Common Microcirculatory Framework for Monitoring Integrated Microcirculation

Wide variation in magnitudes, units, and ranges of the microcirculatory variables brings hindrance in describing and evaluating the integrated microcirculatory function of tissues. We designed to establish common microcirculatory framework that contains microhemodynamic and microcirculatory oxygen parameters. To integrate microcirculatory information, demo microcirculatory permutations were generated by a computer algorithm based on microcirculatory characteristics. Four dimensionless methods (Z-score, Min-max, L2, and median scaling) were applied to transform microcirculatory data set into the dimensionless form. Three-dimensional (3-D) common microcirculatory framework was constructed and visualized by using Python and Apache ECharts. The performance of the four dimensionless methods in the pre-processing of multiple microcirculatory variables and the establishment of the common microcirculatory framework were compared. Microhemodynamic and microcirculatory oxygen parameters were embedded in the common microcirculatory framework. After processing by Min-max normalization, the transformed multiple microcirculatory values remained positive with xed range mapping within [0, 1] and maintained the identity property of microcirculation both of microhemodynamic and microcirculatory oxygen variables in the common microcirculatory framework. Conclusively, Min-max normalization displays preferable integration eciency, compatibility, and adaptability in the establishment of the 3-D visualized multiparametric common microcirculatory framework.


Introduction
Microcirculation, consisting of arterioles, capillaries, and venules less than 150 µm in diameter, is a dynamic determinant contributing to the processes involved in the maintenance of metabolic homeostasis and exchange of material and bio-information, which is responsive to physiological and pathological condition 1,2 . The microvasculature exhibits characteristic phenotype, which has reached a consensus that functionally and structurally disturbed microcirculation has been identi ed to precede involvement in the pathogenesis and development of diseases [3][4][5] . Moreover, complexity 6,7 and integrity [8][9][10] are fundamental properties of microcirculation. Nevertheless, despite its signi cance in health and diseases, assessment of integrated microvasculature function became increasingly neglected in clinical condition during the last decades due to lack of proper methods.
The characteristics of multiple microcirculatory variables are highly varying in magnitudes, units, and ranges. Although various microcirculation function indicators were reported in previous studies, the analysis and interpretation of experimental results are mostly based on one single functional variable, which is a lack of integration and accuracy. Therefore, it possesses necessity and signi cance in establishing a common microcirculatory framework of organs and tissues and optimizing multiple parameters interpretation and visualization, which may contribute to the description and evaluation of microcirculatory function globally 11,12 . Generally, the common microcirculatory framework should include microcirculatory oxygen and microhemodynamic pro les. To date, multiple microcirculatory data set remain inherently biased as a result of reasons ranging from organs and tissues handling to differences caused by the laser Doppler instrumentation. Furthermore, when comparing multiple microcirculatory variables, the differences in units and value ranges demand a proper normalization method, which can embed multiple microcirculatory variables into an integrated common framework for visualization and downstream analysis.
Dimensionless processing refers to the removal of mathematical units of data set with different dimensions through mathematical algorithms for the overall analysis, including normalization, standardization, and scaling algorithm [13][14][15] . Moreover, to avoid that the analytic results of microcirculation varying greatly due to multiple variables with different units, it is needed to bring all microcirculatory features to the same magnitude. Therefore, in the current study, a demo multiple microcirculatory data set was generated by a computer algorithm based on microcirculatory characteristics of biological tissues. We aimed to transform and integrate multiple microcirculatory variables using dimensionless algorithms and to establish three-dimensional (3-D) common microcirculatory framework.

