Physiotherapy Formulas

GAIT FORMULAS

I. BASIC GAIT PARAMETERS

These formulas measure fundamental gait characteristics.

1. Step Length (SL) & Stride Length (STL)

Step Length (SL) = Distance between successive heel contacts of opposite feet
Stride Length (STL) = Distance between successive heel contacts of the same foot
STL = 2 × SL

2. Walking Speed (WS) / Gait Velocity

WS (m/s) = Step Length × Cadence
WS = Distance Walked / Time Taken (Normal: 1.2 – 1.4 m/s)

3. Cadence (Steps per Minute, SPM)

Cadence = (Number of Steps / Time) × 60 (Normal: 90 – 140 steps/min)
Cadence = Walking Speed / Step Length

4. Stride Time (ST) & Step Time (Step Duration, SD)

Stride Time = Time taken to complete one full gait cycle
Step Time = Time taken to complete one step
Stride Time = 2 × Step Time

5. Gait Cycle Duration (GCD)

GCD = 1 / Cadence (in Hz)
GCD = Stance Time + Swing Time

II. TEMPORAL & SPATIAL GAIT PARAMETERS

1. Stance & Swing Phase Durations

% Stance Phase = (Stance Time / Gait Cycle Time) × 100 (Normal: 60%)
% Swing Phase = (Swing Time / Gait Cycle Time) × 100 (Normal: 40%)
% Double Support = (Double Support Time / Gait Cycle Time) × 100 (Normal: 20%)

2. Step Width (Base of Support, BOS)

Step Width = Distance between medial borders of two feet (Normal: 5 – 10 cm)

III. CLINICAL GAIT EFFICIENCY FORMULAS

1. Gait Speed Index (GSI)

GSI = (Observed Walking Speed / Normal Walking Speed) × 100

2. Energy Cost of Walking (ECW) / Oxygen Cost

ECW = Oxygen Consumption (VO₂) / Walking Speed
ECW = mL O₂ / kg / min per m/s (Lower ECW indicates more efficient walking)

3. Functional Ambulation Performance (FAP) Score

FAP Score = (Cadence × Step Length) / Gait Cycle Time (Used for gait efficiency assessment)

4. Froude Number (Fr) – Dynamic Stability

Fr = Walking Speed² / (g × Leg Length) (Fr > 1 = running; Fr < 1 = walking)

IV. BIOMECHANICAL & KINEMATIC FORMULAS

These formulas analyze joint angles, forces, and moments in gait.

1. Joint Angle & Velocity

Joint Angular Velocity (ω) = Change in Angle / Time
Joint Acceleration (α) = Change in Angular Velocity / Time

2. Ground Reaction Force (GRF) & Impact Loading

GRF = Body Mass × Acceleration (Vertical GRF at heel strike = 1.2 – 1.5× BW)

3. Torque & Joint Moment

Torque (T) = Force × Moment Arm
Joint Power = Torque × Joint Angular Velocity

V. GAIT DEVIATION & PATHOLOGY FORMULAS

Used to assess gait abnormalities in neurological and orthopedic disorders.

1. Gait Deviation Index (GDI)

GDI = 100 – (Deviation from Normal Gait Patterns × Scaling Factor)
(Lower GDI indicates more gait abnormality)

2. Symmetry Index (SI) – Step Length Asymmetry

SI (%) = (Step Length R – Step Length L) / (0.5 × (Step Length R + Step Length L)) × 100 (SI < 10% indicates normal symmetry)

3. Paretic Propulsion Ratio (PPR) – Stroke Gait Analysis

PPR = (Paretic Peak Propulsive Force / Total Peak Propulsive Force) × 100 (Used in hemiplegic gait)

VI. ADVANCED GAIT MEASURES (3D MOTION ANALYSIS & WEARABLE SENSORS)

1. Step Variability & Regularity

Step Variability = (Standard Deviation of Step Time / Mean Step Time) × 100 (Higher values indicate unstable gait)

2. Harmonic Ratio (HR) – Gait Smoothness

HR = (Even Harmonics Power / Odd Harmonics Power) (HR < 1 indicates jerky, unstable gait)

