A computer model of fractal myocardial perfusion heterogeneity to elucidate mechanisms of changes in critical coronary stenosis and hypotension

Critical coronary stenosis (critical CS) alone does not lead to an alteration of fractal dimension (D) under resting conditions in a pig model, indicating undisturbed local myocardial perfusion. If critical CS is combined with hypovolemic anemia the resulting hypotension leads to a significant decline of D. The mechanisms involved in this phenomenon have not yet been elucidated. A computer program was developed enabling calculation of D for normal vascular trees, for single vessel coronary stenosis (CS), and for CS in combination with reduced coronary perfusion pressure (CPP). The values of D obtained by the computer program were compared to those available from an existing animal study to confirm that changes of D can largely be explained by changes of arterial branching pattern simulated by the computer program. Using our computer model, D was 1.15 ± 0.06 in normal vascular trees. Third branch critical CS did not alter D (1.14±0.06; n.s.), wheras critical CS combined with a reduction of CPP to 40 mmHg reduced D (1.07 ± 0.03; P < 0.05). These data are comparable to those obtained in the animal study, and therefore show that alterations of vessel diameter and regional blood flow can largely explain changes of fractal dimension during critical CS and hypotension while changes of functional myocardial parameters might play a minor role.     

青藏高原不同草地利用方式对土壤粒径分形特征的影响

研究青藏高原草地土壤粒径结构分形特征,为该地区土壤质量评价和生态恢复提供科学依据。以青藏高原4种高寒草地(放牧、围栏禁牧、围栏禁牧+补植、未干扰)为对象,采用分形理论,研究不同利用方式对高寒草地土壤颗粒组成及分形特征的影响,明确土壤粒径分形特征的影响因素。结果表明：与放牧和围栏禁牧+补植相比,围栏禁牧草地中黏粒和粉粒体积分数分别增加了60%—91.1%、43.5%—80.1%,禁牧能够促进土壤砂粒向黏粒和粉粒转变。不同草地利用方式对分形维数有显著影响,单重分形维数D值依次为放牧草地<围栏禁牧+补植草地<未干扰草地=围栏禁牧草地,多重分形维数,包括信息维数D₁、信息维数/容量维数比值D₁/D₀和关联维数D₂依次为放牧草地<围栏禁牧+补植草地<围栏禁牧草地<未干扰草地。单重分形维数D与土壤黏粒、粉粒呈极显著正相关(P<0.01);砂粒、黏粒、粉粒、有机碳和全氮是多重分形维数的限制因素。信息维数D₁、信息维数/容量维数比值D₁...     

Fractal parameters and vascular networks: facts & artifacts

Background

Several fractal and non-fractal parameters have been considered for the quantitative assessment of the vascular architecture, using a variety of test specimens and of computational tools. The fractal parameters have the advantage of being scale invariant, i.e. to be independent of the magnification and resolution of the images to be investigated, making easier the comparison among different setups and experiments.

Results

The success of several commercial and/or free codes in computing the fractal parameters has been tested on well known exact models. Based on such a preliminary study, we selected the code Frac-lac in order to analyze images obtained by visualizing the angiogenetic process occurring in chick Chorio Allontoic Membranes (CAM), assumed to be paradigmatic of a realistic 2D vascular network. Among the parameters investigated, the fractal dimension D_f proved to be the most robust estimator for CAM vascular networks. Moreover, only D_f was able to discriminate between effective and elusive increases in vascularization after drug-induced angiogenic stimulations on CAMs.

Conclusion

The fractal dimension D_f is likely to be the most promising tool for monitoring the effectiveness of anti-angiogenic therapies in various clinical contexts.     

Scaling distributional patterns of butterflies across multiple scales: Impact of range history and habitat type

Aim

Assessing the threat status of declining but yet widespread species poses a challenge to applied ecologists. Previous studies using a common metric to describe the spatial aggregation of occurrences across multiple scales, the fractal dimension D_ij, have suggested that species’ distributional trends may be deduced from readily understandable spatial patterns: Expanding species are expected to show more aggregated spatial distributions (higher value of D_ij) than declining species (lower value of D_ij). Here, we revisited these predictions using a large‐scale empirical dataset on Finnish butterflies.

Location

Finland.