Results
Common microcirculatory framework derived from the raw microcirculatory data set. To feed the multiple microcirculatory variables embedded into the integrated 3-D common microcirculatory framework, the demo microcirculatory data set generated based on the microcirculatory function of biological tissues was imported into 3-D modules and revealed an unstandardized characteristic (Fig. 2

, Supplementary
Video S1). Notably, in the 3-D module without dimensionless processing, it was not allowed to generalize the integrated microcirculation in a particular condition. From the ve un-normalized variables, there was an unbalanced appearance in the 3-D common framework due to the different ranges of microcirculatory oxygen and microhemodynamic parameters, which completely dominated by the larger scale (microcirculatory blood perfusion). As expected, the distribution of the data set was hard to observe considering the oscillated characteristics of microcirculatory parameters. Therefore, to integrate and visualize the global property of microcirculatory function, we next sought to compare four dimensionless methods, including Z-Score normalization, Min-max normalization, L2 normalization, and median scaling, to t the multiple microcirculatory permutations in the established common microcirculatory framework.
Dimensionless processing in the architecture of the common microcirculatory framework. After generating the original common microcirculatory framework, subsequently, we selected four dimensionless methods that are commonly used in computational and mathematical researches to integrate the multiple microcirculatory data set and to improve the 3-D common microcirculatory framework. The transformed dimensionless microcirculatory variables were imported into the common microcirculatory framework. After dimensionless processing by Z-score normalization, there were both positive and negative values in the common framework (range from − 2 to 2), which led to di cultly couple with dynamically changed microhemodynamic and microcirculatory oxygen data set (Fig. 3 Moreover, the performance in setting a xed range of mixed microcirculatory variables embedding in the common framework was evaluated subsequently among the four dimensionless methods. The Y axis of common microcirculatory frameworks ( Fig. 3-6) and scatter plots (Fig. 7) displaying all ranges of microcirculatory variables. The ranges of the Z-score and median scaling normalized data set were [-2.50, 3.37], and [0.44, 2.12] respectively, which revealed an un xed range. On the contrary, the entire ranges of microcirculatory features transformed by Min-max normalization and L2 normalization were mapped within the speci c range [0, 1]. Therefore, Min-max normalization exhibited better performance in the processing of multiple microcirculatory variables due to both the positive values and xed intervals.
Performance in maintaining the characteristics of multiple microcirculatory data set. To maintain the characteristics of multiple microcirculatory data set, scatter diagrams were plotted to evaluate the adaptivity of the four dimensionless methods in the processing of multiple microcirculatory variables (Fig. 7). Using microcirculatory oxygen (SO 2 , rHb, PO 2 ) and microhemodynamic (blood perfusion and velocity) data set as input into separated dimensionless classi ers, we observed that the Z-score normalization and Min-max normalization illustrated a superior performance in reducing the distributional deformation of the original multiple microcirculatory data set. However, owing to the mathematic algorithm, dimensionless processing with L2 normalization and median scaling led to partial covering of the original characteristics. Consequently, the continuum property of microcirculatory blood perfusion and microcirculatory oxygen distribution had been better reserved after transforming by Z-score normalization and Min-max normalization comparing with L2 normalization and median scaling, which indicated a better adaptivity in the establishment of the common microcirculatory framework.
Convergency and dispersion of four dimensionless methods on multiple microcirculatory data set. The two different but connected issues with the common microcirculatory framework are convergency and dispersion. To further assess the convergency and dispersion performance of the four dimensionless methods, data set with dimensionless processing were compared in boxplots (Fig. 8A). According to the mathematical principle of interquartile range, Z-score normalization revealed a longer box indicating the dispersed microcirculatory variables although the data set had been dimensionless. While boxes of L2 normalization and median scaling limited the sensitivity of the spread of multiple microcirculatory data set and hence none of these dimensionless is desirable. Moreover, it was noted that after being dimensionless by Z-score normalization, L2 normalization, and median scaling, the microcirculatory oxygen and microhemodynamic data set were relatively in uenced by the convergency and dispersion and were, therefore, less reliable. Taken together, compared to the other three dimensionless methods, the Min-max normalization was proper for the integration and visualization of multiple microcirculatory variables in common microcirculatory framework.