3. Step-to-Step Transition Cost

Transition Cost = Work Done to Change Velocity / Total Work Done

VII. CLINICAL GAIT INDEXES & SCORES

1. Timed Up and Go (TUG) Test

TUG Time = Time to Stand, Walk 3m, Turn, Walk Back & Sit (Normal: <10s; Fall risk: >14s)

2. 10-Meter Walk Test (10MWT)

10MWT Speed = Distance / Time (Used for mobility assessment)

3. Dynamic Gait Index (DGI)

DGI Score = Sum of scores from 8 walking tasks (Max = 24 points) (Low scores indicate poor balance)

VIII. PROSTHETIC & ORTHOTIC GAIT FORMULAS

Used for amputees & orthotic users.

1. Prosthetic Gait Efficiency Ratio (PGER)

PGER = (Walking Speed with Prosthesis / Normal Walking Speed) × 100

2. Energy Expenditure Index (EEI)

EEI = Heart Rate Difference / Walking Speed (Higher EEI = inefficient gait)

3. Amputee Mobility Predictor (AMP) Score

AMP Score = Functional Ambulation Score + Balance Score (Used for prosthetic prescription)

BIOMECHANICS & KINESIOLOGY FORMULAS

I. LINEAR KINEMATICS FORMULAS

These describe motion without considering forces.

1. Velocity (v)

v = d / t (Velocity = Distance / Time)
v = (Final Position – Initial Position) / Time

2. Acceleration (a)

a = Δv / t (Acceleration = Change in Velocity / Time)
a = (Final Velocity – Initial Velocity) / Time

3. Displacement (s)

s = ut + ½at² (u = initial velocity, a = acceleration, t = time)

II. ANGULAR KINEMATICS FORMULAS

These describe rotational motion.

1. Angular Velocity (ω)

ω = θ / t (Angular velocity = Angular displacement / Time)
ω = (Final Angle – Initial Angle) / Time

2. Angular Acceleration (α)

α = Δω / t (Angular acceleration = Change in Angular Velocity / Time)

3. Relationship between Linear & Angular Motion

v = rω (Linear velocity = Radius × Angular velocity)
a = rα (Linear acceleration = Radius × Angular acceleration)

III. LINEAR KINETICS FORMULAS

These formulas describe forces affecting motion.

1. Newton’s Second Law (Force, F)

F = m × a (Force = Mass × Acceleration)

2. Impulse (J)

J = F × t (Impulse = Force × Time)
J = Δ Momentum (Impulse changes momentum)

3. Momentum (p)

p = m × v (Momentum = Mass × Velocity)

4. Work (W)

W = F × d × cos(θ) (Work = Force × Displacement × cos(angle))

5. Power (P)

P = W / t (Power = Work / Time)
P = F × v (Power = Force × Velocity)

6. Kinetic Energy (KE)

KE = ½ m v² (Kinetic Energy = ½ × Mass × Velocity²)

7. Potential Energy (PE)

PE = mgh (Potential Energy = Mass × Gravity × Height)

IV. TORQUE & MOMENTS FORMULAS

These explain rotational forces acting on joints.

1. Torque (T)

T = F × r × sin(θ) (Torque = Force × Moment Arm × sin(angle))
T = I × α (Torque = Moment of Inertia × Angular Acceleration)

2. Moment of Inertia (I)

I = Σm r² (Moment of Inertia = Sum of Mass × Radius²)

3. Angular Momentum (L)

L = I × ω (Angular Momentum = Moment of Inertia × Angular Velocity)

V. JOINT & MUSCLE MECHANICS FORMULAS

These help in calculating forces at joints and muscles.

1. Joint Reaction Force (JRF)

JRF = Σ External Forces – Muscle Forces

2. Lever Arm Mechanics (Mechanical Advantage, MA)

MA = Effort Arm / Resistance Arm
MA > 1 → Increased Force Production
MA < 1 → Increased Speed & Range of Motion

3. Muscle Force (Fm)

Fm = (External Load × Load Arm) / Muscle Arm

4. Muscle Work (Wm)

Wm = Muscle Force × Displacement × cos(θ)

5. Muscle Power (Pm)

Pm = Fm × v (Muscle Power = Muscle Force × Muscle Shortening Velocity)

VI. GAIT & LOCOMOTION FORMULAS

Used for walking and running analysis.

