On the behavior of inhaled fibers in a replica of the first airway bifurcation under steady flow conditions

Figures & data

Figure 1. A scheme of the experimental rig for visualization of the flow of glass fibers in a replica of the human trachea and the first bifurcation.

Figure 2. A visualization of the replica of the first bifurcation with indication of the measuring cross-sections.

Table 1. An overview of the camera and light settings for all measured flowrates.

Flow rate [l/min]	Image resolution (w × h) [px]	Frames per second [1/s]	Light pulse duration [ns]
2 l/min	1024 × 1024	5000	800
6 l/min	1024 × 1024	20000	800
12 l/min	1024 × 1024	20000	800
24 l/min	512 × 1024	35000	600
36 l/min	512 × 712	50000	500
48 l/min	512 × 512	60000	400

Table 2. Results of the measurement and statistical analysis in the center of simple straight tube, center of a tube with bifurcation and in the position 0.6R from the center of a tube with bifurcation.

			Center of a straight tube				Center of a tube with bifurcation				Position 0.6R from the center of a tube with bifurcation
Flow rate	Ref	Rep	nǁ	n⟂	T1	H0	nǁ	n⟂	T1	H0	nǁ	n⟂	T1	H0
2 l/min	189	0.08	95	74	1.62	✓					27	33	−0.77	✓
6 l/min	566	0.23	138	116	1.38	✓	153	119	2.06	✓	35	25	1.29	✓
12 l/min	1132	0.45	226	194	1.56	✓					34	26	1.03	✓
24 l/min	2264	0.91	392	352	1.50	✓	182	142	2.22	✓	29	31	−0.26	✓
36 l/min	3395	1.36	146	116	1.85	✓	155	115	2.43	✓	36	24	1.55	✓
48 l/min	4527	1.81	216	179	1.86	✓					33	27	0.77	✓

Figure 3. An illustration of possible rotations of fibers parallel and perpendicular to the streamlines. Rotation (rolling) of both fibers about the main axis cannot be registered by the current system. The rotation of the parallel fiber about axes z and y could be easily recognized directly from the images, but the rotation of the perpendicular fiber about the axis x cannot be recognized from a single camera recording. Such a rotating fiber would appear shorter, but as the true length of that specific fiber is not known, no conclusions can be drawn from the observation of a single fiber. Statistical analysis was used to reveal whether the fiber lengths differed in the two observation planes, which would indicate a possible preferential rotation of the perpendicular fibers.

Figure 4. The ratio of parallelly and vertically oriented fibers as a function of the flow Reynolds number. The error bars represent standard deviations.

Table 3. Results of the statistical test on the prevalence of parallel fibers at the inlet and outlet of the measuring window (T₂), on the difference in the fraction of parallelly oriented fibers between the inlet and outlet of the measuring window (T₃), and on differences between the fractions of parallelly oriented fibers at the inlet and outlet (T₄). Calculated at separated locations, flowrates and views.

Branch	Plane	Flowrate (L/min)	#	Inlet orientation		Outlet orientation		Inlet		Outlet		T3	H0	T4	H0
				nǁ	n⟂	nǁ	n⟂	T2,in	H0	T2,out	H0
Left	Cor.	6	52	27	25	30	22	0.28	✓	1.11	✓	−0.59	✓	−0.59	✓
		24	60	29	31	34	26	−0.26	✓	1.03	✓	−0.91	✓	−0.91	✓
		36	60	29	31	30	30	−0.26	✓	0.00	✓	−0.18	✓	−0.18	✓
	Sag.	6	60	36	24	38	22	1.55	✓	2.07	✓	−0.38	✓	−0.38	✓
		24	60	32	28	40	20	0.52	✓	2.58	✓	−1.49	✓	−1.49	✓
		36	60	32	28	32	28	0.52	✓	0.52	✓	0.00	✓	0.00	✓
Right	Cor.	6	60	20	40	41	19	−2.58	✘	2.84	✓	−3.83	✓	−3.83	✘
		24	60	28	32	35	25	−0.52	✓	1.29	✓	−1.28	✓	−1.28	✓
		36	60	26	34	30	30	−1.03	✓	0.00	✓	−0.73	✓	−0.73	✓
	Sag.	6	60	17	43	46	14	−3.36	✘	4.13	✓	−5.30	✓	−5.30	✘
		24	60	20	40	39	21	−2.58	✘	2.32	✓	−3.47	✓	−3.47	✘
		36	60	19	41	33	27	−2.84	✘	0.77	✓	−2.58	✓	−2.58	✘

