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From the study of resistive circuits, it is understood that employing a series-parallel combination serves as an effective strategy for simplifying circuits. Capacitors can be arranged within a circuit in one of two ways: a series configuration or a parallel configuration. The way these capacitors are connected to a battery will influence both the potential drop across each individual capacitor and the size of the charge that each capacitor can store. This is determined by the specific type of...
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As defined by regulatory standards, pharmaceutical equivalents require generic drug products to have identical dosage forms and chemically identical active pharmaceutical ingredients (APIs). They must adhere to compendial or applicable standards for potency, content uniformity, disintegration times, and dissolution rates. In the case of modified-release dosage forms, variations in drug content are permissible as long as the delivered amount remains consistent with the innovator drug product.
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Mathematical induction is a structured method of proof used to confirm the truth of statements involving natural numbers. Consider the sum of the first n natural numbers:This formula describes a pattern that appears to hold true as more terms are added. To verify that it is valid for all natural numbers, mathematical induction proceeds in two essential steps. The first is the base case, where the formula is tested for the initial value, typically n = 1. Substituting into both sides confirms the...
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Related Experiment Video

Updated: Jan 31, 2026

Generation of a Three-dimensional Full Thickness Skin Equivalent and Automated Wounding
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Generation of a Three-dimensional Full Thickness Skin Equivalent and Automated Wounding

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Mathematical-model-guided development of full-thickness epidermal equivalent.

Junichi Kumamoto1, Shinobu Nakanishi2, Mio Makita2

  • 1Research Institute for Electronic Science, Hokkaido University, Sapporo, Japan.

Scientific Reports
|December 22, 2018
PubMed
Summary

Mathematical modeling accurately predicted epidermal thickness. Researchers created a realistic 3D skin model using keratinocytes on patterned textiles, achieving excellent barrier function and mimicking human epidermis.

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Area of Science:

  • Tissue engineering
  • Biomaterials science
  • Mathematical modeling

Background:

  • Current epidermal models lack physiological thickness (10-20 μm vs. 100 μm in vivo).
  • Mathematical modeling of epidermal homeostasis suggested papillary layer undulations dictate epidermal thickness.

Purpose of the Study:

  • To test the hypothesis that papillary layer structure influences epidermal thickness.
  • To develop a more physiologically realistic epidermal model using passaged keratinocytes and biomimetic substrates.

Main Methods:

  • Human keratinocytes were cultured on polyester textiles with varied fiber patterns.
  • The engineered epidermal model was analyzed for structural, cellular, and barrier properties.
  • Gene silencing of YAP (Yes-associated protein) was performed to assess its role.

Main Results:

  • Textile patterns matching model predictions yielded a 3D epidermal model with a thick stratum corneum and functional barrier.
  • The basal layer mimicked the human papillary layer, with proliferating cells expressing key markers.
  • Appropriate expression of filaggrin, loricrin, claudin 1, and ZO-1 was observed.
  • YAP (Yes-associated protein) silencing disrupted the 3D structure.

Conclusions:

  • Mathematical modeling provides predictive insights for biological processes.
  • Biomimetic textile scaffolds can generate physiologically relevant epidermal equivalents.
  • This approach enhances skin tissue engineering and barrier function studies.