Methods

For each butterfly species (n = 97) and across three spatial scales (grid squares of 10 km, 50 km and 100 km), we calculated the area of occupancy (AOO_i) as the sum of occupied grid squares. We employed values of AOO_i to derive the D_ij for each butterfly species. We then used these metrics to compare the changes in spatial patterns of distribution (?AOO_i and ?D_ij) between two time periods, 2000–2002 and 2009–2011.

Results

Majority of the studied butterfly species showed declining areas of occupancy (at the scale of 10 km, ?AOO₁₀) and fractal dimensions (across the scales from 10 km to 100 km, ?D_10–100) between the two study periods. In contrast to predictions, AOO₁₀ and D_10–100 showed negative impacts on the ?AOO₁₀, an observation that may be explained by the high proportion of declining species in our data. Butterfly species with the greatest fractal dimensions at regional scales (D_10–100) in the years 2000–2002 showed both positive long‐term distributional trends and most notable northern recent range limit shifts.

Main conclusions

Our results were in most cases congruent with the prediction of higher fractal dimension values in expanding compared to declining species. As a novel observation, many butterflies expanded northwards in spite of their occurrences getting simultaneously more scattered, particularly in southern Finland.

     

Retinal Vascular Fractal Dimension,Childhood IQ,and Cognitive Ability in Old Age: The Lothian Birth Cohort Study 1936

Purpose

Cerebral microvascular disease is associated with dementia. Differences in the topography of the retinal vascular network may be a marker for cerebrovascular disease. The association between cerebral microvascular state and non-pathological cognitive ageing is less clear, particularly because studies are rarely able to adjust for pre-morbid cognitive ability level. We measured retinal vascular fractal dimension (D _f) as a potential marker of cerebral microvascular disease. We examined the extent to which it contributes to differences in non-pathological cognitive ability in old age, after adjusting for childhood mental ability.

Methods

Participants from the Lothian Birth Cohort 1936 Study (LBC1936) had cognitive ability assessments and retinal photographs taken of both eyes aged around 73 years (n = 648). IQ scores were available from childhood. Retinal vascular D _f was calculated with monofractal and multifractal analysis, performed on custom-written software. Multiple regression models were applied to determine associations between retinal vascular D _f and general cognitive ability (g), processing speed, and memory.

Results

Only three out of 24 comparisons (two eyes × four D _f parameters × three cognitive measures) were found to be significant. This is little more than would be expected by chance. No single association was verified by an equivalent association in the contralateral eye.

Conclusions

The results show little evidence that fractal measures of retinal vascular differences are associated with non-pathological cognitive ageing.     

Evaluation of the Retinal Vasculature in Hypertension and Chronic Kidney Disease in an Elderly Population of Irish Nuns

Background

Chronic kidney disease (CKD) and hypertension are global public health problems associated with considerable morbidity, premature mortality and attendant healthcare costs. Previous studies have highlighted that non-invasive examination of the retinal microcirculation can detect microvascular pathology that is associated with systemic disorders of the circulatory system such as hypertension. We examined the associations between retinal vessel caliber (RVC) and fractal dimension (D_F), with both hypertension and CKD in elderly Irish nuns.

Methods

Data from 1233 participants in the cross-sectional observational Irish Nun Eye Study (INES) were assessed from digital photographs with a standardized protocol using computer-assisted software. Multivariate regression analyses were used to assess associations with hypertension and CKD, with adjustment for age, body mass index (BMI), refraction, fellow eye RVC, smoking, alcohol consumption, ischemic heart disease (IHD), cerebrovascular accident (CVA), diabetes and medication use.

Results

In total, 1122 (91%) participants (mean age: 76.3 [range: 56–100] years) had gradable retinal images of sufficient quality for blood vessel assessment. Hypertension was significantly associated with a narrower central retinal arteriolar equivalent (CRAE) in a fully adjusted analysis (P = 0.002; effect size = -2.16 μm; 95% confidence intervals [CI]: -3.51, -0.81 μm). No significant associations between other retinal vascular parameters and hypertension or between any retinal vascular parameters and CKD were found.

Conclusions

Individuals with hypertension have significantly narrower retinal arterioles which may afford an earlier opportunity for tailored prevention and treatment options to optimize the structure and function of the microvasculature, providing additional clinical utility. No significant associations between retinal vascular parameters and CKD were detected.     