Furthermore, the score plots were judged on four aspects, namely positive transformed values, xed intervals, convergence and dispersion, and identity microcirculatory property. According to the score plots for microcirculatory oxygen (Fig. 8B) and microhemodynamics (Fig. 8C), Min-max normalization obtained better results (8 points in microcirculatory oxygen and microhemodynamic frameworks) than the other three dimensionless methods. Collectively, Min-max normalization performed better in both convergency, dispersion, and compatibility in microcirculatory data set integration and visualization, which indicated the feasibility of implementing a reliable multi-parametric common microcirculatory framework.

Discussion
Microcirculation refers to the terminal microvasculature of organs and tissues, which includes arterioles, capillaries, venules as well as micro-lymphatic vessels bridging larger and smaller scale physiological and pathological phenotypes. The microcirculation dynamically adjusts oxygen-containing blood perfusion and distribution according to the metabolic demands 16 . Global challenges to monitoring microcirculatory function are viewing the multiple parameters combinedly 17,18 , rather than isolated assessment. In the current study, the common microcirculatory framework was established by computer algorithms and integration of multiple microcirculatory variables. Moreover, the multiple functional microcirculatory oxygen and microhemodynamic variables were integrated into 3-D common microcirculatory framework by Min-max dimensionless processing.
Computational and mathematical approaches have been used to analyze the functioning of the microcirculation and to establish (semi-) quantitative relationship between microvascular processes and phenomena occurring on health and diseases 19,20 , leading to insights which could not be obtained solely by reductionist biological and molecular laboratory experiments. In these approaches, dimensional analysis is a method for reducing the complexity of experimental variables by using a sort of compacting algorithm 21,22 . Due to the integrity and heterogeneity of the microcirculation function of tissues, it is therefore important to develop the interpretation and analysis algorithms to extract the characteristics of the microcirculation function, integrating with the whole microcirculation function. In our case, the comparability of the raw and unstandardized integrated microcirculatory module was poor due to dimensional differences among multiple parameters of microcirculation function.
It was Secomb TW 23 that described the theoretical models of microcirculation into phenomenological, qualitative, quantitative, and predictive. To understand the complex microcirculatory system globally, our group propose to establish the common microcirculatory framework, which have been an accepted and valued aspect of researches in the eld of microcirculation. Considering the characteristics of multiple microcirculatory variables, we focused on the most typical numeric variable transformation widely used.
Min-max normalization can speci cally t the data set with a pre-de ned boundary 24,25 . Moreover, with Min-max normalization, microcirculatory values are converted to the values within 0 to 1, which is highly dependent on the maximum and minimum microcirculatory functional values and therefore particularly sensitive to outliers. This is the reason that we performed a lter by automated pre-process outlier module to x the interval, through which the demo microcirculatory data set are less likely to ock in a speci c subrange and work better in the 3-D coordinate rather than masking the microcirculatory properties.
One advantage of Z-score normalization appears to be the ability to minimize the distortion introduced to the microcirculatory data set. Although Z-score normalization is suitable for normal distribution data 26 , however, an apparent drawback of Z-score normalization is that the return microcirculatory value after processing can be negative. In this situation, we have to extend the X axis and Y axis to deal with negative coordinates, which is not conducive to the integration of dynamically changed microhemodynamic and microcirculatory oxygen data set [27][28][29] in the common microcirculatory framework.
Encoding microcirculatory data set by L2 normalization and median scaling eliminates or partially dilutes the original characteristics due to the mathematic algorithm. The L2 normalization assumes that the values of a data set are separated by a constant. Median scaling simply moves the plot up so that the median difference is 0. Hence, both dimensionless methods are not correct the non-linear bias of microcirculatory variables. Moreover, blood perfusion in the microcirculation differs substantially from blood ow in large vessels. In the microcirculation, inertial effects, as well as pulsatility (so-called vasomotion), are partially neglected. L2 normalization is prone to losing information about the scale of inputs of multiple microcirculatory variables, which hamper separating datapoint for the entire microcirculatory data set. Compared with Z-score normalization, L2 normalization, and median scaling, the continuum property of microhemodynamic and microcirculatory oxygen distribution has been better reserved by Min-max normalization.
