On generalized photocurrent spectral moments and the recovery of speed distribution in laser Doppler flowmetry

A note on the compartmental analysis and related issues in laser Doppler flowmetry

Compartmental analysis (CA) in laser Doppler flowmetry (LDF) means deciphering the nutritional and thermoregulating flows from the measured perfusion flux. Based on the new theories proposed in [1] and [2], the CA is formulated here as an optimal approximation without directly involving the geometric information of the vessel network. It is seen that this approximation approach could also solve the biological zero (BZ) problem simultaneously, therefore, it actually provides a systematic solution to the BZ problem without estimating the BZ flux experimentally. In addition, the BZ problem with compartmental differences is reformulated, and the condition under which multiple compartments can be treated as a single one is investigated. The result, together with some computer simulations, showed that the theory in [2] is still an easy and useful approximation in practice. This note serves as an useful supplement to [1] and [2] and may help to solve and clarify some critical problems in LDF.

A mathematical analysis on the biological zero problem in laser Doppler flowmetry

The biological zero (BZ) problem is a critical issue inherent in laser Doppler flowmetry (LDF). It causes confusion when measuring low tissue blood flows. Many experimental studies have been done on the question of whether the BZ flux should be subtracted from the normally measured flux in various situations. However this problem can only be solved after a proper mathematical analysis. Only then can we clearly define and formulate what flux is truly meaningful in blood perfusion measurement and what movement generates the BZ flux and how can we correctly remove it. Following this motivation, the movement of moving blood cells (MBC's) is decomposed into a net translation and a random wondering based on in vivo observations. This important step leads to a clear definition of the BZ and net perfusion flux and reveals that subtraction of BZ flux from the normal flux will certainly cause an underestimation of the net flux. Using this decomposition, the relationship between the net, BZ and normal flux is established which leads to the correct formula to recover the net flux from the BZ and normal fluxes. This recovered net flux is shown to be bounded by the normal flux and the normal flux minus the BZ flux. Numerical studies, preliminary phantom model and clinical evaluations manifest that the new approach is more accurate and reasonable at measuring low net fluxes. In contrast, subtracting BZ flux causes a systematic underestimation of perfusion and is apparently inappropriate even from a methodological point of view. In addition to the novel BZ solution, a general density function of the speed of MBC's is given which is more faithful than the Maxwell density used in [4]. This general density function offers new possibilities for further theoretical developments in LDF.

Intermittent calf and foot compression increases lower extremity blood flow

PURPOSE

Although foot compression increases foot skin perfusion and calf compression increases popliteal artery blood flow, these compression techniques have not been evaluated in combination. The purpose of this study was to evaluate whether calf and foot compression applied separately and simultaneously increase popliteal artery blood flow and/or foot skin perfusion, and to assess the relative merits of compression in patients with superficial femoral artery occlusion.

METHODS

Twenty-two legs from 12 normal volunteers with ankle/brachial indices (ABIs) > 0.96, and 10 legs from 7 claudicator patients with angiographically documented superficial femoral artery (SFA) occlusion and patent popliteal arteries with ABIs < 0.8 were studied in the sitting position. Calf and foot cuffs connected to a rapidly inflating and deflating timed-pressure pump (Art-Assist-AA 1000; ACI Medical Inc., San Marcos, California) were applied to the subject in the sitting position. Skin blood flow of the great toe was measured with a laser doppler (Laserflo model BPM 403A; TSI Inc., St. Paul, Minnesota), and popliteal artery blood flow was measured using duplex ultrasonography (ATL-Ultramark 9; Advanced Tech Laboratory, Bothell, Washington). Foot and calf compression was applied separately and simultaneously at 120 mm Hg pressure, with a 10-second inflation and 20-second deflation cycle. Popliteal artery blood flow and foot skin perfusion were recorded and the mean of 6 cycles calculated.

RESULTS

Precompression popliteal artery blood flow (mL/min) for volunteers was 38.86 +/- 3.94, and for patients was 86.30 +/- 14.55 (P = 0.001). Precompression foot skin perfusion (mL/min/ 100/g tissue) for volunteers was 1.67 +/- 0.29, and for patients was 4.00 +/- 0.92 (P = 0.01). With the application of calf, foot, and simultaneous calf and foot compression, the popliteal artery blood flow increased in volunteers by 124%, 54%, and 173%, respectively, and in patients by 76%, 13%, and 50%. Foot skin perfusion increased in volunteers by 260%, 500%, and 328%, respectively, and in patients by 116%, 246%, and 188%. Relative increases in popliteal artery blood flow and foot skin perfusion were higher in volunteers compared with patients during compression; however, the absolute values for foot skin perfusion and popliteal artery blood flow were consistently higher in patients.

CONCLUSIONS

Measured in the sitting position, the resting popliteal artery blood flow and foot skin perfusion are greater in patients with SFA occlusion compared with normal volunteers. Following compression, popliteal artery blood flow and foot skin perfusion increased in both groups, but relatively more in volunteers. Increases in popliteal artery blood flow are significantly higher with calf compression than with foot compression for both groups. A patent SFA allows for additive increases in popliteal artery blood flow with simultaneous foot and calf compression in normal persons, whereas this is not observed in patients. However, the increases in foot skin perfusion in patients with an occluded SFA parallel the increases shown in normal volunteers, with separate and simultaneous foot and calf compression.