1. Walking Speed (WS)

WS = Step Length × Cadence

2. Froude Number (Fr)

Fr = v² / (g × l) (Froude number determines walking vs. running)

3. Ground Reaction Force (GRF)

GRF = Body Mass × Acceleration

VII. BALANCE & STABILITY FORMULAS

Used in postural control and rehabilitation.

1. Center of Mass (COM)

COM = Σ(m × x) / Σm (Weighted average position of all mass segments)

2. Stability Index (SI)

SI = (Base of Support Area × Height of COM) / Body Mass (Higher SI = More Stability)

VIII. SPORTS BIOMECHANICS FORMULAS

Used in sports performance assessment.

1. Projectile Motion Equations

Range (R) = (v² × sin(2θ)) / g
Time of Flight = (2v × sin(θ)) / g

2. Stretch-Shortening Cycle (SSC) Power

SSC Power = (Elastic Energy Stored – Energy Used) / Time

3. Plyometric Force

Force = Mass × Velocity² / Displacement

IX. CLINICAL REHABILITATION FORMULAS

Used for injury recovery, muscle strength, and rehabilitation planning.

1. Relative Strength Index (RSI)

RSI = Jump Height / Time to Takeoff (Higher RSI = Better Explosiveness)

2. Rehabilitation Load Calculation

Rehab Load = (1RM × % Intensity) / 100 (1RM = 1 Repetition Max)

3. Fatigue Index (FI)

FI = (Max Power – Min Power) / Max Power × 100 (Higher FI = Greater Fatigue)

X. HUMAN PERFORMANCE & FATIGUE FORMULAS

Used in ergonomics, workplace safety, and endurance testing.

1. Rate of Perceived Exertion (RPE)

RPE Score = HR × 0.1 + 3

2. Work Fatigue Index (WFI)

WFI = (Total Work Done – Work at Fatigue) / Total Work Done × 100

CARDIOPULMONARY FORMULAS

I. CARDIOVASCULAR FORMULAS

Used for heart rate, cardiac output, blood pressure, and perfusion assessment.

1. Heart Rate & Blood Pressure

Maximum Heart Rate (HRmax) = 220 – Age (years)
Mean Arterial Pressure (MAP) = (SBP + 2 × DBP) / 3
Pulse Pressure (PP) = Systolic BP – Diastolic BP
Shock Index = Heart Rate / Systolic BP (Normal: 0.5 – 0.7, Shock > 1.0)

2. Cardiac Output & Stroke Volume

Stroke Volume (SV) = End-Diastolic Volume – End-Systolic Volume
Cardiac Output (CO) = Stroke Volume × Heart Rate (Normal: 4 – 8 L/min)
Cardiac Index (CI) = Cardiac Output / Body Surface Area (BSA) (Normal: 2.5 – 4.0 L/min/m²)
Ejection Fraction (EF%) = (Stroke Volume / End-Diastolic Volume) × 100 (Normal: 55 – 70%)

3. Systemic Vascular Resistance (SVR) & Pulmonary Vascular Resistance (PVR)

SVR = [(MAP – CVP) / Cardiac Output] × 80 (Normal: 900 – 1400 dyn·s/cm⁵)
PVR = [(Mean Pulmonary Artery Pressure – Pulmonary Capillary Wedge Pressure) / Cardiac Output] × 80 (Normal: < 250 dyn·s/cm⁵)

4. Oxygen Delivery & Consumption

Oxygen Content in Arterial Blood (CaO₂) = (1.34 × Hb × SaO₂) + (0.003 × PaO₂) (Normal: 16 – 22 mL O₂/dL)
Oxygen Content in Venous Blood (CvO₂) = (1.34 × Hb × SvO₂) + (0.003 × PvO₂)
Oxygen Delivery (DO₂) = Cardiac Output × CaO₂ × 10
Oxygen Consumption (VO₂) = (CaO₂ – CvO₂) × Cardiac Output × 10 (Normal: 200 – 250 mL/min)

5. Coronary Perfusion & Myocardial Oxygen Demand

Coronary Perfusion Pressure (CPP) = Diastolic BP – Pulmonary Capillary Wedge Pressure (PCWP)
Rate Pressure Product (RPP) = Heart Rate × Systolic Blood Pressure (Indicator of myocardial oxygen demand)

II. PULMONARY FORMULAS

Used for lung function, ventilation, and gas exchange assessments.