Additionally, the accuracy and reliability of the microcirculatory functional values are two important determinants of the common microcirculatory framework. Hence, it is necessary to pre-process outliers for the input data set 30 . Comparing various outlier processing algorithms (missing values, mean correction, etc.) 31,32 , in our case, the pre-process of outliers was managed through the script embedding boxplot and least common multiple algorithm, values beyond the boundary were regarded as outliers and automatically adjusted to the nearest boundary value to maintain the identity characteristics of microcirculatory functional data set.
So far, we have revealed dimensional homogeneity using Min-max normalization for converting a homogeneous physiological relation to a dimensionless type. Although the method is straightforward mathematically, there are certain limitations that need to be discussed. First, the selection of important microcirculatory variables requires judgment. Not all microcirculatory parameters, take the rheological properties (viscosity and hematocrit values) for instance, are available and embedded in our common microcirculatory framework. Researchers should decide whether viscosity can be neglected in the speci c application. Furthermore, once the dimensionless analysis is performed, the similarity between the models and algorithms are needed su cient testing.
In conclusion, important microhemodynamic and microcirculatory oxygen variables are embedded in the proposed function through the scaling law of Min-max normalization, which converts the microcirculatory data set from multiple parameters to an integrated 3-D common microcirculatory framework. Therefore, our current study provides methodological support and a novel paradigm for the analysis of integrated microcirculation function of organs and tissues, and pave the way for further exploring the associations between microcirculation and diseases.

Methods
Construction and description of the common microcirculatory framework. The common microcirculatory framework was generally constructed by multimodal laser Doppler-equipped devices and computer algorithm-based modules (Fig. 1). Oxygen to See (O2C, LEA Medizintechnik GmbH, Giessen, Germany), micro ber-optic oxygen transmitter (Microx TX3, PreSens, Precision Sensing GmbH, Regensburg, Germany), and a dual-channel laser Doppler monitoring instrument (VMS-LDF2, Moor Instruments, Ltd., Axminster, UK) were employed to generate microcirculatory oxygen and microhemodynamic parameters, including hemoglobin oxygen saturation (SO 2 ), the relative amount of hemoglobin (rHb), partial oxygen pressure (PO 2 ), microvascular blood perfusion, and blood ow velocity.
Demo microcirculatory permutations were generated by a computer algorithm based on the technical guideline of equipment and the characteristics of microcirculatory oxygen and microhemodynamics of biological tissues. The ranges and dimensions (units) of microcirculatory SO 2 , rHb, PO 2 , blood perfusion, and blood ow velocity were listed in Supplementary Table S1. Subsequently, Python (version 3.7.4, https://www.python.org) and Apache ECharts (Version 4.2.0-RC.2, https://echarts.apache) were used to establish the 3-D common microcirculatory framework, in which the time course, multiple variables, and demo microcirculatory values were de ned as X, Y, and Z axes, respectively.
Data preprocessing of common microcirculatory framework. Outliers are extreme values that deviate from the majority of observations on the microcirculatory data set. In our preprocessing module, outliers in the common microcirculatory framework were detected by the boxplot algorithm. We de ned Q 1 as the 25th percentile largest value and Q 3 as the 75th percentile largest value, so that the difference between Q 3 and Q 1 is the interquartile range (IQR). Values of microcirculatory variables over the range from (Q 1 -1.5×IQR) to (Q 3 1.5×IQR) were considered as outliers and were adjusted to the nearest boundary value automatically. With the outliers preprocessing procedure, all microcirculatory data set were embedded into the common microcirculatory framework. Besides, the least common multiple algorithm was used to ensure the consistency of data size exhibiting in the common microcirculatory framework.
