Mice

All animal experiments were performed in accordance with German guidelines and laws, were approved by local animal ethic committees and were conducted according to the guidelines of the Federation of European Laboratory Animal Science Associations. For all experiments, female mice were used with the exception of the DBA/1 DEREG strain. Here both sexes were used. The age of all mice was between 7 and 12 weeks unless stated otherwise.

C57BL/6JOlaHsd, C57BL/6Rj, LysM-EGFP, CatchupIVM-red, Ctnnb1ex2fl/fl;Col10a1-Cre+ and Ctnnb1ex3fl/+;Col10a1-Cre+ mice were bred and housed under specific pathogen-free conditions at the animal facility of the University Duisburg-Essen. LysM-EGFP, CatchupIVM-red, Ctnnb1ex2fl/fl;Col10a1-Cre+ and Ctnnb1ex3fl/+;Col10a1-Cre+ mice were described previously26,41,46. Ctnnb1ex2fl/fl;Col10a1-Cre+ mice were generated by crossing Ctnnb1tm2.1Kem78 and Tg(Col10a1-cre)1427Vdm mice79, while Ctnnb1ex3fl/+;Col10a1-Cre+ mice were generated by crossing Ctnnb1tm1Mmt80 and Tg(Col10a1-cre)1427Vdm mice. Gpr15gfp/+ Foxp3ires-mrfp mice were described previously81, and were bred and housed together with C57BL/6JRj mice under specific pathogen-free conditions in the Laboratory Animal Facility of University Hospital Essen. Reportable experiments involving C57BL/6JOlaHsd, C57BL/6JRj, LysM-EGFP and CatchupIVM-red mice were approved by Landesamt für Natur, Umwelt und Verbraucherschutz (LANUV) of North-Rhine Westphalia, registration numbers 84-02.04.2013.A328, 84-02.04.2013.A129 and 81-02.04.2017.A456.

The DBA/1-DEREG mice were generated by speed congenic back-cross of DEREG mice82 onto the DBA/1J strain, and were housed in the specific pathogen-free facility of University Hospital Jena. All experiments involving DBA/1-DEREG mice were conducted following approval by Thüringer Landesamt für Verbraucherschutz, Bad Langensalza, Germany, registration number 02-079/14.

To generate CX3CR1-cre;tdTomato mice, STOCK Tg(Cx3cr1-cre)MW126Gsat/Mmucd mice (identification number 036395-UCD) were obtained from the Mutant Mouse Regional Resource Center, a NIH-funded strain repository, and were donated to the MMRRC by the NINDS-funded GENSAT BAC transgenic project. They were crossed with B6;129S6-Gt(ROSA)26Sortm9(CAG-tdTomato)Hze/J mice83, resulting in CX3CR1-cre;tdTomato mice. CX3Cr1-Cre;tdTomato mice were bred and housed together with hTNFtg mice45 at the animal facilities of the University of Erlangen, under specific pathogen-free conditions. Experiments involving hTNFtg mice were approved by the Veterinary Office of the Government of Lower Franconia, registration number 54-2532.1-26/12. All mouse strains used are listed in further detail in the reporting summary document and in Supplementary Table 1.

Cryo-sectioning of murine long bones

Murine long bones were fixed in 4% PFA/PBS for 4 h at room temperature after perfusion with EDTA/PBS and 4% PFA/PBS, embedded in OCT compound (Sakura Finetek GmbH) and snap-frozen in liquid nitrogen. A Thermo Fisher cryostat and Cryofilm Type 2 C(9) (Section-Lab Co) were used for sectioning of bone samples.