1. Respiratory Parameters

Minute Ventilation (VE) = Tidal Volume × Respiratory Rate (Normal: 5 – 10 L/min)
Alveolar Ventilation (VA) = (Tidal Volume – Dead Space) × Respiratory Rate (Normal: 4 – 5 L/min)
Dead Space Ratio (VD/VT) = (PaCO₂ – PECO₂) / PaCO₂ (Normal: 0.2 – 0.4)

2. Gas Exchange & Oxygenation

A-a Gradient = (FiO₂ × (760 – 47) – (PaCO₂ / 0.8)) – PaO₂ (Normal: < 15 mmHg, increases with age)
PaO₂/FiO₂ Ratio = PaO₂ / FiO₂ (Used for ARDS classification, Normal: > 400)
Shunt Fraction (Qs/Qt) = (CcO₂ – CaO₂) / (CcO₂ – CvO₂) (Normal: < 5%)

3. Acid-Base Balance & CO₂ Compensation

Henderson-Hasselbalch Equation:
pH = 6.1 + log (HCO₃⁻ / 0.03 × PaCO₂)
Winter’s Formula (Expected CO₂ in Metabolic Acidosis)
PaCO₂ = (1.5 × HCO₃⁻) + 8 ± 2
Anion Gap (AG) = Na⁺ – (Cl⁻ + HCO₃⁻) (Normal: 8 – 12 mEq/L)
Corrected Anion Gap = AG + (2.5 × (4 – Albumin))

III. VENTILATOR & CRITICAL CARE FORMULAS

1. Ideal Body Weight (IBW) for Ventilator Settings

Males: IBW = 50 + (2.3 × [Height in inches – 60])
Females: IBW = 45.5 + (2.3 × [Height in inches – 60])
Tidal Volume for Ventilator = 6 – 8 mL/kg of IBW

2. Static & Dynamic Compliance

Static Compliance (Cstat) = Tidal Volume / (Plateau Pressure – PEEP) (Normal: 60 – 100 mL/cmH₂O)
Dynamic Compliance (Cdyn) = Tidal Volume / (Peak Pressure – PEEP)

3. PEEP & Oxygenation Indices

Oxygenation Index (OI) = (FiO₂ × Mean Airway Pressure × 100) / PaO₂ (Normal: < 5, Severe ARDS: > 40)
Ventilator Dead Space Ratio = (PaCO₂ – ETCO₂) / PaCO₂ (Normal: < 0.3)

IV. SHOCK & SEPSIS FORMULAS

1. Septic Shock Indicators

Lactate Clearance = (Initial Lactate – Repeat Lactate) / Initial Lactate × 100 (Goal: > 10%)
MAP Goal in Shock = ≥ 65 mmHg
Fluid Challenge = 30 mL/kg of Crystalloids in First 3 Hours

V. MISCELLANEOUS CRITICAL FORMULAS

1. Body Surface Area (BSA) (Mosteller Formula)

BSA (m²) = sqrt([Height (cm) × Weight (kg)] / 3600)
BSA-Based Drug Dosing = Drug Dose × BSA

2. Fraction of Inspired Oxygen (FiO₂) Approximation

FiO₂ Estimate in L/min Flow = (O₂ Flow Rate × 4) + 21 (e.g., 2 L/min ≈ 29%)

ELECTROTHERAPY FORMULAS

I. GENERAL ELECTRICAL STIMULATION FORMULAS

Used for calculating electrical stimulation parameters.

1. Ohm’s Law (Basic Electrical Principle)

$\times R$

V = Voltage (Volts)
I = Current (Amperes)
R = Resistance (Ohms, Ω)

II. TENS & NMES (NEUROMUSCULAR ELECTRICAL STIMULATION) FORMULAS

Used for pain management, muscle stimulation, and rehabilitation.

