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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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Related Experiment Video

Updated: Feb 1, 2026

Dermoscopy Aids in the Diagnosis of Discoid Lupus Erythematosus
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Dermoscopy Aids in the Diagnosis of Discoid Lupus Erythematosus

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Disease course patterns in systemic lupus erythematosus.

K Tselios1, D D Gladman1, Z Touma1

  • 1Centre for Prognosis Studies in Rheumatic Diseases, Toronto Lupus Clinic, Toronto, Canada.

Lupus
|December 12, 2018
PubMed
Summary

Most systemic lupus erythematosus patients experience a relapsing-remitting disease course. Early treatment response in lupus patients is linked to a less severe outcome and better prognosis, with ~10% achieving prolonged remission.

Keywords:
Patterns of disease courseprognosissystemic lupus erythematosus

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Area of Science:

  • Rheumatology
  • Immunology
  • Clinical Medicine

Background:

  • Systemic lupus erythematosus (SLE) disease activity presents as quiescent, relapsing-remitting, or persistently active.
  • Patterns of SLE disease course since diagnosis are not well-characterized.
  • This study investigates the prevalence and characteristics of SLE disease patterns over a decade.

Purpose of the Study:

  • To assess the prevalence of different SLE disease activity patterns over 10 years.
  • To characterize the clinical and immunological features associated with each pattern.
  • To identify factors influencing SLE disease severity and prognosis.

Main Methods:

  • Analysis of an inception cohort from the Toronto Lupus Clinic with ≥10 year follow-up.
  • Defined prolonged remission (SLEDAI=0 for ≥10 years), relapsing-remitting (≥2 remission periods), and persistently active (no remission).
  • Compared baseline characteristics, cumulative damage, flare rates, mortality, and comorbidities across disease course groups.

Main Results:

  • Out of 267 SLE patients, 10.1% achieved prolonged remission, 67.4% had a relapsing-remitting course, and 9.4% were persistently active.
  • Persistently active patients accumulated significantly more damage and experienced higher rates of osteoporosis, osteonecrosis, and cardiovascular events.
  • Black race and higher SLEDAI in the first 2 years were associated with more severe disease courses.

Conclusions:

  • Approximately 70% of SLE patients exhibit a relapsing-remitting disease course.
  • About 10% of SLE patients achieve prolonged remission, while another 10% have a persistently active disease course.
  • Early response to treatment in SLE is associated with a less severe disease course and improved prognosis.