Spirometry And Flow Sensors

Foundations and mechanisms

What spirometry measures

Spirometry is the measurement of inspired and expired gas volume as a function of time; flow is the first derivative of volume, and volume may alternatively be obtained by integrating flow. In anaesthetic practice, “spirometry” commonly refers to respiratory flow-volume measurement within the breathing system or ventilator, whereas laboratory spirometry describes forced expiratory manoeuvres used to classify ventilatory defects. The same physical principles apply: accurate measurement requires correction for temperature, pressure, water vapour, gas composition, resistance, compliance and dynamic response.

Static lung volumes measured directly by simple spirometry include tidal volume, inspiratory reserve volume and expiratory reserve volume. Residual volume, functional residual capacity and total lung capacity cannot be measured by simple spirometry because they include gas remaining in the thorax after maximal expiration; they require gas dilution, nitrogen washout or body plethysmography. Forced spirometry adds time-dependent indices, particularly forced expiratory volume in 1 second and forced vital capacity.

Variable	Typical adult value	Key examination relevance
Tidal volume	6–8 mL kg-1 predicted body weight during lung-protective ventilation	Ventilator spirometry should display delivered and expired volume; disparity suggests leak, circuit compliance or gas compression.
Vital capacity	Approximately 60–70 mL kg-1	Reduced in restrictive disease, respiratory muscle weakness and poor effort.
FEV1/FVC	Usually >0.70 in adults; preferably interpreted against lower limit of normal	Obstruction is defined by reduced ratio; fixed 0.70 threshold overdiagnoses obstruction in older adults.
Peak expiratory flow	Often 400–700 L min-1 in healthy adults, sex/height dependent	Highly effort-dependent; useful for monitoring but not definitive classification.

Physiological patterns and mechanisms

Obstructive disease reduces maximal expiratory flow because airway resistance rises and dynamic airway compression occurs earlier during forced expiration. The equal pressure point moves proximally as elastic recoil falls or small airway resistance increases, producing a concave expiratory limb on the flow-volume loop. FEV₁ falls disproportionately compared with FVC. Restrictive disease reduces lung volume, usually preserving or increasing FEV₁/FVC because FEV₁ and FVC fall together. Upper airway obstruction alters loop shape: fixed lesions flatten both inspiratory and expiratory limbs; variable extrathoracic obstruction predominantly flattens inspiration; variable intrathoracic obstruction predominantly flattens expiration.

• Obstructive defect: FEV₁/FVC below lower limit of normal; severity often graded by FEV₁ percentage predicted. GOLD COPD staging uses post-bronchodilator FEV₁: GOLD 1 ≥80%, GOLD 2 50–79%, GOLD 3 30–49%, GOLD 4 <30% predicted.
• Bronchodilator reversibility: ATS/ERS criteria traditionally require an increase in FEV₁ or FVC of ≥12% and ≥200 mL; newer interpretative strategies emphasise change >10% of predicted value.
• Restrictive pattern on spirometry: reduced FVC with normal/high ratio is suggestive only; confirmation requires TLC < lower limit of normal, commonly <80% predicted in simplified reporting.

Flow sensor physics

Modern anaesthetic machines and ventilators usually measure flow rather than volume and calculate volume by numerical integration. Flow sensors must tolerate humidified gases, secretions, changing gas density, high fresh gas flows, leaks, reverse flow and rapid changes during controlled ventilation. The desired clinical range is approximately 0–200 L min^-1, with neonatal systems requiring accurate resolution at very low flows and volumes. Calibration is commonly checked with a 3 L syringe; ATS/ERS laboratory spirometry standards require volume accuracy within ±3.0% or ±50 mL, whichever is greater.

