Key Formulas & Equations
Muscle Strength (MMT): 0 = No contraction; 1 = Flicker; 2 = Movement with gravity eliminated; 3 = Movement against gravity; 4 = Movement against some resistance; 5 = Normal strength
Goniometry: Measures joint angles in degrees
Target Heart Rate (Karvonen): THR = (HRmax - HRrest) × intensity + HRrest
Max Heart Rate: HRmax = 220 - age
Heart Rate Reserve: HRR = HRmax - HRrest
Power: P = W / t
Torque: τ = F × r × sin(θ)
Mechanical Advantage: MA = Load / Effort
Barthel Index: 0-100 scale for ADL independence
Visual Analog Scale (VAS): 0-10 pain scale
Borg Scale: 6-20 RPE (Rate of Perceived Exertion)
Gait Speed: Speed = Distance / Time (normal: 1.2-1.4 m/s)
Step Length: Step length = Distance / Number of steps
Cadence: Steps per minute
Core Concepts
Musculoskeletal Physiotherapy
Treatment of injuries and conditions affecting muscles, bones, joints, and ligaments. Includes manual therapy, exercise prescription, and electrotherapy.
Neurological Physiotherapy
Rehabilitation for conditions affecting the nervous system: stroke, spinal cord injury, Parkinson's, multiple sclerosis, and peripheral nerve injuries.
Cardiorespiratory Physiotherapy
Treatment of heart and lung conditions: COPD, asthma, post-surgical rehabilitation, and cardiac rehabilitation programs.
Exercise Prescription
Design of individualized exercise programs based on FITT principles: Frequency, Intensity, Time, and Type. Tailored to patient goals and abilities.
Manual Therapy
Hands-on techniques including joint mobilization, manipulation, soft tissue massage, and myofascial release to reduce pain and improve movement.
Electrotherapy
Use of electrical modalities for treatment: TENS, ultrasound, interferential therapy, and laser therapy for pain relief and tissue healing.
Biomechanics
Study of mechanical laws relating to human movement. Includes gait analysis, posture assessment, and ergonomic evaluation.
Pediatric Physiotherapy
Treatment of infants, children, and adolescents with developmental, neuromuscular, and orthopedic conditions. Uses play-based therapy.
Worked Examples
Example 1: Target Heart Rate
Problem: A 40-year-old with resting HR 70 bpm wants to exercise at 70% intensity. Calculate THR using Karvonen.
Solution:
HRmax = 220 - 40 = 180 bpm
HRR = 180 - 70 = 110 bpm
THR = 110 × 0.70 + 70 = 147 bpm
Example 2: ROM Measurement
Problem: Knee flexion: start at 0° (full extension), end at 135°. Calculate ROM.
Solution:
ROM = 135° - 0° = 135° (normal knee flexion: 135-150°)
Example 3: Gait Speed
Problem: A patient walks 10 meters in 8 seconds. Calculate gait speed.
Solution:
Speed = 10/8 = 1.25 m/s (normal: 1.2-1.4 m/s)
Practice Problems
Problem 1
Calculate HRmax for a 55-year-old patient.
Answer: HRmax = 220 - 55 = 165 bpm
Problem 2
Calculate THR at 60% intensity for a 30-year-old with resting HR 65 bpm.
Answer: HRmax = 190; HRR = 125; THR = 125 × 0.60 + 65 = 140 bpm
Problem 3
Calculate work done lifting a 10 kg weight through 2 m (g = 9.81 m/s²).
Answer: W = 10 × 9.81 × 2 = 196.2 J
Problem 4
Calculate power if 200 J of work is done in 4 seconds.
Answer: P = 200/4 = 50 W
Problem 5
Calculate gait speed for a patient walking 6 meters in 5 seconds.
Answer: Speed = 6/5 = 1.2 m/s
Problem 6
Calculate BMI for a patient weighing 75 kg and 1.70 m tall.
Answer: BMI = 75/(1.70)² = 26.0 kg/m² (overweight)
Problem 7
Calculate torque if a force of 50 N is applied at 0.3 m lever arm at 90°.
Answer: τ = 50 × 0.3 × sin(90°) = 15 N·m