Detection of Glucose and Related Analytes by Biosensors: A Fractal Analysis

A fractal analysis is used to model the binding and dissociation kinetics of connective tissue interstitial glucose, adipose tissue interstitial glucose, insulin, and other related analytes on biosensor surfaces. The analysis provides insights into diffusion-limited analyte-receptor reactions occurring on heterogeneous biosensor surfaces. Numerical values obtained for the binding and the dissociation rate coefficients are linked to the degree of heterogeneity or roughness [fractal dimension (D_f)] present on the biosensor chip surface. The binding and dissociation rate coefficients are sensitive to the degree of heterogeneity on the surface. For example, for the binding of plasma insulin, as the fractal dimension value increases by a factor of 2.47 from D_f1 = 0.6827 to D_f2 = 1.6852, the binding rate coefficient increases by a factor of 4.92 from k₁ = 1.0232 to k₂ = 5.0388. An increase in the degree of heterogeneity on the probe surface leads to an increase in the binding rate coefficient. A dual-fractal analysis is required to fit the binding kinetics in most of the cases presented. A single fractal analysis is adequate to describe the dissociation kinetics. Affinity (ratio of the binding to the dissociation rate coefficient) values are also presented. Interferents for glucose, such as uric acid and ascorbic acid, were also detected by using glucose biosensors based on carbon nanotube (CNT) nanoelectrode ensembles (NEEs) (Lin Y, Lu F, Tu Y, Ren Z. Nano Lett 2004, 4, 191–195).     

Fractal dimensions of metropolitan area road networks and the impacts on the urban built environment

The fractal dimension of road networks emerges as a measure of the complexity of road transport infrastructures. In this study, we measured fractal dimensions of both the geometric form (i.e., the layout of the roads) and structure hierarchy (i.e., the connections among roads) of the major road networks in the largest 95 U.S. metro areas. We explained the causes of the variances in these fractal dimensions, especially the one for structure hierarchy. Further, we hypothesized the impacts of these fractal dimensions on the urban built environment and validated our hypotheses using path analysis. We found that a larger geometric fractal dimension (D_g) shows a more uniform distribution of roads over the metro area, which provides the accessibility to suburban areas and incentives to low-density development. A larger structural fractal dimension (D_s) indicates the highly-connected roads (e.g., highways) tend to join to other highly-connected roads so that most roads can be reached by a small number of neighboring roads (i.e., the small-world phenomenon). As D_s increases and the small-world effect become more significant, daily vehicle miles traveled per capita (DVMT/Cap) decline. However, D_s should be kept low in order to reduce the DVMT/Cap as population size increases. We consider that the low D_s can contribute to more mixed, polycentric and more uniform on an urban area-wide basis. Overall, higher D_g and D_s of the major road network in a metro area leads to higher per capita carbon emissions of transport, and lower quality of life as population increases. In the end, we conclude that fractal dimensions can provide valuable insight into the nature of the transportation land use nexus.     

A New Preparation Method of Coenzyme A with Microorganisms

The structure of aggregates formed by heating dilute BSA solution was analyzed with the fractal concept using light scattering methods. BSA was dissolved in HEPES buffer of pH 7.0 and acetate buffer of pH 5.1 to 0.1% and 0.001% solutions, respectively, and heated at 95°C, varying the heating time t_a. The fractal dimension D_f of the aggregate in the solution was evaluated from static light scattering experiments. The polydispersity exponent τ and the average hydrodynamic radius <R_h> of the aggregates were calculated from dynamic light scattering experiments using master curves obtained by Klein et al. The values of D_f and τ of heat-induced aggregates of BSA at pH 7.0 were about 2.1 and 1.5, respectively, the values of which agreed with those predicted by the reaction-limited cluster–cluster aggregation (RLCCA) model. On the other hand, D_f of heat-induced aggregates at pH 5.1 was about 1.8, which agreed with that predicted by the diffusion-limited cluster–cluster aggregation (DLCCA) model. The dependence of <R_h> for the sample of pH 7.0 on t_a was similar to that of the polystyrene colloids reported previously.     

