{
  "id": 8325697,
  "title": "Probabilistic model discovery reveals distinct constitutive behavior of kidney cortex and medulla",
  "url": "https://urgent.news/2026/09/18/probabilistic-model-discovery-reveals-distinct-constitutive-behavior",
  "topic": "science",
  "section": "Science",
  "published": "2026-09-18T00:00:00.000Z",
  "source": {
    "name": "bioRxiv",
    "slug": "biorxiv",
    "url": "https://www.biorxiv.org/content/10.64898/2026.09.12.751158v1?rss=1"
  },
  "original_language": "en",
  "account": "Understanding the internal structure of the kidney is crucial for predicting tissue behavior and stress. Current models simplify the kidney's properties, treating strain energy functions as fixed and ignoring variability between the kidney's cortex and medulla. To address this, a team used artificial neural networks to uncover probabilistic strain energy functions for both regions based on experimental data. The findings show that the medulla is significantly stiffer than the cortex in tension, compression, and shear. Effective Young's moduli for the medulla are 3.41, 5.04, and 4.48 kPa, while those for the cortex are 1.43, 2.32, and 2.87 kPa. The kidney's mechanical properties exhibit tension-compression asymmetry, meaning they respond differently to tensile and compressive forces. When trained on all three modes of deformation, the neural network discovered strain energy functions in the second invariant alone within the tested deformation range. The cortex model incorporated two exponential I2 terms, whereas the medulla model included an additional linear I2 term. By incorporating Gaussian external weights, the models can account for variability between individual specimens, enabling closed-form probabilistic stress predictions. Ultimately, these region-specific probabilistic models accurately capture the kidney's mechanical heterogeneity and variability, facilitating more realistic simulations of kidney deformation and stress for various medical applications, including surgical planning, needle interventions, and handling renal trauma.",
  "summary": "The kidney is a critical soft-tissue organ responsible for blood filtration. Accurate constitutive models of the kidney are essential to predict tissue deformation and stress, yet existing models prescribe the strain energy function a priori, largely treat tissue variability as deterministic, and do not distinguish between cortex and medulla. Here we use Gaussian constitutive artificial neural…",
  "key_points": [],
  "editors_take": null,
  "illustration": null,
  "coverage": {
    "outlets": 1,
    "also_reported_by": []
  },
  "ai_generated": true,
  "disclaimer": "Summaries, key points and the editor’s take are written by software from other outlets’ reporting and may contain errors — always check the linked original."
}