Sensor	Mechanism	Advantages	Limitations
Fleisch pneumotachograph	Laminar flow through multiple parallel capillaries; pressure drop proportional to flow by Poiseuille principles.	Accurate, linear over moderate flows, good dynamic response.	Condensation and secretions obstruct capillaries; requires heating and differential pressure transducer.
Lilly pneumotachograph	Resistive mesh/screen creates a pressure drop proportional to flow when flow remains near-laminar.	Compact; common in ventilators.	Non-linearity at high flows; affected by humidity, contamination and gas viscosity.
Variable-orifice sensor	Flexible flap or diaphragm changes aperture; pressure-flow relationship approximates square-root behaviour at higher flows.	Low resistance, disposable options, robust in breathing circuits.	Requires linearisation; affected by orientation, secretions and manufacturing tolerances.
Turbine/rotating vane	Gas flow rotates a low-inertia turbine; rotational frequency proportional to volume or flow.	Portable and inexpensive.	Inertia under-reads rapidly changing flow; friction and humidity impair accuracy; poor for bidirectional ventilator flow.
Hot-wire anemometer	Electrical power required to maintain a heated wire at constant temperature relates to mass flow and convective heat loss.	Fast response and sensitive at low flows.	Dependent on gas composition, temperature and contamination; fragile.
Ultrasonic sensor	Transit-time difference of ultrasound pulses upstream and downstream is proportional to gas velocity.	No moving parts, low resistance, can be bidirectional.	Sound velocity depends on gas composition, temperature and humidity; electronics more complex.

Core physical constraints

For laminar flow in a circular tube, resistance is described by Poiseuille’s law: flow is proportional to pressure gradient and the fourth power of radius, and inversely proportional to gas viscosity and tube length. Laminar flow is expected at Reynolds number below approximately 2000, transitional flow at 2000–4000 and turbulent flow above approximately 4000; turbulence makes pressure drop more proportional to flow squared and dependent on gas density. This distinction is central to pneumotachograph design: a resistive element is engineered to maintain predictable flow, but excessive flow, water droplets or secretions introduce non-linearity.

Gas volume reporting requires standardisation. Spirometry values are generally reported as BTPS—body temperature, ambient pressure, saturated with water vapour—because expired gas leaves the lung at 37°C and fully saturated. Calibration devices may contain gas at ambient temperature and pressure, requiring correction. In anaesthetic circuits, displayed inspired and expired tidal volumes may differ because fresh gas flow, compliance of hoses, compression of gas, leaks around tracheal tubes or supraglottic devices, and sampling flows alter the volume passing the sensor compared with the volume reaching the alveoli.

Clinical assessment and investigations

Clinical presentation and indications for spirometric assessment

Spirometry is indicated when symptoms or risk factors suggest abnormal ventilatory mechanics: exertional dyspnoea, chronic cough, wheeze, sputum production, recurrent “chest infections”, occupational exposure, smoking history, neuromuscular weakness, chest wall disease, or unexplained hypoxaemia/hypercapnia. In perioperative practice, spirometry is most useful when it will change management: suspected undiagnosed obstructive disease, quantification of known COPD/asthma before major thoraco-abdominal surgery, assessment before lung resection, or evaluation of respiratory muscle weakness. It should not be used as a non-discriminating screening test in asymptomatic patients, as abnormal results are common and poorly predictive of postoperative pulmonary complications unless integrated with functional capacity, surgical site, frailty, anaemia and gas exchange.

Differential diagnosis of abnormal ventilatory patterns

Pattern	Key spirometric finding	Typical causes	Exam-relevant clues
Obstructive	Reduced FEV1/FVC below lower limit of normal; concave expiratory limb	Asthma, COPD, bronchiectasis, cystic fibrosis, bronchiolitis obliterans, upper airway obstruction	Air-trapping may reduce FVC, producing pseudo-restriction; confirm with lung volumes
Restrictive	Reduced FVC with preserved or high FEV1/FVC	Interstitial lung disease, pleural disease, obesity, kyphoscoliosis, neuromuscular weakness, diaphragmatic palsy	Spirometry suggests restriction; total lung capacity <LLN confirms it
Mixed	Reduced FEV1/FVC and reduced FVC/TLC	COPD with fibrosis, bronchiectasis with scarring, sarcoidosis, combined obesity and airway disease	Requires static lung volumes; FVC alone is insufficient
Variable extrathoracic obstruction	Flattened inspiratory limb	Vocal cord dysfunction, laryngeal tumour, tracheomalacia above thoracic inlet	Flow-volume loop more diagnostic than numerical indices
Fixed large-airway obstruction	Flattening of inspiratory and expiratory limbs	Tracheal stenosis, goitre, endotracheal/tracheostomy stenosis	May present as “refractory asthma”; peri-induction risk is high

Conduct of the investigation and quality control

Accurate interpretation requires acceptable and repeatable manoeuvres rather than reliance on the printed diagnosis. Standards from ATS/ERS 2019 require rapid maximal inspiration, a blast start with extrapolated volume <5% of FVC or <0.100 L, no cough in the first second, no leak or glottic closure, and adequate end-expiration with a plateau or expiratory time typically ≥6 s in adults. Repeatability should be within 0.150 L for the two largest FEV₁ values and within 0.150 L for the two largest FVC values; if FVC ≤1.0 L, the tolerance is 0.100 L. At least three acceptable manoeuvres are expected, with a maximum of eight attempts in routine testing.