Table 4. Results of the statistical test on the prevalence of parallel fibers at the inlet and outlet of the measuring window (T₂), on the difference in the fraction of parallelly oriented fibers between the inlet and outlet of the measuring window (T₃), and on differences between the fractions parallelly oriented fibers at the inlet and outlet (T₄) – aggregated views.

Branch	Flowrate (L/min)	#	Inlet orientation		Outlet orientation		Inlet		Outlet		T3	H0	T4	H0
			nǁ	n⟂	nǁ	n⟂	T2,in	H0	T2,out	H0
Left	6	112	63	49	68	44	1.32	✓	2.27	✓	−0.68	✓	−0.68	✓
	24	120	61	59	74	46	0.18	✓	2.56	✓	−1.69	✓	−1.69	✓
	36	120	61	59	62	58	0.18	✓	0.37	✓	−0.13	✓	−0.13	✓
Right	6	120	37	83	87	33	−4.20	✘	4.93	✓	−6.46	✓	−6.46	✘
	24	120	48	72	74	46	−2.19	✘	2.56	✓	−3.36	✓	−3.36	✘
	36	120	45	75	63	57	−2.74	✘	0.55	✓	−2.34	✓	−2.34	✘

Table 5. Results of the statistical test on the equality of the length of the fibers with parallel and perpendicular orientation - separated locations, and views.

			Orientation of fibers	# of fibers	Median of length	Wilcoxon rank-sum test
Straight tube - sagittal			Parallel	1407	36.9	p-value: 0.60070 H0: Not rejected ✓
			Perpendicular	1218	36.8
Upstream of the bifurcation – sagittal			Parallel	490	34.5	p-value: 2.2523E-10 H0: Rejected ✘
			Perpendicular	376	29.9
Downstream of the bifurcation	Left	Coronal	Parallel	123	29.3	p-value: 0.28965 H0: Not rejected ✓
			Perpendicular	124	29.8
	Left	Sagittal	Parallel	99	19.4	p-value: 4.65E-06 H0: Rejected ✘
			Perpendicular	71	23.8
	Right	Coronal	Parallel	61	31.0	p-value: 0.56325 H0: Not rejected ✓
			Perpendicular	60	29,1
	Right	Sagittal	Parallel	35	25.9	p-value: 0.00388 H0: Rejected ✘
			Perpendicular	38	30.1

Figure 5. Trajectories of fibers for Reynolds number of 3400 in the left and right main bronchus, respectively, in the coronal plane. The asterisks denote flip from perpendicular to parallel orientation, the circles the opposite flip.

Table 6. Overview of flips observed in all measured locations and views.

Branch	Observation plane	Total # of recorded fibers	Local Ref	Perp. -> Paral.	Paral. -> Perp.	Perp. -> Perp.
				Flip 90°	Flip 90°	Flip 180°	inlet nǁ/n⟂ ratio	outlet nǁ/n⟂ ratio
Left	Coronal	110	393	2.7%	0%	0%	0.9	1
		400	1572	6.3%	1.3%	0%	0.9	1.1
		150	2358	6.7%	3.3%	0%	0.9	1
	Sagittal	192	393	1.0%	0%	0%	1.5	1.7
		200	1572	5.0%	0%	0%	1.1	2
		200	2358	2.5%	1.5%	0%	1.1	1.1
Right	Coronal	200	393	40.5%	0%	0%	0.5	2.2
		199	1572	26.6%	0%	0%	0.9	1.4
		101	2358	6.9%	4.0%	0%	0.8	1
	Sagittal	200	393	45.5%	0%	0%	0.4	3.3
		200	1572	33.0%	0%	0%	0.5	1.9
		93	2358	31.2%	18.3%	1.1%	0.5	1.2