Within the last decade, archaeogenetic analysis has revolutionized archaeological research and enabled novel insights into mobility, relatedness and health of past societies. Now, it is possible to develop these results further and integrate archaeogenetic insights into biological relatedness with radiocarbon dates as means of chronologically sequenced information. In our article, we demonstrate the potential of combining relative chronological information with absolute radiocarbon dates by Bayesian interpretation in order to improve age determinations. Using artificial pedigrees with four sets of simulated radiocarbon dates we show that the combination of relationship information with radiocarbon dates improves the age determination in many cases at least between 20 to 50%. Calibrated age ranges are more constrained than simply calibrating radiocarbon ages independently from each other. Thereby, the precision of modelled ages depends on the precision of the single radiocarbon dates, the number of modelled generations, the shape of the calibration curve and the availability of samples that can be precisely fixed in time due to specific patterns in the calibration curve (“anchor points”). Ambiguous calibrated radiocarbon dates, which are caused by inversions of the calibration curve, can be partly or almost entirely resolved through Bayesian modelling based upon information from pedigrees. Finally, we discuss selected case studies of biological pedigrees achieved for Early Bronze Age Southern Germany by recent archaeogenetic analysis, whereby the sites and pedigrees differ with regard to the quality of information, which can be used for a Bayesian model of the radiocarbon dates. In accordance with the abstract models, radiocarbon dates can again be better constrained and are therefore more applicable for archaeological interpretation and chronological placement of the dated individuals. Radiocarbon dating, developed by Willard F. Libby in the 1940s, led to a revolution in our understanding of our past  and can 14C fluctuations will always limit the calibrated uncertainty.Since past atmospheric radiocarbon content varied over time, one high-precision radiocarbon measurement can result in multiple calibrated calendric date ranges, resulting in much larger uncertainties over the initial radiocarbon result. While more precise radiocarbon dates do improve the uncertainty of the calibrated dates and result in narrower age ranges, the nature of the atmospheric Bayesian modelling of radiocarbon data ,4 has shSo far, such specifications in archaeological contexts are only available via physical stratigraphic contexts (see ), as for1⁴C ages, thus reducing the calibration ranges by informing the calibration procedure about the chronological order of the generations. Sedig et al. 2021  and child[ren]) is necessary to make statements about their relative chronological relation to each other. All individuals which can be placed within the pedigree must have been radiocarbon dated to increase the information density in the model. To avoid as many unknowns/uncertainties from the outset and to refine the overall outcome of the statistical models, the anthropologically determined age-at-death (AaD) of the individuals is of great advantage in quantifying the difference in calendric years between the years-of-death (YoDs) of each individual. In addition, we only used radiocarbon dates from uncremated skeletal remains to exclude any taphonomic issues associated with charcoals or other organic remains from the filling of the grave pit.The general idea of the paper is to use the pedigrees provided by biological kinship analyses of ancient DNA to prescribe a chronological order to the year-of-death (YoD) of the individuals and to their However, one main prior assumption has to be made–the reproductive age is set at 20 years of age for all simulations, determining the difference of the year-of-birth (YoB) from one generation-level to the next, which is plausible as a mean value for pre-industrial societies. This is necessary to calculate the generation gap/intervals used in the simulations, but we are well aware that it is rather a reproductive time span in reality ,17. Howe2, which was then reduced to graphite. The 14C analysis was performed at CEZA (Curt-Engelhorn-Center Archaeometry) using a MICADAS-type AMS system Boundary("Gen 1/2");Phase("Gen 2"){R_Date;R_Date;};Boundary("End Gen 2");};};The excavated and documented part of the Early Bronze Age cemetery of Haunstetten contained at least 40 graves with 41 individuals . Due to The skeletal remains of every individual were analysed anthropologically. Unfortunately, the gravel soil caused physical damage to bones, causing difficulties in determining the AaD . Most individuals were adults, with AaD ranging from 17 up to probably 55 years, and two individuals  at the end of the lineage died during childhood or youth .22 individuals were sampled for DNA analyses, 19 of which provided mitochondrial genomes. 