Circulation,metabolic rate,and body size in mammals

Summary This paper attempts to explain Kleiber's rule, which relates metabolic rate of mammals to their body mass, from the structure and function of the blood circulation system.Abbreviations a scaling factor - fractal dimension - hydrodynamic conductivity - l _n length of an arterial blood vessel at bifurcation level n - M body mass - N maximal number of bifurcation levels - p pressure - Q flow - r size of Bohr effect - r _n radius of an arterial blood vessel at bifurcation level n - V volume - VO ₂ rate of oxygen unloading - Z _n number of arterial blood vessels at bifurcation level n     

A cytoskeletal basis for wood formation in angiosperm trees: the involvement of microfilaments

The cortical microfilament (MF) component of the cytoskeleton within axial elements of the secondary vascular system of the angiosperm tree, Aesculus hippocastanum L. (horse-chestnut) was studied using transmission electron microscopy of ultrathin sections and indirect immunofluorescence microscopy of actin in thick sections. As seen by electron microscopy, MF bundles have a net axial orientation within fusiform cambial cells and their secondary vascular derivatives (i.e. in the axial xylem and phloem parenchyma, xylem fibres, vessel and sieve elements, and companion cells). Immunofluorescence studies, however, reveal that this axial orientation can be more accurately described as a helix of extremely high pitch; it is a persistent feature of all axial secondary vascular elements during their development. Helical MF arrays are the only arrangement seen in secondary phloem cells. However, in addition to helices, other MF arrays are seen in secondary xylem cells. For example, fibres possess ellipses of MFs associated with simple-pit formation, and vessel elements possess circular arrays of MFs that associate with the developing inter-vessel bordered pits, ray–vessel contact pits, and with the perforation plate. Linear MF arrays are seen co-oriented with the developing tertiary wall-thickenings in vessel elements. The possible roles of MFs during the cytodifferentiation of secondary vascular cells is discussed, and compared with that of microtubules. Received: 7 June 1999 / Accepted: 23 December 1999     

A mathematical model for the distribution of hemodynamic parameters in the human retinal microvascular network

To quantitatively assess the arteriovenous distribution of hemodynamic parameters throughout the microvascular network of the human retina, we constructed a retinal microcirculatory model consisting of a dichotomous symmetric branching system. This system is characterized by a diameter exponent of 2.85, instead of 3 as dictated by Murray’s law, except for the capillary networks. The value of 2.85 was the sum of a fractal dimension (1.70) and a branch exponent (1.15) of the retinal vasculature. Following the feeding artery (central retinal artery), each bifurcation was recursively developed at a distance of an individual branch length [L(r) = 7.4r ^1.15] by a centrifugal scheme. The venular tree was formed in the same way. Using this model, we evaluated hemodynamic parameters, including blood pressure, blood flow, blood velocity, shear rate, and shear stress, within the retinal microcirculatory network as a function of vessel diameter. The arteriovenous distributions of blood pressure and velocity in the simulation were consistent with in vivo measurements in the human retina and other vascular beds of small animals. We therefore conclude that the current theoretical model was useful for quantifying hemodynamics as a function of vessel diameter within the retinal microvascular network.     

1,25-Dihydroxyvitamin D3 inhibits parathyroid hormone-related peptide mRNA expression in fetal rat long bones in culture

Summary When fetal rat long bones are incubated in the presence of 10⁻⁸ M 1,25-dihydroxyvitamin D₃ [1,25(OH)₂D₃], steady-state parathyroid hormone-related peptide (PTHrP) mRNA levels are decreased. This decrease is temporary: it is observed as soon as after 3 h of exposure and reaches a nadir after 6 h. At that time, PTHrP mRNA levels are significantly lower in the experimental than in the control bones. However the inhibitory effect vanishes after 24 h, despite continuous exposure to 1,25(OH)₂D₃ for even 48 h. This is the first report showing that PTHrP mRNA expression can be regulated in rat fetal long bones in vitro by 1,25(OH)₂D₃.     

The duality of fractals: roughness and self-similarity

The fractal dimension (D _HB) is an interesting metrics because it is supposed to quantify by a single value, scale independence and roughness of ecological objects. However, we show here that those two properties may be quantified by a single dimension only in some specific cases. In general, a non-integer D _HB quantifies only the roughness, and self-similarity needs to be evidenced or postulated by other means. Second, we revisit some aspects of the practical estimation of D _HB. We recommend the use of madogram instead of variogram for estimations based on geostatistics. We propose a simplification of its estimation for 2D fields and discuss its possible relationship with self-similarity. We finally underline the problem of scale and resolution. Field data recorded during a scientific acoustic survey on the North Sea herring are used for illustrations. The paper concludes on a synthesis of practical recommendations to ecologists when using fractal dimension.     