Histological TRAP staining

After removal, all soft tissue bone samples from CX3CR1-cre;tdTomato mice were fixed in 4% PFA/BS overnight and subsequently incubated for 7 days in decalcification buffer (14% EDTA, 25% ammoniac) under agitation. After completion of decalcification, the remaining bone tissue was saturated with 30% sucrose overnight and then cryo-embedded. Cryo-sections of 7 µm were obtained, washed with distilled water to remove the cryo-embedding matrix and incubated for 5–15 min with TRAP staining solution (Sigma-Aldrich, Acid Phosphatase, Leukocyte (TRAP) Kit, no. 387 A) according to the manufacturer's instructions until proper purple staining of osteoclasts was complete. Nuclei of the same samples were stained with DAPI, 0.2 µg ml–1 (Sigma-Aldrich, no. D9542) for a further 10 min. After washing with distilled water, samples were mounted with fluorescence mounting medium (DAKO, no. S3023) for preservation. Imaging was performed with a Keyence Fluorescence Microscope BZ-X700, where bright-field was used for TRAP staining and fluorescence light was used for DAPI staining (Ex 360/40, DM 400, BA 460/50) and tdTomato signal (Ex 545/25, DM 565, BA 605/70).

Histological immunofluorescence staining

For staining cryo-sections of murine long bones, samples were blocked and permeabilized with 1% BSA and 1% Tween20 in PBS for 1 h at room temperature. Blood vessels were stained, with the antibodies listed in Supplementary Table 2, for 4 h at room temperature. Primary antibodies were washed off with PBS. ICAM-1, VCAM-1 and NG2 were counterstained with chicken anti-rat AF647 antibody, Ephrin B4 with donkey anti-goat AF647 antibody and CD34 with Streptavidin AF488for 4 h at room temperature, and washed three times with PBS. Bone sections were DAPI-stained by embedding with DAPI Fluoromount-G (cat. no. 0100-20, Southern Biotech). Detailed information on all antibodies used is listed in Supplementary Table 2.

Pimonidazole staining

To clarify oxygen transport via TCVs, pimonidazole staining (Hydroxprobe Red 549 Kit, Hydroxyprobe, cat. no. HP7-200Kit) indicating hypoxia was performed.

Female 7–12-week-old C57BL/6J mice received 120 mg kg–1 pimonidazole hydrochloride in PBS by intravenous injection and were sacrificed 2 h later. Histological cryo-sections and immunofluorescence staining of long bones were processed as described above. Detection of hypoxia was performed using a kit including mouse Dyligh549 anti-pimonidazole antibody (1:100 for 4 h at room temperature).

Whole-mount staining and optical clearing of human bone tissue

An adult human femoral head and neck was obtained from a patient undergoing total hip arthroplasty for osteoarthritis. The patient gave informed consent prior to surgery, and the institutional ethics committee of University Hospital Erlangen approved the study. The femoral neck was fixed in 4% PFA/PBS for 24 h at 4–8 °C. Tissue samples were blocked and permeabilized with 1% BSA and 1% Tween20 for 7 days under slight shaking at 4–8 °C. For staining of endothelium we used an anti-human CD31-AF594 antibody (Biolegend, cat. no. 303126, 1:200), and for arterial staining an AF647-labelled anti-human alpha-smooth muscle actin antibody (Novus Biologicals, cat. no. NBP2-34522AF647, 1:200). For tissue staining, samples were incubated for 7 days with slight shaking at 4–8 °C. Samples were then washed twice with 1% Tween 20/PBS for 24 h and cleared with an adjusted simpleCLEAR protocol. According to sample size, bone tissues were each dehydrated with 50, 70 and twofold 100% ethanol for 24 h in gently shaken 50 ml tubes at 4–8 °C, and finally cleared with ethyl cinnamate (Sigma-Aldrich, cat. no. 112372-100 G) at room temperature for 24 h.

Further information on patient recruitment and software versions used for data collection and processing can be found in the reporting summary document and Supplementary table 4.

Induction and assessment of arthritis

Recombinant human G6PI was prepared as previously described47. DEREG mice were immunized on day 0 with a subcutaneous injection of 400 μg recombinant human G6PI emulsified 1:1 (vol/vol) with CFA (Sigma-Aldrich), cat. no. F5881-10ML), with PBS/CFA alone or with PBS without CFA.

Mice were examined for signs of arthritis at least three times per week, and disease severity was recorded for each mouse. The score comprises the number of swollen toes, each assigned 0.5 points, as well as the level of swelling and redness in each of the metatarsal/metacarpal regions and the carpal–metacarpal/tarsal–metatarsal joints. Swelling and redness were determined using the following scoring system: 0, normal; 1, mild redness and swelling; 2, moderate swelling; 3, severe swelling with oedema. The maximum score for each mouse was 33.

