Mathematical Model for the Hemodynamic Response to Venous Occlusion Measured With Near-Infrared Spectroscopy in the Human Forearm

Abstract

We propose a mathematical model to describe the hemodynamic changes induced by a venous occlusion in a human limb. These hemodynamic changes, which include an increase in blood volume, a reduction in blood flow, and modifications to the oxygen saturation of hemoglobin, can all be measured noninvasively with near-infrared spectroscopy (NIRS). To test the model, we have performed NIRS measurements on the human forearm, specifically on the brachioradialis muscle, during venous occlusion induced by a pneumatic cuff inflated around the upper arm to pressures within the range 10-60 mmHg. We have found a good agreement between parameters measured by NIRS (total hemoglobin concentration and hemoglobin saturation) and the corresponding model parameters (capacitor voltage and arterial/capillary branch current). In particular, model and experiment indicate that the time constant for blood accumulation during venous occlusion (approximately 73-79 s) is much slower than the time constant for blood drainage following cuff release (approximately 5 s). These results indicate that this mathematical model can be a valuable analytical tool to characterize, optimize, and further develop diagnostic measurement schemes that use venous occlusion approaches.

Spectral and spatial dependence of diffuse optical signals in response to peripheral nerve stimulation

“…In addition to studying the spectral and spatial dependence of optical responses to nerve stimulation to obtain indications on their origins, we also introduce controlled hemodynamics and oxygenation changes in the tissues under study by means of vascular occlusions. This is accomplished in the human forearm by placing a pressure cuff around the upper arm and inflating the cuff above venous pressure (typical inflation pressure: 50-60 mmHg) to achieve venous occlusion [15–17], or above systolic arterial pressure (typical inflation pressure: 200-260 mmHg or lower, depending on individual systolic pressure values [16]) to achieve arterial occlusion [16,18–20]. Near-infrared spectroscopy studies have characterized the effects of venous occlusion and arterial occlusion on muscle hemodynamics.…”

Assessing Skeletal Muscle Variations in Microvascular Pressure and Unstressed Blood Volume at the Bedside

“…To calculate ΔMBV, we converted the Δ[Hb]tot measured when each cuff compression ended (mean recorded values between 110 and 120 seconds) into grams of Hbtot based on the Hb molecular weight: Δ μ mol[Hb]tot × 64,500/10 6 . Finally, we calculated blood volume per 100 mL T as a proportion between Hbtot in grams and the Hb concentration measured for each subject . Microvascular compliance was calculated from the linear ΔMBV regression in the range from 20 to 50 mmHg expressed as mL per mmHg in 100 mL tissue (mL/100 mL T).…”

“…Considering Pt as the difference between P i and P ext to vessels, we assumed that blood volume stretches vein until Pt is negative ( P i exceeds P ext ). For P i values exceeding P ext , the MBV varies as a function of Pt as follows : MBV = C cv Pt + ( V u ) cv, where cv is capillary and venular compartment and C its compliance. In the forearm, P i stretches vein linearly until a value of ~18 mmHg ( P crit ), as previously reported .…”

“…For P i values exceeding P ext , the MBV varies as a function of Pt as follows : MBV = C cv Pt + ( V u ) cv, where cv is capillary and venular compartment and C its compliance. In the forearm, P i stretches vein linearly until a value of ~18 mmHg ( P crit ), as previously reported . Below this value, the relationship between Pt and MBV changes in linearity possibly because some blood vessels change their shape becoming elliptical in cross section.…”

“…A noninvasive optical technique widely applied in vivo for assessing skeletal muscle perfusion and tissue metabolism after vascular occlusion is NIRS. Because variations in light absorption after incremental P cuff presumably relate only to changes in Hb concentrations, several research groups have used quantitative NIRS technology to relate these changes in the microvascular bed to the applied P cuff , thus calculating vascular compliance in the limbs . An unsolved problem in assessing the microvascular bed with NIRS is that the NIRS signals from Hb and Mb overlap.…”