15 were selected for targeted nuclear DNA capture and relatedness analyses. A biological affiliation to the biological pedigree was detected for 10 individuals, and 7 of them could be placed in an explicit pedigree, with an additional individual added on the basis of the mitochondrial DNA. The pedigree consists of four or five generations, depending on the positioning of POST_44, who could be placed as either grandfather in the first or uncle in the second generation. After the third generation, the pedigree splits into two paternally related lineages. These individuals were buried in close proximity to each other in the northern half of the cemetery, partly occupying the prominent burial mounds, and were very well equipped with grave goods.Radiocarbon dates without HBCO correction gathered from skeletal remains fall between 2197 and 1772 cal BC (2-sigma), with most of them between 2140 and 1880 cal BC, covering a small section of the calibration curve with wiggles  and a steep section . The radiocarbon ages of individuals from the pedigree lie between 3707 and 3608 BP with a standard deviation of 20–24 years and result in unmodelled calibrated dates from 2196 cal BC to 1906 cal BC (2-sigma), thus, 290 calendric years. The individual 2-sigma spans range from 121–188 years .The Early Bronze Age of Königsbrunn—Obere Kreuzstraße (OBKR), formerly called “Baugebiet 110” , was fulAll skeletal material was anthropologically analysed . ExcelleAll 23 of the sampled individuals yielded mitochondrial genomes. 18 were selected for nuclear capture. The pedigree spans four generations, with 4 individuals attributed to it through the analyses of nuclear DNA and an additional individual through mitochondrial DNA. One further individual is related to the biological family but cannot be explicitly placed in the pedigree. The subadult sisters 81 and 82 were buried side by side, whereas the adult brothers 80 and 86 were buried ca. 60 m apart from each other.Skeletal remains of 24 individuals were radiocarbon dated. Calibrated, unmodelled dates without HBCO correction range between 2136 and 1780 cal BC (2-sigma). Most of them do not exceed the steep section of the calibration curve . The radiocarbon ages of individuals within the pedigree range between 3664 and 3600 BP with standard deviations of 23–24 years. They result in unmodelled calibrated dates from 2134–1894 cal BC with single 2-sigma ranges between 126 and 175 years .The Early Bronze Age graveyard of Kleinaitingen—Gewerbegebiet Nord (AITI) contained 63 graves with a total of 72 individuals. The site was almost entirely excavated; only a part on the southern border is still preserved under a modern track. Apart from five cremations, two of them in biritual double burials, all graves contained inhumations in crouched positions aligned along the N-S-axis . Three fThe skeletal material was analysed anthropologically in its entirety . Due to 31 individuals were sampled for targeted DNA capture, and 27 provided sufficient data for kinship analysis. We find one mother (AITI_87) with three sons  . AdditioRadiocarbon dates were obtained from skeletal remains of 35 individuals. The calibrated, unmodelled dates without HBCO correction range between 2116 and 1505 cal BC (2-sigma). Most of them cover the period between 2040 and 1700 cal BC. Five dates show ranges as late as ca. 1500 cal BC. The four individuals of the small biological pedigree delivered radiocarbon ages ranging from 3480 to 3417 BP with standard deviations of 27–34 years. Their calibrated dating ranges stretch from 1891–1638 cal BC (2-sigma), mainly covering two wiggle-sections of the calibration curve . The individual ranges span between 186 and 228 years .14C ages (black bars), modelled without interval between generations (darker colored bars) and modelled using known intervals (lighter colored bars) compared to the prescribed YoD (black arrowhead) of the individuals. Models were rerun with five down to only two generations within a pedigree as priors. Already, the unmodelled calibrated date ranges of most individuals of the pedigree are restricted to a time before 510 cal BC. Only the dating range of A1 stretches beyond, even spanning the entire Hallstatt plateau. The unmodelled dating range of A1 stretches as far as 415 cal BC .Adding a generation interval to the models constrains the calibrated ages even further. This is due to the additional information of chronological minimal distance between the generations, cutting off the dating range on the older or younger side. Especially the first two and the last generations benefit from this additional information/prior.nd-4th) on which bracketing has effect. If an individual or a generation is already affected by the bracketing effect, adding more generation levels did slightly improve the modelled ranges. In this example, the improvements of B1 and B2 stayed almost stable after a three-generation simulation  or 220 years (65%)  Panel IIInversions or permutations, a seeming reversal of the order of dated events, are due to down-wiggles in the calibration curve, as seen with individual A1 . The YoDThe plateau model exemplifies the potential and limits of Bayesian modelling of a series of events  when the overall period of interest is shorter than the plateau itself and no other chronological information is available (cf. ). Withou14C ages. Most calibrated dates of the individuals are placed within the steep section, while the latest generation (E1 and E2) show unmodelled calibrated dates that are affected by the wiggle between 7470 and 7330 cal BC  was chosen because of its long, steep section in the calibration curve, which causes very narrow calibrated date ranges even for unmodelled l BC see . In contl BC see .The dating range