To deplete regulatory Tregs, DEREG mice were each treated with 0.5 mg diphtheria toxin (Calbiochem, cat. no. 322326-1MG) intraperitoneally on days −2, −1, +4 and +5 relative to immunization with G6PI, as previously described50,82.

At 14, 28 or (66) 67 days after immunization, animals were narcotized with 1.5–2.0% isoflurane (Forene 100%, AbbVie Deutschland GmbH & Co.) and injected intravenous with 10 µg CD31-AF647, in a total volume of 150 µl PBS with an insulin syringe into the retro-bulbar plexus. Twenty minutes after antibody injection, the mice were killed by CO 2 inhalation and perfused with 15 ml cold 5 mM EDTA/PBS, followed by perfusion with 15 ml cold 4% PFA/PBS. Subsequently the legs were fixed in 4% PFA/PBS overnight at 4–8 °C. After fixation the bones were prepared for optical clearing as described above.

Colitis-associated colonic cancer induction by azoxymethane/dextran sulfate sodium

For induction of colonic cancer, female 7–12-week-old Gpr15gfp/+ Foxp3ires-mrfp mice were injected intraperitoneal with 12.5 mg kg–1 body mass of the pro-carcinogen azoxymethane (AOM, Sigma-Aldrich, cat. no. A5486-25MG). In weeks 1, 4 and 7 following AOM administration, mice received drinking water supplemented with 2% dextran sulfate sodium salt (DSS, MP Biomedicals, cat. no. 0216011010) for 5 days. Mice were sacrificed at week 12, and bone samples were prepared for LSFM as described above.

Zolendronic acid treatment

To inhibit osteoclast activity, female 7–12-week-old hTNFtg and C57BL/6 WT littermates were treated with 100 µg kg–1 body mass zolendronic acid (4 mg 100 ml–1, medac GmBH) in 100 µl PBS once weekly for four weeks. Control mice received pure PBS once per week for four weeks. All treatments were administered by intraperitoneal injection. Mice were examined for signs of arthritis at least three times per week, and body weight and grip strength were recorded for each mouse.

Five weeks after starting zolendronic acid treatment, the animals were narcotized with 1.5–2.0% isoflurane (Forene 100%, AbbVie Deutschland GmbH & Co.) and injected intravenous with 10 µg CD31-AF647, in a total volume of 150 µl PBS with an insulin syringe into the retro-bulbar plexus. Twenty minutes after antibody injection, mice were killed by CO 2 inhalation and perfused with 15 ml cold 5 mM EDTA/PBS, followed by a perfusion with 15 ml cold 4% PFA/PBS. Subsequently the legs were fixed in 4% PFA/PBS overnight at 4–8 °C. After fixation, the bones were prepared for optical clearing as described above.

Lethal irradiation and reconstitution of mice with donor bone marrow

Bone marrow from four female 7–12-week-old C57BL/6JRj donor mice was flushed out of the tibia and femur with sterile PBS. The marrow was re-suspended in sterile PBS to break up any clumps and passed through a 70 µm strainer to remove large fragments. When ready for injection, cells were centrifuged for 10 min at 1,200 r.p.m. and re-suspended in PBS to give a final concentration of 34 million cells ml–1.

The night before irradiation, recipients were denied food then irradiated with 9.5 Gy (950 Rad) before being housed again with access to food and antibiotic-supplemented water (1:100 ciprofloxacin 200). Six hours after irradiation, mice were injected intravenous with 5 million cells in 150 µl sterile PBS. They were maintained on antibiotic water for 2 weeks before being sacrificed 4 weeks after irradiation, when bone marrow and bone samples were prepared for LSFM as described above.

