An 88-year-old woman is brought to the casualty by her family after a fall 12 hours prior to presentation. She complains of pain in her left wrist, leg, and lower back. She has recently been told by her PHC doctor that she has osteoporosis. On physical examination, her left wrist is tender and has a deformity. She is tender in her low lumbar region. Her left lower extremity is shoened and externally rotated. She is has normal motor strength, sensation, and pulses in her upper and lower extremities. X-ray films reveal a dorsally angulated and displaced fracture of her distal radius. X-ray films of her lumbar spine reveal a compression fracture of the T12 veebra. X-ray films of her left leg reveal a left femur fracture. The basic abnormality affecting this patient's bones is which of the following?