of A1 is limited to 49 years , whereas those of E1 and E2 stretch over 169 years . Unmodelled and calibrated range probabilities of A2-D2 vary from 49 to 91 years.Our Bayesian approach already shows significant improvements when modelling with only the first two generations  Panel I.Taking the five-generation model as a baseline, modelled dating ranges lie between 24 and 52 years, which is an incredible accuracy for absolute dating methods used in archaeology, apart from dendro-chronology  Panel IIImprovements differ quite substantially between the generations because of the aforementioned wiggle after 7470 cal BC, which affects only individuals E1 and E2  were chosen to be similar to the real case studies of the Early Bronze Age pedigrees discussed in this paper, for which some information is missing  or which have a higher uncertainty (AaD-estimation). The unmodelled, calibrated dates fall onto two small wiggles  and a short steep section of the calibration curve in between them see . Date rard, 4th and 5th generations show significant constraints when modelled according to their pedigree-placement.Adding information from aDNA results in substantial constraints for almost every individual in this simulation. Even running the modelling process with solely the two first generations, a significant improvement is visible, especially for the dating ranges of the second generation, which now do not begin before ca. 1970 cal BC (B1 and B2). The bracketing effect is visible for all intermediate generations (gen. 2–4). Adding more generations down the pedigree does not show any enhancements thereafter. All individuals of the 3Within this model setup, no substantial differences can be observed between sequenced and additional generation-gap modelling  Panel IIDue to the wiggles and small plateaus in the calibration curve, the radiocarbon dates of C1-D2 resulted in wide dating ranges. Because of this, constraints are the highest for those four individuals  to a steep section , while aRunning the Bayesian model with two generations  already reduces the probability span of A1 significantly from 216 down to 33 years, an improvement of 85%. With regard to the second generation, only a reduction of around 18% can be observed. The five-generation simulation produces substantial shortenings for at least the first two generations , whereas the reduction of dates of the following generations is more restricted. At least an unambiguous assignment to the first half of the Hallstatt plateau, or even before, can be made for the individuals down to D2 .The structure of the vast plateau section with its ups and downs is also responsible for the substantial differences seen between a model setup solely with a sequence and a sequence in combination with a generation interval . Here, these differences can be clearly observed for all individuals that are affected by the bracketing effect. This is most obvious for individuals B1-C2. All individuals in the last generations are thus not influenced by any bracketing and show similar values with or without intervals  Panel IIA bracketing effect is quite visible for all individuals framed by other generations. However, in contrast to the other three simulations, the bracketing effect enlarges with the number of subsequent generations, meaning the constraints of modelled dates increase with every simulation run with a generation level added. Here, the effect is best visible at the second generation . For example, the dating ranges of individual B1 show subsequent improvements of 17.8%, 36.9%, 60.9% and 16%, with a total reduction of 83%, in the simulation without intervals and 20.2%, 14.2%, 26% and 4%, with a total reduction of 51.4%, in the simulation with intervals.This observation is caused by the course of the calibration curve, with its peaks and lows over the entire length of the plateau, and the particular chronological placement of the pedigree members Figs . With evThe same inversion as seen in the plateau model with individual A1 can also be observed for individuals, whose real YoD would fall in the first down-wiggle (trough) between 745 and 690 cal BC. Here, this is demonstrated by individuals C2-E2 in the anchor point simulation. The calibrated dates of individuals A1 and B1-C1 only scratch the peaks and upper parts of the first half of the Hallstatt plateau, whereas C2-E2 coincide with the down-wiggles and both plateau areas, resulting in dating ranges of up to 340 years (2-sigma). In general, more individuals are aligned in the correct order of their YoD, due to the steep section of the curve at the beginning. Counterintuitively, though, with the pedigree in this anchor point scenario shifted 135 years backwards in time compared to the plateau simulation, more individuals (4 out of 10) seem to date even later, with date probability ranges up to 414 cal BC. This graphic should also make one aware of the positioning of the actual YoD of a sample compared to the unmodelled dating probability ranges, as unmodelled radiocarbon dates are still one of the main chronological estimates used in archaeology. Except for individual A2 in this case, the true YoD lies at least within the first fifth of the dating range, and for most of them even within the first tenth .All predefined or true YoDs lie within the modelled time frames. Simply sequencing the radiocarbon dates according to