Images and videos of exposed human long bones

Demonstrating the clinical impact of our hypothesis, cortical bleeding was documented by images and videos of patients undergoing orthopaedic procedures on diaphyseal long bones (fibula/tibia/femur) and femoral neck. Individuals were selected randomized and incidentally by the orthopaedic surgeon. Here, informed consent was given following the institutional guidelines (Orthopaedic and Trauma Department, University of Duisburg-Essen).

Further information on patient recruitment is listed in the reporting summary document.

LSFM of optically cleared samples

For LSFM imaging of simpleCLEAR optically cleared samples, we used an LaVision BioTec Ultramicroscope (LaVision BioTec) with an Olympus MVX10 zoom microscope body (Olympus), a LaVision BioTec Laser Module, an Andor Neo sCMOS Camera with a pixel size of 6.5 µm, and detection optics with an optical magnification range 1.263–12.63 and a numerical aperture (NA) of 0.5. Because a non-specific autofluorescence signal is useful for visualizing general tissue morphology, a 488 nm optically pumped semiconductor laser (OPSL) was used for generation of autofluorescent signals. For CD31-AF594 excitation, we used a 561 nm OPSL and, for CD31-AF647, Sca-1-AF647 and SMA-AF647 excitation, a 647 nm diode laser. Emitted wavelengths were detected with specific detection filters: 525/50 nm for autofluorescence, 620/60 nm for CD31-AF594 and 680/30 nm for CD31-AF647, Sca-1-AF647 and SMA-AF647. The optical zoom factor for measurements ranged from 1.26 to 12.60, and the light-sheet thickness ranged from 5 to 10 µm.

Further information on software versions used for data collection and processing is listed in the reporting summary document and Supplementary table 4.

X-ray microtomography imaging

For X-ray microtomography imaging of hTNFtg tibiae, simpleCLEAR optically cleared samples were rehydrated by incubation in 1% Tween20 in 70% ethyl alcohol, followed by 1% Tween in 50% ethyl alcohol and two further treatments with pure PBS. All incubations were performed at room temperature with gentle shaking in 5 ml Eppendorf tubes.

Micro-CT imaging was performed using the cone-beam desktop micro-computer tomograph µCT 40 (SCANCO Medical AG). Settings were optimized for calcified tissue visualization at 45 peak kilovoltage (kVp), with a current of 177 µA and 240 ms integration time for 500 projections per 180° and, furthermore, 8.0 µm was set as isotropic voxel size for optimal resolution. For the segmentation of 3D volumes, respective greyscale thresholds were determined using the operating system Open VMS from SCANCO Medical. The entire tibial cortex only was chosen as volume of interest for bone volume analysis.

Further information on software versions used for data collection and processing is listed in the reporting summary document and Supplementary Table 4.

Single- and two-photon laser scanning microscopy of cleared organs

For high-magnification imaging of ethyl cinnamate-cleared bones, a Leica TCS SP8 fully automated epifluorescence confocal microscope (Leica Microsystems) with Acousto-Optical Tunable Filter (AOTF) and Acousto-Optical Beam Splitter (AOBS) scanoptics, HyD detection, two-photon and compact OPO on a DM6000 CFS frame was used. Imaging of ethyl cinnamate-cleared tibiae and fibulae was performed with a ×25 HCX IRAPO L water-immersion objective with a NA of 0.95.

Since optical clearing is reversible, the cleared samples were embedded in ethyl cinnamate-filled microscopy chambers, which were sealed with a cover slip. Fluorescence signals were generated via sequential scans, exciting Sca-1-AF647 via single-photon excitation using an HeNE laser at 633 nm and detecting in confocal mode with an internal HyD at 660–720 nm. The second confocal mode sequence included a DPSS single-photon laser at 561 nm for excitation of CD31-AF594, and an internal PMT detector at 600–640 nm. The third sequence was performed with a Titan-Sapphire laser tuned to 960 nm for SHG detection at 460/50 nm detected with an external photomultiplier tube (PMT NDD1).