Flow sensors must be considered when results are physiologically implausible. Pneumotachographs infer flow from pressure drop across a resistive element and require correction for gas viscosity, temperature, humidity and density. Turbine and ultrasonic devices may under-read at low flows or with condensation, secretions, poor alignment or turbulent flow. Calibration verification with a 3 L syringe should be within ±3% (approximately 2.91–3.09 L). Results are reported at BTPS; failure of temperature correction is a classic cause of systematic error.

Interpretation, thresholds and diagnostic criteria

Modern interpretation should use Global Lung Function Initiative reference equations and the lower limit of normal (LLN; 5th centile, z-score <−1.645), not a fixed ratio alone. A fixed post-bronchodilator FEV₁/FVC <0.70 is used by GOLD for COPD because of simplicity, but it overdiagnoses obstruction in older patients and underdiagnoses it in younger adults. In examinations, state both approaches and recognise the clinical context.

Index	Definition	Interpretation
FEV1	Volume exhaled in first second of forced expiration	Severity marker in obstruction; effort-dependent but highly reproducible if technique adequate
FVC	Total forced expired volume after maximal inspiration	Reduced in restriction, air-trapping, poor effort, pain or neuromuscular weakness
FEV1/FVC	Proportion of vital capacity exhaled in first second	Primary discriminator for airflow obstruction; compare with LLN
PEF	Maximal expiratory flow	Effort-dependent; useful for asthma monitoring but insensitive for small airway disease
FEF25–75	Mid-expiratory flow	Variable and poorly specific; should not drive diagnosis alone

Bronchodilator reversibility is assessed after inhaled salbutamol 400 micrograms via spacer, or equivalent short-acting bronchodilator, with repeat spirometry after 10–15 minutes. ATS/ERS 2021 defines a significant response as an increase in FEV₁ or FVC of >10% of the predicted value. Older criteria, still widely quoted, are an increase in FEV₁ or FVC of ≥12% and ≥200 mL from baseline. Marked variability supports asthma but does not exclude COPD; conversely, absent reversibility during a single test does not exclude asthma. Peak-flow variability supporting asthma is diurnal variability >10% in adults, or improvement in FEV₁ >12% and >200 mL after 4 weeks of anti-inflammatory treatment, as reflected in GINA guidance.

Severity grading and perioperative thresholds

Condition/use	Threshold	Clinical implication
GOLD airflow limitation in COPD	Post-bronchodilator FEV1/FVC <0.70; FEV1 ≥80%, 50–79%, 30–49%, <30% predicted for GOLD 1–4	Grades airflow limitation, but symptoms/exacerbations determine treatment group
Suggestive restriction	FVC <LLN with FEV1/FVC normal or high	Confirm with TLC; evaluate DLCO to separate parenchymal from extrapulmonary restriction
Lung resection screening	Predicted postoperative FEV1 or DLCO <40% predicted indicates increased risk; <30% often triggers formal exercise testing	Use segment-counting or perfusion methods; CPET VO2peak <10 mL kg−1 min−1 is high risk
Neuromuscular weakness	FVC <50% predicted or supine fall >20–30%	Suggests diaphragmatic weakness; plan postoperative ventilatory support

Investigations complementary to spirometry include pulse oximetry, arterial blood gas analysis when SpO₂ is low or hypercapnia is suspected, chest imaging, full pulmonary function testing with TLC/residual volume and DLCO, FeNO where eosinophilic asthma is suspected, and cardiopulmonary exercise testing for unexplained dyspnoea or major resection risk stratification. The anaesthetist should interpret spirometry as a physiological measurement with technical limitations, not as an isolated “fitness for anaesthesia” test.

