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The Integrated Rate Law: The Dependence of Concentration on Time02:39

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While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...
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The rate of reaction is the change in the amount of a reactant or product per unit time. Reaction rates are therefore determined by measuring the time dependence of some property that can be related to reactant or product amounts. Rates of reactions that consume or produce gaseous substances, for example, are conveniently determined by measuring changes in volume or pressure.
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Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
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Related Experiment Video

Updated: Jan 29, 2026

Calculating Heart Rate Variability from ECG Data from Youth with Cerebral Palsy During Active Video Game Sessions
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Variability in Post-Discharge Mortality Rates and Predictors over Time: Data from a Five-Year Ward-Wide Study.

Giuseppe A Ramirez1,2, Bruno N Germinario3, Giovanni Benanti1,3

  • 1Unit of Immunology, Rheumatology, Allergy and Rare Diseases, IRCCS Ospedale San Raffaele, via Olgettina 60, 20132 Milan, Italy.

Journal of Clinical Medicine
|January 28, 2026
PubMed
Summary

Over half of patients hospitalized for complex chronic conditions died within five years. Identifying predictors of mortality can improve care and palliative referrals for these vulnerable individuals.

Keywords:
after dischargecomplexityfrailtymortality ratespalliative care

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Area of Science:

  • Gerontology
  • Internal Medicine
  • Public Health

Background:

  • Complex chronic disorders are increasing, leading to frequent hospitalizations.
  • Long-term post-discharge mortality and its predictors in these patients are poorly understood.
  • This knowledge gap may result in suboptimal care and delayed palliative care referrals.

Purpose of the Study:

  • To evaluate the five-year post-discharge mortality rates.
  • To identify predictors of mortality in elderly, multi-morbid patients admitted to Internal Medicine.
  • To inform patient management and palliative care integration.

Main Methods:

  • Analysis of a cohort of elderly, multi-morbid patients admitted to Internal Medicine over 12 months.
  • Utilized public health registries to track five-year mortality (up to 2022) for discharged patients.
  • Examined clinical factors, frailty, care intensity, and patient complexity as predictors.

Main Results:

  • Five-year post-discharge mortality reached 57%, with a 32% one-year peak.
  • Cancer, neurological, liver, and respiratory disorders predicted early/intermediate mortality.
  • Renal disorders, dependence, and immunodepression predicted first-year mortality.
  • Cardiovascular and GI disorders predicted late mortality.
  • Frailty and care complexity predicted mortality across all timeframes.

Conclusions:

  • A significant proportion of Internal Medicine patients may benefit from palliative care.
  • Understanding differential mortality predictors aids patient management.
  • Early or simultaneous palliative care identification is crucial for at-risk individuals.