For histological CLSM data, a Leica SP5 II confocal microscope (Leica Microsystems) with AOTF and AOBS, and HyD detection on a DMI6000 CS frame, was used. Imaging of coverslip-embedded samples was performed using an HCX PL APO ×100 oil objective with a NA of 1.44. Fluorescence signals were generated via sequential scans, exciting tdTomato or AF555 using a DPSS laser at 561 nm and detecting with an HyD tuned to 600–650 nm. The second sequence for visualizing AF488 signals comprised an Argon laser at 488 nm for excitation and an HyD detector tuned to 500–550 nm. As a third sequence, a 633 nm Helium–Neon laser for Alexa Fluor 647 excitation and an HyD tuned to 650–700 nm for detection were used. The fourth sequence included a 405 nm laser Diode for DAPI excitation and HyD detection at 470–520 nm.

Further information on software versions used for data collection and processing is listed in the reporting summary document and Supplementary table 4.

Intravital TPLSM

Mice were prepared for intravital TPLSM as previously described4. TPLSM was performed with a Leica system as described above. EGFP+ cells of female 7–12-week-old LysM-EGFP mice and tdTomato+ cells of CatchupIVM-red mice were excited at 960 nm, at which point bone tissue additionally emits a SHG signal at 480 nm. Fluorescent cells were detected with specific filters at either 525/50 nm (EGFP) or 585/50 nm (tdTomato), and SHG was detected via a 460/50 nm filter.

Blood flow was visualized by injecting (intravenous) either 1.5 mg ml–1 rhodamine dextran (Sigma-Aldrich, cat. no. R9379–100MG) or 1 µM Qtracker 655 Vascular Labels (Thermo Fisher, cat. no. Q21021MP) in a total volume of 100 µl PBS. Fluorescence was excited at 960 nm and detected with either a 585/40 nm (rhodamine dextran) or a 650/50 nm (Qtracker 655) filter. Imaging was performed in both resonant and non-resonant detection mode. Scan speed was adjusted individually for different vessel types, from 600 Hz to 12 kHz.

Neutrophils were activated by injecting (intravenous) 100 µg kg–1 body weight human recombinant granulocyte-stimulating factor (Neupogen, Amgen GmbH) in a total volume of 100 µl PBS. The raw data were reconstructed and analysed using Imaris software (Bitplane) and ImageJ.

Further information on software versions used for data collection and processing is listed in the reporting summary document and Supplementary table 4.

X-ray microscopy of murine long bones

Female 7–12-week-old C57BL/6J mice were painlessly killed via cervical dislocation, and the hind legs were prepared. Surrounding muscle tissue was circumspectly removed from the entire leg. The remaining tissue was digested in a collagenase solution consisting of 1 mg ml–1 collagenase Type IV and 10 mM HEPES in HBSS, with gentle shaking for 12 h at 37 °C. After incubation, the remaining tissues were dissected into their constituent parts. The separated tibiae were collected and incubated again in collagenase solution for 12 h at 37 °C.

The X-ray microscope is a sample-rotating system providing a suitably long working distance and adjustable energy range for obtaining 3D density data from a sample, whereas conventional 2D radiographs capture the X-ray density of a sample from hundreds of different angles. The data are reconstructed into a 3D data set with each voxel containing a value of X-ray density of that location in space. This method can capture complex internal geometries where there is sufficient contrast between material densities34. Recent advances in this field allow voxel sizes below the micrometre range84.

Scanning of the tibia was performed using an isotropic voxel size of 1.7 μm with the ×4 objective on a Zeiss Versa 520 (Carl Zeiss). A high signal–noise ratio was achieved by collecting 1,885 projections per rotation with a projection exposure time of 8 s (40 kVp voltage, 3 W power, 360° angle range). Generated data were reconstructed and analysed using Imaris (Bitplane).

Further information on software versions used for data collection and processing is listed in the reporting summary document and Supplementary table 4.