their generation level, without specific order within a generation, gives surprisingly good results, with an agreement index of the entire model of 164 and no value of single events lower than 97 . The agrBecause of its special setting, improvements between unmodelled and modelled radiocarbon dates vary significantly  is 407 years , which is definitely too long for five generations of a family from pre-industrial times. Regarding archaeological dating, this would include the end of the Late Bronze Age until the beginning of the Latène period. Simply using the generation sequence in the Bayesian model, the entire span is reduced to 296 years .st generation + (ngen-1)*YoD separation in years. In our five-generation model, this would be the youngest end of the modelled 2-sigma-range of A1 and/or A2 + (5–1)*20/25/25 years to constrain the modelled dates of E1 and E2 and therefore the overall duration of the pedigree. Using a 20-year YoD separation results in -772 + 80 years = -692 or 692 cal BC; with a 30 year YoD-separation: 656 cal BC, because of the gap between the first and second generation, which is smaller than 30. The overall duration of the pedigree in the unmodelled version is 408 years, 296 years when sequenced and between 116 and 152 years when sequenced with varying YoD separations.The overall constraints of the entire pedigree are defined by the number of generations: the end of the 2-sigma-range from the latest individual of the 1Looking at the details of the constraints for individuals of the last generation, the given/prescribed YoD of E1 = 695 and E2 = 707. Unmodelled 2-sigma ranges are E1 = 753–415 cal BC and E2 = 755–415 cal BC. Modelled 2-sigma ranges forE1 and E2 = 750–515 cal BC. Modelled 2-sigma ranges with additional YoD separation of 20 years give dating spans from 750 to 692 BC (58 years instead of 338/340 years). The improvement of dates is around 280/282 years when modelled and constrained. Even with this narrow YoD separation of 20 years, the prescribed YoDs fall within the widely constrained ranges. However, with an assumed generation gap of 25 or 29 years  their parents. Additionally, we modelled once with a generation-gap between individuals 44 and 50/35 and once without, making it a pedigree with 4 or 5 generations in total. Because of its incompleteness and specific structure, the pedigree of OBKR can be modelled by sequencing on a generation level to show the potential of this method using only the most basic setup. The 2-generation pedigree of AITI demonstrates the difficulties of children comprising the pedigree when they possibly died before their parents. Varying arrangements of the chronological order in which the individuals died will affect the model setup and outcome. The three case studies also cover two different sections of the calibration curve, similar to the mixed simulation setup described above, and therefore display different initial situations of pedigrees.Incorporating AaD information through HBCO correction does not seem to make a big difference in the overall outcome of the calibrated, but unmodelled, dates . Howeverth generation and the uncertain placement of POST_137. Basically, two models were set up: the first one comprises four generations, with POST_44 being the uncle of POST_50, and the second one puts 44 as the grandfather of 50, adding another generation and resulting in a generation gap between them.The overall dating range of the pedigree, affected by two subsequent wiggles on the calibration curve, spans 287 years . The individual 2-sigma spans range from 114–188 years. In this case, we discarded the subadult individuals of the last generation (POST_131 and POST_137) placed on one strand of the pedigree because of the information gap in the 4Based on the AaD estimates the following assumptions are made for the chronological order of deaths of the individuals: all individuals on the right side of the pedigree  were of Sequencing the pedigree with individual 44 being the uncle of 50, resulting in four generations in total, and not adding any other priors  gives a satisfying outcome with an agreement index of the model of 73 and those of the single radiocarbon dates ranging between 69 and 116 . The shiAdding another generation between individuals 44 and 50 does not change the outcome of the entire pedigree significantly, and the agreement indices of the model, as well as single radiocarbon dates, do not show any differences Figs . Unforturd generation is ignored in this setup.In total, the overall dating range of the pedigree is 240 years . The single results of the radiocarbon dating vary from 126 to 175 years (2-sigma). This pedigree is suitable for showing the simplest way of applying a Bayesian approach. The individuals and generations are directly put into chronological order and sequenced without further information of generation gaps, etc. Additional information about the gap in the 3Overall, the agreement index of the model is surprisingly high (99), given the simple setup of the Bayesian model. Also, the single agreement indices range between 67 and 117, with four out of five lying above 100 . The radThe overall dating span of this two-generation pedigree is 256 years . However, this long dating range is caused by the prolonged wiggle of the calibration curve between 1880 and 1760 cal BC. We will demonstrate the possibilities and