Comparison of dimensionless methods on the establishment of the common microcirculatory framework. Normalization is one of the most important steps in multiple microcirculatory variables analysis. For our common microcirculatory framework, the data set of ve microcirculatory variables differ in dimension and range. To integrate these microcirculatory variables and visualize the global functional status of microcirculation, four common dimensionless methods, including Z-score normalization, Min-max normalization, L2 normalization, and median scaling, were selected to make the microcirculatory data set dimensionless. Z-score normalization is a strategy of normalizing data set that avoids outlier issue. After Z-score processing, the original microcirculatory data set was converted to be squished on the same scale for the features. The absolute value of z represents the distance between that raw microcirculatory data set and the mean in units of the standard deviation. The data set processing equation of Z-score normalization is as follows: L2 normalization is an alternative method widely used in dimensionless scaling for multiple data set 33 , which measures the length or size of vectors and scales the components of feature vector. Each microcirculatory component was divided by the Euclidean length of the vector. The data set processing equation of L2 normalization is: Visualization and video recording of dynamic common microcirculatory framework. A video recording software, ScreenToGif (version 2.19.3, URL: https://www.screentogif.com/), was employed to record the dynamic common microcirculatory framework processed with Z-Score normalization, Min-Max normalization, L2 normalization, and median scaling, respectively. Each video was saved in the format of MP4 with duration of approximately 1 min. The bitrate of the video was approximately 1000 Kbps with 1518 × 816 in resolution ratio.
Scoring of the performance of dimensionless methods. To qualify the performance of four dimensionless methods (Z-score normalization, Min-max normalization, L2 normalization, and median scaling) in the pre-processing of multiple microcirculatory variables and the establishment of the common microcirculatory framework, a scoring system was constructed. In the scoring system, the nal score is a weighted composite of the four scores from each independent performance category. The four categories are positive values, xed intervals, convergence/dispersion, and the extent of maintaining identity property of microcirculatory data set, re ecting the integration e ciency, compatibility, and adaptivity of four dimensionless methods on the establishment and visualization of the common microcirculatory framework. Each category was scored individually (2 points for each category) and summed to calculate the nal score. Moreover, considering the heterogeneity of microcirculatory variables, dimensionless performance in microcirculatory oxygen and microhemodynamics were scored separately.

Declarations Data availability
Requests for access to data should be addressed to the corresponding author.  Figure 1 Schematic of the multimodal device and computer algorithm-based common microcirculatory framework and dimensionless analysis. Arrows denote the directional ow of the demo microcirculatory data set. Multiple microcirculatory parameters, including hemoglobin oxygen saturation (SO2), the relative amount of hemoglobin (rHb), partial oxygen pressure (PO2), microvascular blood perfusion, and blood ow velocity, were generated and inputted into the data processing module. After the automated adjustment of outliers, the microhemodynamic and microcirculatory oxygen data set were transformed to be dimensionless in the data processing module by Z-score normalization, Min-max normalization, L2 normalization, and median scaling, respectively. The pre-processed and dimensionless microcirculatory variables were then integrated and visualized as a three-dimensional (3-D) common microcirculatory framework. The integration e ciency, compatibility, and adaptability of four dimensionless methods on establishing the 3-D common microcirculatory framework were scored and assessed.      Performance of four dimensionless methods in maintaining identity property of microcirculatory data set. After transforming by the four dimensionless methods (Z-score normalization, Min-max normalization, L2 normalization, and median scaling), microcirculatory oxygen and microhemodynamic values (including SO2, rHb, PO2, blood perfusion, and velocity) were illustrated in the scatter plots, which represents the property of multiple microcirculatory parameters.  Performance of four dimensionless methods in microcirculatory data set processing. The integration e ciency, compatibility, and adaptivity of the four dimensionless methods (Z-score normalization, Minmax normalization, L2 normalization, and median scaling) in the pre-processing of multiple microcirculatory variables and in the establishment of common microcirculatory framework were compared and scored. (A) The capabilities of convergency and dispersion were illustrated as boxplots.

Figures
The boxplot covered the values from the 25th percentile largest value to the 75th percentile largest value with the median values marked as black lines in each of the boxes. The whiskers indicated the minimum