Quantification of Tortuosity and Fractal Dimension of the Lung Vessels in Pulmonary Hypertension Patients

Pulmonary hypertension (PH) can result in vascular pruning and increased tortuosity of the blood vessels. In this study we examined whether automatic extraction of lung vessels from contrast-enhanced thoracic computed tomography (CT) scans and calculation of tortuosity as well as 3D fractal dimension of the segmented lung vessels results in measures associated with PH.In this pilot study, 24 patients (18 with and 6 without PH) were examined with thorax CT following their diagnostic or follow-up right-sided heart catheterisation (RHC). Images of the whole thorax were acquired with a 128-slice dual-energy CT scanner. After lung identification, a vessel enhancement filter was used to estimate the lung vessel centerlines. From these, the vascular trees were generated. For each vessel segment the tortuosity was calculated using distance metric. Fractal dimension was computed using 3D box counting. Hemodynamic data from RHC was used for correlation analysis.Distance metric, the readout of vessel tortuosity, correlated with mean pulmonary arterial pressure (Spearman correlation coefficient: ρ = 0.60) and other relevant parameters, like pulmonary vascular resistance (ρ = 0.59), arterio-venous difference in oxygen (ρ = 0.54), arterial (ρ = −0.54) and venous oxygen saturation (ρ = −0.68). Moreover, distance metric increased with increase of WHO functional class. In contrast, 3D fractal dimension was only significantly correlated with arterial oxygen saturation (ρ = 0.47).Automatic detection of the lung vascular tree can provide clinically relevant measures of blood vessel morphology. Non-invasive quantification of pulmonary vessel tortuosity may provide a tool to evaluate the severity of pulmonary hypertension.

Trial Registration

ClinicalTrials.gov {"type":"clinical-trial","attrs":{"text":"NCT01607489","term_id":"NCT01607489"}}NCT01607489     

Fractals and the analysis of growth paths

A simple practical method exists for classifying and comparing planar curves composed of connected line segments. This method assigns, a single numberD, the fractal dimension, to each curve.D=log(n)/[log(n)+log(d/L)], where:n is the number of line segments,L is the total length of the line segments, andd is the planar diameter of the curve (the greatest distance between any two endpoints). At one end of the spectrum, for straight line curves,D=1; at the other end of the spectrum, for random walk curves,D→2. Standard statistics are done on the logarithms of the fractal dimension [log(D)]. With this measure, trails of biological movement, such as the growth paths of the cells and the paths of wandering organisms, can be analyzed to determine the likelihood that these trails are random walks and also to compare the straightness of the trails before and after experimental interventions.     

Effects of 50‐Hz magnetic field exposure on hormone secretion and apoptosis‐related gene expression in human first trimester villous trophoblasts in vitro

Evidence from epidemiological and animal studies showed that exposure to extremely low frequency magnetic fields (ELF‐MF) could produce deleterious effects on reproduction. In order to investigate the possible mechanism of MF exposure on reproductive effects, first trimester human chorionic villi at 8–10 weeks' gestation were obtained, and trophoblasts were isolated, cultured, and exposed to a 50‐Hz MF for different durations. The human chorionic gonadotropin (hCG) and progesterone in the culture medium was measured by electrochemiluminescence immunoassay. The mRNA levels of apoptosis‐related genes bcl‐2, bax, caspase‐3, p53, and fas in trophoblasts were analyzed using real‐time RT‐PCR. The results showed that exposure of trophoblasts to MF at 0.2 mT for 72 h did not affect secretion of hCG and progesterone from these cells. There was also no significant change in secretion of these hormones when trophoblasts were exposed to a 0.4 mT MF for 48 h. However, MF significantly inhibited hCG and progesterone secretion of trophoblasts after exposure for 72 h at 0.4 mT. Results of apoptosis‐related gene expression analysis showed that, within 72 h of exposure at 0.4 mT, there was no significant difference between MF exposure and control on the expression pattern of each gene. Based on results of the present experiment, it is suggested that exposure to MF for a longer duration (72 h) could inhibit secretion of hCG and progesterone by human first trimester villous trophoblasts, however, the effect might not be related to trophoblast apoptosis. Bioelectromagnetics 31:566–572, 2010. © 2010 Wiley‐Liss, Inc.     