Field emission scanning electron microscopy of murine long bones

Female 7–12-week-old C57BL/6J mice were painlessly killed via cervical dislocation and the hind legs were prepared. The muscles were circumspectly removed from bones (femurs and tibiae), the latter then being fixed in a solution of 2% glutaraldehyde, 3% formaldehyde, 0.01 M calcium chloride, 0.01 M magnesium chloride and 0.09 M saccharose for 12 h at room temperature. Fixed samples were washed twice for 10 min with TE buffer (20 mM TRIS, 1 mM EDTA, pH 6.9) and dehydrated with a graded series of acetone (10, 30, 50, 70, 90%) for 30 min for each step on ice. Samples in the 100% acetone step were allowed to reach room temperature before a further change of 100% acetone. Samples were then subjected to critical-point drying with liquid CO 2 (CPD 30, Bal-Tec). Dried samples were fixed onto aluminium stubs with plastic conductive carbon cement (PLANOCARBON, Plano, cat. no. N650) and covered with gold film by sputter-coating (SCD 500, Bal-Tec) before examination with a field emission scanning electron microscope, Zeiss Merlin (Zeiss), using an Everhart Thornley HESE2 detector and an in-lens SE detector (at a ratio of 25:75) with an acceleration voltage of 5 kV.

Further information on software versions used for data collection and processing is listed in the reporting summary document and Supplementary table 4.

Magnetic resonance imaging of a human shank

Approval from the local institutional ethics committee of the medical faculty of the University of Duisburg-Essen was gained prior to this study. After signing informed consent, the right lower leg of a healthy 47-year-old male subject was imaged on a 7-Tesla research whole-body magnetic resonance system (Magnetom 7 T, Siemens Healthcare). The leg was placed feet-first and supine within an in-house-developed eight-channel radiofrequency transmit/receive head coil85. An additional seven-channel loop receive-only radiofrequency array was placed on top of the tibia and fixed with a vacuum pillow and Velcro strips86. Transmitter adjustment was performed with a vendor-provided B1 mapping sequence based on a spin-echo and a stimulated echo87. For high-resolution imaging, T1-weighted, fat-saturated pulse sequences were acquired in 2D (fast low-angle shot, FLASH) and 3D (volume-interpolated breath-hold examination, VIBE). Additionally, a time-of-flight sequence was used to distinguish the direction of blood flow88. Time-of-flight MR angiography images are expected to show blood flowing in the caudocranial direction hyper-intensely when the 80 mm (width) saturation band is placed cranially (11 mm gap to excitation slab), while flow in the craniocaudal direction will be hyper-intense when the saturation band is placed caudally. Further imaging details are summarized in Supplementary Table 5.

Image evaluation was performed on the magnetic resonance console Syngo VB17 (Siemens Healthcare), and then data export was reconstructed using ImageJ and Imaris (Bitplane). All MR sequences were acquired in transverse orientation with phase-encoding direction anterior–posterior. A parallel imaging factor of 2 was applied for each sequence89.

Further information on patient recruitment and on software versions used for data collection and processing is listed in the reporting summary document and Supplementary Table 4.

Blood vessel diameter measurement

Arteries and veins were identified by their specific antibody staining (veins: CD31+/Sca-1–, arteries: CD31+/Sca-1+) in Imaris. To measure the diameter of the vessel types identified, 5 µm optical sections were generated with the 'slice' tool and diameters were measured via the 'measurement point' tool in Imaris. This analysis was done with LSFM data of entire tibiae, intravital TPLSM data and histological bone sections. In the case of intravital TPLSM, only TCVs and sinusoids were measured as these were identifiable by their characteristic morphology and location within the bone.

The quantification of total vessel numbers in entire tibiae was based on 100 µm optical sections of LSFM data generated by the slice tool in Imaris. These sections were exported as tiff. files and imported into ImageJ. The vessels were quantified by manual counting via the 'cell counter' tool in ImageJ. In this process we also included vessel orientation and distribution, taking into account the anterior and posterior aspects as well as the upper and lower half of the tibia. The results were confirmed by individual quantification by four independent persons.

TCV type analysis

Quantification of arterial and venous TCVs, plus the quantification of intracortical loops and direct, bifurcated and complex TCVs, was based on manual counting of vessels in 100 µm optical sections via the cell counter tool of ImageJ as described above.

To analyse the straightness of dTCVs, the measurement point tool in Imaris was used, where every shift in direction was set as a new measurement point. The corresponding thickness of the compact bone was analysed with the 'this tool. Here the measured distance was defined as the position of the particular dTCV from the endosteum to the periosteum perpendicular to the bone shaft. The results were confirmed by individual quantification by four independent persons.