1. Pulse Charge (Q)

$\times t$

Q = Charge (Coulombs)
I = Current (Amperes, A)
t = Time (Seconds, s)

2. Pulse Duration (PD)

$\frac{1}{Frequency}$

Used to calculate pulse width in microseconds (µs).

3. Duty Cycle

$\ Cycle \ (\%) = \left( \frac{On \ Time}{On \ Time + Off \ Time} \right) \times 100$

Used in NMES and muscle re-education programs.

4. Strength-Duration Curve Formula

$\frac{Rheobase \times Chronaxie}{t}$

I = Current required for stimulation
Rheobase = Minimum current required for muscle contraction
Chronaxie = Minimum pulse duration required for contraction at twice the rheobase current

III. IONTOPHORESIS FORMULAS

Used for transdermal drug delivery using electrical current.

1. Iontophoresis Dosage

$\cdot min) = Current (mA) \times Time (min)$

Typical dose range: 40–80 mA·min
Example: If using 2 mA current for 20 minutes → Dose = 40 mA·min

2. Electrode Polarity & Current Density

$\ Density = \frac{Current (mA)}{Electrode \ Area (cm^2)}$

For cathode (negative electrode): ≤ 0.5 mA/cm²
For anode (positive electrode): ≤ 1.0 mA/cm²

IV. ULTRASOUND THERAPY FORMULAS

Used for deep tissue heating and healing.

1. Ultrasound Intensity Calculation

$(W/cm^2) = \frac{Power (W)}{Effective \ Radiating \ Area (cm^2)}$

Higher intensity = Greater heating effect

2. Beam Non-Uniformity Ratio (BNR)

$\frac{Peak \ Intensity}{Average \ Intensity}$

Lower BNR (≤ 6:1) = Safer treatment with fewer hotspots

3. Spatial Average Temporal Average (SATA)

$(W/cm^2) = SAI \times Duty \ Cycle$

Used for pulsed ultrasound treatments
SAI = Spatial Average Intensity

V. INTERFERENTIAL THERAPY (IFT) FORMULAS

Used for deep pain relief and muscle stimulation.

1. Beat Frequency Calculation

$Beat \ Frequency = |Carrier \ Frequency_1 – Carrier \ Frequency_2|$

Pain relief: 80–150 Hz
Muscle stimulation: 1–10 Hz

2. Amplitude Modulation Frequency (AMF)

$\frac{Beat \ Frequency}{Time (seconds)}$

Helps in preventing accommodation.

VI. SHORTWAVE DIATHERMY (SWD) FORMULAS

Used for deep tissue heating with electromagnetic waves.

1. Power Calculation

$\times Current (A)$

Higher power = Increased tissue heating

2. Energy Absorption Rate

$\frac{Power (W)}{Tissue \ Mass (kg)}$

Used to monitor energy absorbed by tissues

VII. LASER THERAPY FORMULAS

Used for wound healing and pain relief.

1. Energy Dose (Joules/cm²)

$\frac{Power (W) \times Time (s)}{Treatment \ Area (cm^2)}$

Higher dose = Increased tissue penetration

2. Fluence (Energy Density)

$(J/cm^2) = \frac{Power (W) \times Time (s)}{Spot \ Area (cm^2)}$

Adjusting power and time changes the treatment intensity.

VIII. TRANSCUTANEOUS ELECTRICAL NERVE STIMULATION (TENS) SETTINGS

Acute Pain:
- Frequency: 80–150 Hz
- Pulse Duration: 50–100 µs
- Intensity: Sensory level
Chronic Pain:
- Frequency: 2–10 Hz
- Pulse Duration: 200–300 µs
- Intensity: Motor level (strong but comfortable contraction)

MUSCLE STRENGTH & ENDURANCE FORMULAS

I. MUSCLE STRENGTH FORMULAS

Used to quantify maximal force production and muscle performance.

1. One-Repetition Maximum (1RM) – Epley Formula

$\times (1 + 0.0333 \times Reps)$

Weight = Amount lifted (kg/lbs)
Reps = Maximum reps performed before failure
Used for measuring maximum strength in resistance exercises.

2. Brzycki Formula (Alternative 1RM Calculation)

$\frac{Weight}{1.0278 – (0.0278 \times Reps)}$

More accurate for lower repetitions (≤10 reps).