challenges of pedigree-based Bayesian modelling when parents had children that eventually died before them. Therefore, this pedigree was broken down into three pairwise Bayesian models. The main issue here is the chronological order of times of death . The firIn total, five different specifications of the Bayesian model have been calculated, which are the result of the chronological order of YoDs:AITI_87 died before or simultaneously with AITI_120, with an interval of 20 ± 10 years.AITI_87 died before or simultaneously with AITI_119, with an interval of 7.5 ± 7.5 years.AITI_119 died before or simultaneously with AITI_87, with an interval of 5 ± 5 years.AITI_87 died before or simultaneously with AITI_86, with an interval of 2.5 ± 2.5 years.AITI_86 died before or simultaneously with AITI_87, with an interval of 10 ± 10 years.Just by looking at the order of unmodelled radiocarbon dates plotted against the calibration curve, the above indicated orders of YoDs seemed to be verified already, where the mother died after her two sons AITI_86 and AITI_119, whereas the adult son AITI_120 died after her.The Bayesian model including a 20 ± 10 year interval between mother (AITI_87) and adult son (AITI_120) works quite well and shows an agreement index of the model of 104; the single radiocarbon dates are comparable (108) . While tModelling the other two pairs (AITI_87 with AITI_119 and AITI_86) does not result in a significant reduction of the modelled date ranges in comparison with the unmodelled ones, no matter in which chronological order the generations are placed cf. . NeverthMoreover, the probability densities of AITI_87 in models C, D2 and E2 are surprisingly similar, which is yet another indicator that AITI_119 and AITI_86 died before their mother AITI_87 and brother AITI_120 see. . It is tOne of the major results of the four simulations using artificial pedigrees is that the sequencing of individuals grouped in generations without additional priors already has a substantial effect on the constraints, whereby Bayesian modelling is applied to the radiocarbon dates based upon information of biological relationships.Recognisable improvements to the precision of calibrated dates were achieved at all three main layouts of the calibration curve . Both simulations placed within the Hallstatt plateau (plateau and anchor point) showed that Bayesian modelling excluded a dating in the second half of the Hallstatt plateau , an enhancement with high relevance for an archaeological chrono-interpretation. Basically, our method is applicable to pedigrees at all sections of the calibration curve and therefore for all detected family trees of the past with sufficient coverage of radiocarbon dates. Constraints that impact the modelling results are the precision of the single radiocarbon dates, the number of modelled generations, the shape of the calibration curve and the availability of “anchor points”.Integrating additional priors can lead to slightly different outcomes: adding an interval between generations can have a positive or negative effect on the precision of the calibrated ages in comparison to sequence-only simulations due to the specific shape of the calibration curve and the exact chronological positioning of the individuals of the pedigree. Adding intergenerational intervals did not change the results at the steep and mixed simulations significantly. In the plateau simulation, it reduced the modelled timespans, while they increased for the anchor point simulation.One could also use further pedigree information if available, e. g. caused by a larger number of individuals within a generation, to prescribe a length to a generation [“Span”] within the OxCal code , which The bracketing effect always reduces modelled dating ranges, at least for the first run. Adding yet another subsequent generation level to the pedigree did not further improve those in the steep and mixed simulation. In the plateau simulation, this continuous improvement was only visible in the setup with intervals, whereas the modelled radiocarbon dates got constrained bit by bit with each generation level added in the anchor point simulation, which can be attributed to the role of the “anchor point” of the pedigree and the consequences thereof.Supposed inversions of radiocarbon dates, which are always a cause of the specific shape of the calibration curve, can be partly or almost entirely resolved through Bayesian modelling based upon information from the pedigree.Adding further constraints after modelling based on duration estimates of generation levels and entire pedigrees (see e.g. ) can eveSimilar to our anchor point simulation, dendro dates of graves with a very narrow dating range can be used as an anchor point for the Bayesian model . EspThe case studies presented in this paper partly demonstrate the complexity of real pedigrees but also their incompleteness. Every site and pedigree provides a varying amount and quality of information, which can be used for a Bayesian model of the radiocarbon dates (c.f. ). TherefIn our first case study of POST, we demonstrated the possibility to divide a multi-strand pedigree into separate parts. For one part, we applied our Bayesian approach, because of its high density of information. Here, the most probable chronological order of deaths of the individuals was most important, as they all died as adults