Co-localization analysis

For co-localization analysis of histological sections, 3D CLSM stacks were used. Data files were de-convolved using Huygens Professional software and imported into ImageJ. Freehand regions of interest (ROIs) were defined around TCVs and analysed for co-localization with Coloc 2 Plugin.

Estimation of cell velocity from TPLSM images

Erythrocyte velocity was estimated from scanning microscopy images as follows. We extracted ROIs from scanning microscopy images of blood vessels. ROIs contained dark traces left by individual, unlabelled erythrocytes moving with fluorescently labelled blood flow in a horizontal direction (parallel to scanning direction). Typically, several parallel straight linear traces, either diagonally or vertically, could be identified per ROI. The horizontal length, Δx cell , of each trace was interpreted as the distance covered by an erythrocyte while being scanned over time Δt. Thus the velocity of the erythrocyte could be estimated as

$${\rm{\Delta }}{x}_{{\rm{cell}}}{\rm{\Delta }}t={\ell }_{{\rm{pix}}}\times {\rm{\Delta }}{n}_{{\rm{col}}}{\rm{\Delta }}{t}_{{\rm{row}}}\times {\rm{\Delta }}{n}_{{\rm{row}}}={\ell }_{{\rm{pix}}}{\rm{\Delta }}{t}_{{\rm{row}}}\times 1\beta$$ (1)

with ℓ pix the length of a pixel; Δt row the time needed by the microscope to scan a complete single row of pixels; Δn col and Δn row the number of pixel columns and rows, respectively, spanned by the trace; and the slope β = Δn row ⁄ Δn col of the trace. Thus, we estimated erythrocyte velocity from the measurement parameters ℓ pix and Δt row , and the slopes β of the traces extracted from the ROIs.

For each ROI, the slope β was estimated from cross-correlations

$$R({\rm{\Delta }}c,{\rm{\Delta }}r)=\sum _{c,r\in {\rm{ROI}}}{I}_{c,r}{I}_{c+{\rm{\Delta }}c,r-{\rm{\Delta }}r}$$ (2)

of grey-level intensity in pixel columns c and c + Δc at pixel row lags Δr. One or more traces induce a maximum of R(Δc, Δr) for Δr ∝ βΔc. Moving through a series of Δc allows this maximum of cross-correlation to wander through a corresponding series of Δr values. The slope β was then computed by a linear least-square fit to the series of maximum positions (Δc, Δr).

Total blood flow can be calculated from the estimated cell velocity and total cross-sectional area of vessel types defined. Based on total vessel numbers per tibia and vessel diameters defined, the total cross-sectional area (A total ) of the vessel types identified was calculated as follows:

$${A}_{{\rm{(total)}}}=\left(\pi \times {r}^{2}\right)\times n$$ (3)

Here, r2 is the squared radius of the vessel type and n is the total number of vessel types.

As blood flow of the central sinus was not measureable via intravital TPLSM, blood egression was calculated based on NA influx, arterial TCV influx and venous TCV-based blood effusion.

Reporting Summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Code availability

A Julia package implementing the computational procedure for the estimation of blood vessel speed is freely available as a source code at https://github.com/DanielHoffmann32/CellSpeedEstimation.jl.

Statistics

For normal quantile plots, evaluated data were ranked. Rank-based z-scores were calculated based on the mean (µ), standard deviation (x) and sample number (σ):

$${z}=\left({\mu }-x\right)/{\sigma }$$ (4)

Finally the z-scores were converted to predicted data values by calculating

$$Y=\left(z\times {\rm{s.d.}}\right)+{\rm{mean}}$$ (5)

and fit into the normal quantile plot.

For calculation of statistical significance, GraphPad Prism 7 was used. Data are presented as mean ± s.e.m. and were analysed using two-sided Student’s t-test, two-sided Mann–Whitney U-test or Kruskal–Wallis H-test, with Dunn’s multiple comparisons test as a post hoc procedure. P < 0.05 was considered significant.