Response Characteristics of Soil Fractal Features to Different Land Uses in Typical Purple Soil Watershed

As a fundamental characteristic of soil physical properties, the soil Particle Size Distribution (PSD) is important in the research on soil moisture migration, solution transformation, and soil erosion. In this research, the PSD characteristics with distinct methods in different land uses are analyzed. The results show that the upper bound of the volume domain of the clay domain ranges from 5.743μm to 5.749μm for all land-use types. For the silt domain of purple soil, the value ranges among 286.852~286.966 μm. For all purple soil land-use types, the order of the volume domain fractal dimensions is D_clay<D_silt<D_sand. However, the values of D_silt and D_sand in the Pinus massoniana Lamb, Robinia pseudoacacia L and Ipomoea batatas are all higher than the corresponding values in the Citrus reticulate Blanco and Setaria viridis. Moreover, in all the land-use types, all of the parameters in volume domain fractal dimension (D_vi) are higher than the corresponding parameter values from the United States Department of Agriculture (D_vi(U)). The correlation study between the volume domain fractal dimension and the soil properties shows that the intensity of correlation to the soil texture and soil organic matter has the order as: D_silt>D_silt(U)>D_sand (U)>D_sand and D_silt>D_silt(U)>D_sand>D_sand(U), respectively. As it is compared with all D_vi, the D_silt has the most significant correlativity to the soil texture and organic matter in different land uses of the typical purple soil watersheds. Therefore, D_silt will be a potential indictor for evaluating the proportion of fine particles in the PSD, as well as a key measurement in soil quality and productivity studies.     

Influence analysis for the behavior of dewaterability of excess sludge in a two-stage vermifilter

To improve excess sludge dewaterability, a two-stage vermifilter was developed to qualitatively and quantitatively analyze sludge physico-chemical properties (fractal dimension, zeta potential, extracellular polymeric substances (EPS), particle size distribution, etc.) and to correlate them with sludge dewatering characteristics (specific resistance to filtration (SRF) and capillary suction time (CST)). Results demonstrated that sludge dewatering performance was significantly improved after the primary vermifilter VF₁ and the second-stage vermifilter VF₂. In addition, the further VF₂ treatment exhibited higher effects on sludge dewatering performance. The particle boundary of sludge after VF₂ treatment was clearer and smoother than VF₁ sludge (VF₁S), apart from the fact that sludge morphological structure got denser and more compact. Comparing with VF₁S, the fractal dimension D₁ calculated within 1D topological space was closer to 1 after VF₂ treatment, and the fractal dimension D₂ within 2D topological space closer to 2, indicating a better dewatering performance after VF₂ treatment. Additionally, the changes of sludge floc surface properties (such as zeta potential and EPS) resulted in small particles agglomerating into larger ones and then the increase of particle diameter. In summary, the two-stage vermifilter got a better sludge dewatering performance, and thus beneficial for subsequent processing of sludge.

     

Power scaling of ammonitic suture patterns from Cretaceous Ancyloceratina: constraints on septal/sutural complexity

The spatial scaling of 77 hemisutures from 65 species of Cretaceous heteromorphic ammonites was quantified with the fractal box‐counting method. Fractal dimensions within Baculites compressus did not significantly differ between adult hemisutures; however, the juvenile suture of this species did exhibit a significantly lower fractal dimension. This suggests that variation in sutural complexity between explicitly adult ontogenetic stages may not contribute to significant noise in comparisons between other species/morphotypes. High‐spired, three‐dimensionally coiled heteromorphs with a larger degree of septal asymmetry exhibit higher fractal dimensions in outer whorl hemisutures than inner whorl hemisutures due to their elongation and improved space occupation over a larger whorl surface. Three‐dimensionally coiled ammonites also have higher fractal dimensions on average (mean D_b = 1.45) with respect to their 2‐D coiled counterparts (mean D_b = 1.38). All ammonites in this study exhibit a positive trend between sutural complexity and shell size (proxied by whorl height). These relationships suggest that septal frilling is constrained by shell morphology and whorl section geometry during septal morphogenesis. This, in turn, influences the scaling, space‐filling properties and scaling limits of ammonitic suture patterns. Sutural/septal complexity is also found to positively influence the amount of liquid retained in marginal septal recesses. However, as these septa approach larger scales, less cameral liquid is retained per septal mass. This may further explain the positive relationship between sutural complexity and shell size.