and an inversion of YoDs compared to their generation level is unlikely.rd generation was also neglected. Nevertheless, the model proved its applicability by resulting in a calculated overall duration of 113 years for four generations instead of 240 years and a major improvement of single radiocarbon dates for individuals from within the pedigree.The power of a simple Bayesian model setup was demonstrated in the pedigree of OBKR, where no additional priors were included and an information gap in the 3In contrast to the significant constraints of radiocarbon dates in the other two case studies, the Bayesian model of the pedigree of AITI has proven yet another application of this method. Here, the chronological order of the YoDs of the mother and her three children was unknown before modelling. The sequence of deaths within this nuclear family was plausibly reconstructed through pairwise comparisons in individual Bayesian models see . Those pA seeming inversion of unmodelled radiocarbon dates is seen in all three case studies. Without any stratigraphic information, resolving these is only possible with Bayesian modelling and prior information. Our suggested simulations are of course only an approximation of the reality; nonetheless, the priors and parameters can be adapted and complemented according to the specific research questions and contexts. Hereby, we chose a setup without chronologically overlapping generations and only adult individuals in a single-stranded pedigree. In most cases, real family trees could be way more complex concerning structure, layout and information gaps. Therefore, we suggest not to simply copy the OxCal code for upcoming studies without carefully checking its applicability in specific cases.Our case studies show that using pedigree information does actually work when sequencing only on a generation level without priors and does often improve calibrated ages significantly. In general, applying a Bayesian approach to radiocarbon dates based on biological relations is and will be of major importance at improving dating accuracy in future studies.Our simulations were run on single-strand pedigrees, but radiocarbon dated multi-strand pedigrees  can be mUpcoming studies in different fields of research will deliver evidence for some of the parameters/priors used to set a Bayesian model, like higher accuracy in determining the AaD (e.g. ), the agS1 FigLower panel: calibrated radiocarbon dates (2-sigma) with 10 (black), 20 (grey) and 30 (red) years uncertainty in 5-year intervals from approximately 5600 cal BC to 25 cal AD. Upper panel: differences of the 2-sigma ranges between 10 and 30 years of uncertainty.(TIF)Click here for additional data file.S2 FigEach branch of the pedigree can be modelled separately or put into a Bayesian model including every individual and/or strand.(TIF)Click here for additional data file.S3 Fig(green) AaD minima; (blue) AaD uncertainty added to AaD min. Overall average of AaD uncertainties is 8.06 years. All parameters of the case studies are listed in (TIF)Click here for additional data file.S1 TableThe file contains four sheets, each one with an added generation level (summarized results in (XLSX)Click here for additional data file.S2 TableThe file contains four sheets, each one with an added generation level (summarized results in (XLSX)Click here for additional data file.S3 TableThe file contains four sheets, each one with an added generation level (summarized results in (XLSX)Click here for additional data file.S4 TableThe file contains four sheets, each one with an added generation level (summarized results in (XLSX)Click here for additional data file.S5 TableAgreement indices for single radiocarbon dates as well as for the entire model above 60% are considered to show the accordance between the model and the measured dating probabilities.(XLSX)Click here for additional data file.S6 TableIn each sheet (1–12) a varying bayesian model was calculated using different variables . (1–4) entire pedigree with four generations (POST_44 being the uncle of POST_50). (5–8) only the right strand of the four generation pedigree with adult individuals. (9–12) only the right strand of the five generation pedigree with adult individuals (POST_44 being the grandfather of POST_50) Click here for additional data file.S7 TableIn each sheet (1–4) a varying Bayesian model was calculated using different variables  Click here for additional data file.S8 TableIn each sheet (1–25) a varying bayesian model was calculated using different variables . (1–4) entire pedigree with two generations, with the sequence in the Bayesian model according to their generation level Click here for additional data file.S1 TextGeneral remarks and supporting information about the case studies.(DOCX)Click here for additional data file.S1 Codes(LOG)Click here for additional data file.S2 Codes(LOG)Click here for additional data file.S3 Codes(LOG)Click here for additional data file.S4 Codes(TXT)Click here for additional data file.S5 CodesThe codes are labeled according to the sheets in (TXT)Click here for additional data file.S6 CodesThe codes are labeled according to the sheets in (TXT)Click here for additional data file.S7 CodesThe codes are labeled according to the sheets in (TXT)Click here for additional data file.S8 CodesThe codes are labeled according to the sheets in (TXT)Click here for additional data file.S9 CodesThe codes are labeled according to the sheets in (TXT)Click here for additional data file.S10 CodesThe codes are labeled according to the sheets in (TXT)Click here for additional data file.S11 CodesThe codes are labeled according to the sheets in (TXT)Click here for additional data file.S12 CodesThe codes are labeled according to the sheets in (TXT)Click here for additional data file.S13 CodesThe individuals are assigned to sequence levels based on the results of the pairwise comparisons cf.  and mode(TXT)Click here for additional data file.