3. Lombardi Formula (For Powerlifting)

$\times Reps^{0.1}$

Used by powerlifters for explosive strength estimation.

4. Strength-to-Body Weight Ratio

$\ Ratio = \frac{1RM}{Body \ Weight}$

Helps determine relative strength in athletes and patients.
Higher ratio = Greater strength efficiency.

5. Peak Torque Measurement (Isokinetic Strength)

$\ Torque = \frac{Force \times Lever \ Arm}{Body \ Mass}$

Used in isokinetic dynamometry to measure muscle force in Nm/kg.

II. MUSCLE ENDURANCE FORMULAS

Used to assess how long a muscle can sustain contractions.

6. Muscular Endurance Index (MEI)

$\frac{Number \ of \ Repetitions}{Time \ (seconds)}$

Higher MEI = Better muscle endurance.

7. Fatigue Index (FI)

$\frac{(Initial \ Power – Final \ Power)}{Initial \ Power} \times 100$

Used for anaerobic endurance assessment.
Higher FI = Greater fatigue (poor endurance).

8. Maximum Voluntary Contraction (MVC)

$\frac{Force_{Maximal} – Force_{Fatigue}}{Time}$

Measures decline in muscle force over time.
Used in electromyography (EMG) & rehabilitation studies.

III. ISOMETRIC & ISOKINETIC STRENGTH FORMULAS

Used for static and controlled-speed muscle testing.

9. Isometric Strength Index (ISI)

$\frac{Peak \ Isometric \ Force}{Body \ Weight}$

Used in rehabilitation & sports assessments.

10. Rate of Force Development (RFD)

$\frac{\Delta Force}{\Delta Time}$

Measures explosive muscle strength.
Used in sports science & physiotherapy.

11. Work Done in Muscle Contraction

$\times Distance$

Used in rehabilitation to calculate energy output.

IV. MUSCLE POWER FORMULAS

Used to measure muscle speed & explosive strength.

12. Power Calculation (Watts)

$\frac{Force \times Distance}{Time}$

Higher power = More explosive strength.

13. Wingate Power Index

$\ Power (W) = \frac{Body \ Mass \times Distance}{Time}$

Used in anaerobic cycling & sprint testing.

14. Margaria-Kalamen Power Test

$\frac{Mass \times Gravity \times Height}{Time}$

Used for lower body power measurement.

V. AEROBIC & ANAEROBIC ENDURANCE FORMULAS

Used for muscle fatigue and recovery analysis.

15. VO2 Max Estimation (Aerobic Capacity)

$VO2Max=15.3×HRMaxHRRestVO2_{Max} = 15.3 \times \frac{HR_{Max}}{HR_{Rest}}$

Higher VO2 max = Greater endurance capacity.

16. Oxygen Debt (Anaerobic Fatigue)

$O_2 Debt = Total \ O_2 \ Consumed – O_2 \ Required$

Used for monitoring fatigue & recovery rates.

RANGE OF MOTION FORMULAS

I. Basic Range of Motion (ROM) Formula

$\ Angle – Initial \ Angle$

Measured in degrees (°) using a goniometer or motion sensors.
Used for joints like knee, elbow, shoulder, hip, spine, etc.

Example:
If a knee moves from 0° (fully extended) to 120° (bent position):

$ROM = 120° - 0° = 120°$

✅ Indicates a normal knee flexion range.

II. Percentage Range of Motion Formula

$ROM)×100\% ROM = \left(\frac{Measured \ ROM}{Normal \ ROM}\right) \times 100$

Compares patient’s movement to standard values.
Helps in tracking recovery & joint function.

Example:
If shoulder flexion is 120°, but normal is 180°:

$%ROM=(120180)×100=66.6%\% ROM = \left(\frac{120}{180}\right) \times 100 = 66.6\%$

✅ Indicates a 33.4% ROM deficit.

III. Joint Stiffness Index (JSI)

$\frac{Torque}{Change \ in \ ROM}$

Used for assessing stiffness & joint restriction.
Higher JSI = Increased joint stiffness (common in arthritis).