Management, pharmacology and procedures

Clinical use in peri-operative and critical care management

Spirometry and flow sensing are not therapeutic interventions, but they directly alter management by quantifying ventilatory mechanics, airway obstruction, gas trapping and response to bronchodilator or ventilator adjustment. In anaesthesia, the most useful “spirometric” information is often dynamic: inspiratory and expiratory flow–time curves, pressure–volume loops and flow–volume loops generated from a proximal pneumotachograph, ultrasonic sensor or ventilator-internal flow sensor. These should be interpreted alongside airway pressure, capnography, oxygenation and clinical context.

Measured abnormality	Likely mechanism	Management implication
Expiratory flow fails to return to zero before next breath	Dynamic hyperinflation; expiratory time too short; bronchospasm; COPD/asthma	Reduce respiratory rate, increase expiratory time, reduce tidal volume, treat bronchospasm, measure intrinsic PEEP with end-expiratory hold
Scooped expiratory limb on flow–volume loop	Small airway obstruction; expiratory flow limitation	Bronchodilator therapy, deepen anaesthesia if reflex bronchoconstriction, avoid excessive minute ventilation
Flattened inspiratory and expiratory limbs	Fixed upper airway obstruction; kinked tube; obstructed filter/HME; tracheal stenosis	Immediate airway/circuit check, suction, replace blocked filter, consider bronchoscopy or tube exchange
Reduced delivered tidal volume with discrepancy between inspired and expired volume	Leak, uncuffed airway, circuit disconnection, bronchopleural fistula, sensor malposition	Check cuff pressure, circuit integrity and sensor orientation; quantify leak and adjust ventilation strategy
Increased peak pressure with unchanged plateau pressure	Increased airway resistance: bronchospasm, secretions, tube obstruction	Bronchodilator, suction, tube assessment; flow sensor helps distinguish resistance from compliance change
Increased peak and plateau pressures with reduced compliance	Atelectasis, pulmonary oedema, pneumoperitoneum, ARDS, endobronchial intubation	Recruitment/PEEP titration, exclude mainstem intubation, lung-protective ventilation

Pharmacological testing and bronchodilator response

Formal spirometry is frequently combined with pharmacological challenge. The standard reversibility procedure is baseline spirometry followed by inhaled short-acting bronchodilator and repeat testing after an appropriate onset interval. Salbutamol is commonly administered as 400 micrograms by pressurised metered-dose inhaler via spacer, with repeat spirometry after 10–15 minutes. Terbutaline 500 micrograms inhaled is an alternative. Ipratropium bromide 80 micrograms may be used, particularly when antimuscarinic response is relevant; repeat testing is usually delayed for 30–45 minutes because onset is slower.

Traditional ATS/ERS criteria defined significant bronchodilator reversibility as an increase in FEV₁ or FVC of at least 12% and 200 mL from baseline. The 2021 ERS/ATS interpretative strategy favours a change exceeding 10% of the predicted value for FEV₁ or FVC, reducing baseline-dependence. For COPD diagnosis, GOLD retains post-bronchodilator FEV₁/FVC <0.70 as the defining spirometric threshold, while recognising age-related misclassification compared with lower limit of normal.

Agent/test	Usual protocol	Positive criterion	Important risks
Salbutamol reversibility	400 micrograms via spacer; repeat at 10–15 min	>10% predicted increase in FEV1 or FVC; older criterion ≥12% and ≥200 mL	Tremor, tachycardia, hypokalaemia, arrhythmia in susceptible patients
Methacholine challenge	Incremental inhaled concentrations under supervised laboratory conditions	PC20 causing 20% fall in FEV1; commonly <8 mg/mL supports airway hyperresponsiveness	Bronchospasm; contraindicated if low baseline FEV1, recent MI/stroke, uncontrolled hypertension
Exercise/eucapnic hyperventilation challenge	Standardised ventilation or exercise stimulus	Fall in FEV1 typically ≥10% from baseline	Wheeze, desaturation, arrhythmia in high-risk patients

Procedural standards and quality assurance

Accurate management decisions require technically acceptable measurements. The patient should be seated, wearing a nose clip, with a tight seal around a low-resistance mouthpiece. A maximal inspiration to total lung capacity is followed by an explosive start and continued expiration until a plateau is reached or forced expiratory time is adequate; adults usually require at least 6 seconds, though obstructed patients may need longer. Repeatability requires the two best FEV₁ values and the two best FVC values to agree within 150 mL, or within 100 mL when FVC is ≤1.0 L. At least three acceptable manoeuvres are usually required, with a maximum of eight attempts to avoid fatigue and syncope.

