: 10.4103/1673-5374.153674

Richard J McMurtrey. Patterned and functionalized nanofiber scaffolds in three-dimensional hydrogel constructs enhance neurite outgrowth and directional control, Journal of Neural Engineering (2014). DOI: 10.1088/1741-2560/11/6/066009

Related Stories

Reconstructing 3D neural tissue with biocompatible nanofiber scaffolds and hydrogels

April 1, 2015
Damage to neural tissue is typically permanent and causes lasting disability in patients, but a new approach has recently been discovered that holds incredible potential to reconstruct neural tissue at high resolution in ...

New advancements in 3D designs for neural tissue engineering

April 6, 2015
It is well known that neurological diseases and injuries pose some of the greatest challenges in modern medicine, with few if any options for effectively treating such diagnoses, but recent work suggests a unique approach ...

Human embryonic stem cells induced to spontaneously form cortical tissue

February 7, 2014
During development, the nervous system forms as a flat sheet called the neuroepithelium on the outer layer of the embryo. This sheet eventually folds in on itself to form a neural tube that gives rise to the brain and spinal ...

Stem cell-derived 'organoids' help predict neural toxicity

September 21, 2015
A new system developed by scientists at the Morgridge Institute for Research and the University of Wisconsin-Madison may provide a faster, cheaper and more biologically relevant way to screen drugs and chemicals that could ...

Specific roles of adult neural stem cells may be determined before birth

June 18, 2015
Adult neural stem cells, which are commonly thought of as having the ability to develop into many type of brain cells, are in reality pre-programmed before birth to make very specific types of neurons, at least in mice, according ...

Recommended for you

Space-like gravity weakens biochemical signals in muscle formation

May 23, 2018
Astronauts go through many physiological changes during their time in spaceflight, including lower muscle mass and slower muscle development. Similar symptoms can occur in the muscles of people on Earth's surface, too. In ...

Deep space radiation treatment reboots brain's immune system

May 21, 2018
Planning a trip to Mars? You'll want to remember your anti-radiation pills.

Receptor proteins that respond to nicotine may help fat cells burn energy

May 21, 2018
The same proteins that moderate nicotine dependence in the brain may be involved in regulating metabolism by acting directly on certain types of fat cells, new research from the University of Michigan Life Sciences Institute ...

Atomic-level study reveals why rare disorder causes sudden paralysis

May 21, 2018
A rare genetic disorder in which people are suddenly overcome with profound muscle weakness is caused by a hole in a membrane protein that allows sodium ions to leak across cell membranes, researchers at the University of ...

New era for blood transfusions through genome sequencing

May 18, 2018
Most people are familiar with A, B, AB and O blood types, but there are hundreds of additional blood group "antigens" on red blood cells—substances that can trigger the body's immune response—that differ from person to ...

Robots grow mini-organs from human stem cells

May 17, 2018
An automated system that uses robots has been designed to rapidly produce human mini-organs derived from stem cells. Researchers at the University of Washington School of Medicine in Seattle developed the new system.


Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.