IV. Functional ROM Index

$\frac{Patient’s \ ROM}{ROM \ required \ for \ activity} \times 100$

Measures how much ROM is needed for daily activities.

Example:
Knee flexion required for walking = 60°, but patient achieves 45°:

$\left(\frac{45}{60}\right) \times 100 = 75\%$

✅ Indicates mild functional limitation.

V. Angular Velocity of Joint Motion

$ω=ΔθΔt\omega = \frac{\Delta \theta}{\Delta t}$

Used in sports biomechanics & rehabilitation.
Measures speed of joint movement in degrees/second.

Example:
If elbow flexion moves from 0° to 90° in 2 seconds:

$ω=90°−0°2s=45°/s\omega = \frac{90° – 0°}{2s} = 45°/s$

✅ Useful in sports performance & injury prevention.

VI. ROM Deficit Calculation

$ROM_{Deficit} = Normal \ ROM – Measured \ ROM$

Used to track joint restrictions in injury cases.

Example:
Hip flexion normal = 120°, patient achieves 80°:

$ROM_{Deficit} = 120° – 80° = 40°$

✅ Indicates a significant limitation.

VII. Work Done in Joint Motion

$\times Angular \ Displacement$

Used in muscle strength assessment & rehabilitation.

NEUROPHYSIOLOGY FORMULAS

I. Nerve Conduction Velocity (NCV) Formula

$\frac{Distance}{Time}$

Measured in meters per second (m/s).
Used to diagnose peripheral nerve disorders (e.g., carpal tunnel, neuropathy).

Example:
If a nerve impulse travels 0.5 meters in 5 milliseconds (0.005 sec):

$\frac{0.5}{0.005} = 100 \text{ m/s}$

✅ Indicates normal conduction velocity.

II. Synaptic Delay Formula

$\frac{Distance}{Velocity}$

Measures time taken for a signal to pass through a synapse.

III. Resting Membrane Potential (RMP) – Goldman Equation

$Em=RTFln⁡(PK[K+]o+PNa[Na+]o+PCl[Cl−]iPK[K+]i+PNa[Na+]i+PCl[Cl−]o)E_m = \frac{RT}{F} \ln \left( \frac{P_K [K^+]_o + P_Na [Na^+]_o + P_Cl [Cl^-]_i}{P_K [K^+]_i + P_Na [Na^+]_i + P_Cl [Cl^-]_o} \right)$

Determines the electrical potential across the neuronal membrane.
Important for understanding neuron excitability.

IV. Action Potential Propagation Time

$\frac{Axon \ Length}{Conduction \ Velocity}$

Used to calculate the time taken for an action potential to travel along a nerve fiber.

V. Nernst Equation (Equilibrium Potential)

$Ex=RTzFln⁡([X]o[X]i)E_x = \frac{RT}{zF} \ln \left( \frac{[X]_o}{[X]_i} \right)$

Determines ion equilibrium potential (Na+, K+, Cl−, Ca2+).

VI. Refractory Period Formula

$\frac{1}{Maximum \ Firing \ Rate}$

Used to calculate neuron’s ability to fire repetitive signals.

VII. Motor Unit Recruitment Ratio

$\frac{Active \ Motor \ Units}{Total \ Motor \ Units}$

Measures muscle activation efficiency.

VIII. EEG Frequency Bands (Brain Waves)

$(s)\text{Frequency (Hz)} = \frac{1}{Period \ (s)}$

Used in neurological monitoring, epilepsy studies, and sleep analysis.

Brain Wave	Frequency (Hz)	Function
Delta	0.5 – 4	Deep sleep, unconscious state
Theta	4 – 8	Drowsiness, meditation
Alpha	8 – 12	Relaxation, awake but calm
Beta	12 – 30	Active thinking, problem-solving
Gamma	30 – 100	High cognitive function

IX. Cerebral Blood Flow (CBF) Formula

$\frac{CPP}{CVR}$

Where:

CPP = Cerebral Perfusion Pressure
CVR = Cerebral Vascular Resistance

X. Oxygen Consumption of the Brain (CMRO₂)

$MassCMRO_2 = \frac{CBF \times (CaO_2 – CvO_2)}{Brain \ Mass}$

Measures brain oxygen usage.

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