Flow sensors require calibration and biological plausibility checks. Volume calibration is performed with a certified 3 L syringe; acceptable error is generally within ±3%, i.e. 2.91–3.09 L. Pneumotachographs are sensitive to gas viscosity, density, condensation and secretions; heated Fleisch heads reduce water deposition. Turbine sensors may under-read at low flows because of inertia and over-read after rapid acceleration. Hot-wire anemometers depend on convective heat loss and are affected by gas composition and temperature. Ultrasonic sensors avoid moving parts and measure transit-time differences, but alignment and gas composition remain relevant. In anaesthetic circuits, the sensor should be correctly oriented, zeroed, protected from secretions and positioned with awareness of added dead space, particularly in neonates and small children.

Complications, contraindications and follow-up

Forced spirometry can provoke cough, bronchospasm, dizziness, syncope, chest pain, urinary incontinence and rarely pneumothorax or wound dehiscence. Relative contraindications include recent myocardial infarction or pulmonary embolism, unstable angina, haemoptysis of unknown cause, recent thoracic, abdominal, intracranial or ophthalmic surgery, active respiratory infection where aerosol generation is a concern, and inability to cooperate. Bronchial challenge testing requires immediate access to inhaled β₂-agonist, oxygen, monitoring and trained staff.

Follow-up depends on the clinical question. Asthma monitoring uses variability in FEV₁, peak expiratory flow and symptom control rather than a single measurement. COPD severity is staged using post-bronchodilator FEV₁ percentage predicted, but contemporary GOLD treatment grouping also incorporates exacerbation history and symptom burden. Peri-operatively, abnormal spirometry should prompt optimisation rather than automatic cancellation: smoking cessation for at least 4–8 weeks where feasible, treatment of bronchospasm or infection, airway clearance, and planning of postoperative ventilatory support when restrictive disease, obesity hypoventilation or neuromuscular weakness is present.

Exam controversies and advanced synthesis

Standards, reference equations and the “normality” problem

Modern spirometry is not simply “measure FEV₁ and FVC”; it is a standardised physiological test whose interpretation depends critically on technical quality and reference selection. The relevant examination answer should cite ATS/ERS technical standards: spirometers should be accurate to within ±3% or ±50 mL for volume, operate over flows up to approximately ±14 L s⁻¹, and be checked with a 3 L calibration syringe, typically requiring readings within ±3%. Results are reported at BTPS conditions; failure to appreciate gas expansion from ambient to body temperature is a common viva trap.

The major interpretative controversy is the use of a fixed FEV₁/FVC ratio of <0.70 versus the lower limit of normal (LLN), usually the 5th centile or z-score < −1.645. GOLD still operationalises COPD using post-bronchodilator FEV₁/FVC <0.70, whereas ATS/ERS and GLI approaches emphasise age-, sex-, height- and ethnicity-adjusted LLN. The fixed ratio overdiagnoses obstruction in older patients and underdiagnoses it in younger adults. For anaesthetic practice, this matters less for labelling disease and more for recognising gas trapping, dynamic hyperinflation and ventilatory reserve.

Issue	Exam-relevant position	Pitfall
Obstruction	Reduced FEV1/FVC; severity often graded by FEV1 % predicted or z-score	Low FVC from air trapping may mimic restriction
Restriction	Suggested by low FVC with normal/high ratio; confirmed by low TLC	Spirometry alone cannot diagnose restriction definitively
Bronchodilator response	Older criterion: ≥12% and ≥200 mL rise in FEV1 or FVC; newer ERS/ATS: >10% of predicted	“Reversibility” does not equal asthma; COPD may respond
Acceptability	Rapid start, no cough in first second, adequate exhalation, repeatable best values	Reporting a poor-quality trace as physiology

Quality control: what examiners expect you to challenge

A technically valid manoeuvre requires maximal inspiration to TLC, explosive start, continued expiration to an end-test criterion and reproducibility. Repeatability targets are typically best two FEV₁ and FVC within 150 mL, or 100 mL when FVC is ≤1 L. A plateau is conventionally minimal volume change, around <25 mL in 1 s, although prolonged exhalation may be required in severe obstruction. Back-extrapolated volume should be small, classically <5% of FVC or <150 mL. In Primary FRCA vivas, a flow-volume loop with poor effort, cough artefact, early termination, variable extrathoracic obstruction or fixed upper airway obstruction is more likely than a request to recite diagnostic labels.

Flow sensors in anaesthesia: integration, drift and gas dependence

Ventilator spirometry is usually derived from flow measurement integrated over time; hence small zero errors create clinically significant volume drift. The anaesthetic workstation adds additional errors: circuit compliance, compressible volume, leaks, water condensation, secretions, changing gas mixtures and sensor position. A machine-end sensor may accurately measure delivered volume but not necessarily alveolar tidal volume, whereas a proximal airway sensor better detects leaks and patient effort but is vulnerable to condensation, dead space and added resistance.

Sensor	Principle	Advantages	Important limitations
Fleisch/Lilly pneumotachograph	Pressure drop across known resistance; flow derived from ΔP	Good dynamic response; common in respiratory physiology	Gas viscosity/density dependence; blocked by water; requires laminar assumptions
Variable-orifice pneumotach	ΔP across deformable orifice	Robust, compact; common in ventilators	Non-linear calibration; affected by secretions and humidity
Hot-wire anemometer	Cooling of heated element proportional to mass flow	Sensitive at low flows	Gas composition and temperature dependent; fragile, contamination-prone
Ultrasonic sensor	Transit-time difference of ultrasound upstream/downstream	No obstruction; bidirectional; less condensation effect	Depends on gas composition and speed of sound; requires compensation
Turbine	Rotational speed proportional to flow	Simple portable spirometry	Inertia under-reads rapid changes; poor at low flows; contamination

The physical distinction between viscosity-dependent laminar flow and density-dependent turbulent flow is a high-yield synthesis point. In laminar flow, resistance follows Poiseuille behaviour and depends mainly on viscosity; in turbulent flow, pressure drop is more related to gas density and approximately to flow squared. Therefore helium-oxygen mixtures may alter measured flow if the sensor assumes air/oxygen calibration. Nitrous oxide, high oxygen fractions, volatile agents, humidification and temperature all require correction algorithms in modern workstations.

Guidelines and clinical integration in perioperative assessment

Routine spirometry before non-thoracic surgery is not recommended solely to “clear” patients for anaesthesia. Contemporary perioperative guidelines emphasise clinical assessment, exercise tolerance, smoking status, recent exacerbations, oxygen saturation, anaemia and surgical site. Spirometry is most useful when it will change management: unexplained dyspnoea, suspected undiagnosed obstructive disease, preoperative optimisation, lung resection planning, or neuromuscular/chest wall disease. For lung resection, predicted postoperative values are central: ppoFEV₁ and ppoDLCO <40% predicted traditionally indicated increased risk, with many modern algorithms using <30% plus exercise testing thresholds such as stair climb, shuttle walk or CPET; peak VO₂ <10 mL kg⁻¹ min⁻¹ denotes high risk, whereas >20 mL kg⁻¹ min⁻¹ is reassuring.

Viva-level pitfalls and defensible statements

• Do not diagnose restriction from spirometry alone: confirm with TLC, preferably plethysmography or gas dilution, recognising gas dilution underestimates TLC in severe obstruction.
• A low measured tidal volume on the ventilator is not necessarily hypoventilation: consider leak, compliance compensation, circuit compression and sensor location.
• Minute ventilation is not alveolar ventilation: apparatus dead space from proximal sensors, filters and connectors is clinically relevant, especially in paediatrics and low tidal volume ventilation.
• Flow-volume loops are more informative than scalar numbers: variable extrathoracic obstruction flattens inspiration; variable intrathoracic obstruction flattens expiration; fixed obstruction flattens both limbs.
• Calibration is not sterilisation: bacterial/viral filters reduce contamination but add resistance and dead space; condensation may invalidate pneumotach readings.
• Numerical precision is not biological certainty: effort dependence, diurnal variation, recent bronchodilator use, pain, sedation and postoperative splinting all affect results.

The best exam synthesis is to link the measured variable to the sensor physics, then to the clinical consequence: a spirometer does not directly “know” lung volume; it infers volume from moving gas under assumptions about temperature, pressure, humidity, composition, resistance and time. Most errors in practice arise when those assumptions are violated.