In pupillometry, no significant differences were found for average PPD , average peak pupil dilation timing (p = 0.527) and for pupil dilation growth curves with both processors. The findings of this study suggest that BAHS users allocate similar listening effort with PP and P3SP when processing speech-in-noise at a sound pressure level not saturating Ponto Pro and at a fixed performance level of 95%. This finding applies to the patients who meet the qualification criteria for bone conduction devices and have BC in situ threshold average below 45 dB HL.The goal of this study is to assess speech comprehension and listening effort by means of pupillometry, in patients with bone-anchored hearing system (BAHS). The study was performed prospectively in a group of 21 hearing-impaired adults, unilaterally implanted with BAHS Ponto. Listening effort was compared in patients wearing two sound processors : Ponto 3 SuperPower (P3SP) and Ponto Pro (PP). Every patient was invited to two visits, separated by a 3-month break. The first session was to establish the noise level needed to obtain 95% correct sentence recall in the hearing in noise test (HINT), when speech is presented at 70 dB SPL. During the second session, pupillometry, with the use of the above-mentioned conditions, was performed. The mean HINT scores obtained during the second visit were 96.3% for PP and 97.7% for P3SP ( The change of pupil size and reactivity in response to certain neurological processes was discovered well over a 100 years ago . Large-sListening effort is one of the most common problems people with hearing loss must face, especially in a noisy environment. In challenging listening situations, hearing-impaired people are more fatigued after an hour of conversation than normal-hearing people. This is because the cognitive processes required during speech comprehension in these individuals are associated with more effortful listening . ListeniThe primary means to assess the listening abilities of an individual with hearing loss is a speech intelligibility performance test, the first of which was developed over 70 years ago . NeverthThe attempt to decrease listening effort in hearing-impaired people has been the major focus for hearing aid manufacturers in the last decade. They have been constantly trying to improve their devices by advanced signal processing, in order to reduce the background noise and enhance the target speech signal that reaches the listener. The concept of assessing listening effort and cognitive load in hearing-impaired patients has been studied quite extensively in recent years ,17,18,19The goal of this study is to assess speech comprehension and listening effort by means of pupillometry, in patients with BAHS. More specifically, the aim is to compare listening effort for patients wearing two sound processors : Ponto 3 SuperPower (P3SP) and Ponto Pro (PP), at an ecologically valid sound pressure level of 70 dB SPL and at a fixed performance level of 95%. The experimental conditions were designed as an extension of the work of Bianchi et al. , where lIn this study, we are extending the work of Bianchi et al. by introducing a condition with a fixed speech level of 70 dB SPL—a value similar to the average level in condition 2 from Bianchi et al. (71 dB SPL)—while controlling for performance to be at 95% with PP. Hence, we would rule out the audibility limitation and verify whether we still observe a difference in pupil dilation at a speech level of 70 dB SPL. Another reason for choosing this level is that it reflects sound pressure levels that hearing-impaired people are much more likely to encounter during conversations in real-world noisy environments ,21,22. WThe study was performed prospectively in a group of 21 hearing-impaired adults, unilaterally implanted with BAHS Ponto. Every patient was invited to two visits, separated by a 3-month break. The first session was to establish the noise level needed to obtain 95% correct sentence recall when speech is presented at 70 dB SPL for measurement of pupil dilations. During the second session pupillometry, with the use of the above-mentioned conditions, was performed. The investigation was approved by the local Ethics Committee (decision number 470/19).The participants were recruited from the BAHS database of our department. They have bilateral conductive or mixed hearing loss and were experienced BAHS users with at least 5 years of wearing the Ponto device. All of them were unilaterally implanted and there were no adverse events observed since the operation. Ponto users with single-sided deafness were not included in the study. There were 21 native Polish participants—9 males and 12 females—between 23 and 77 years old  and Ponto 3 SuperPower . Both PP and P3SP devices have the same maximum force output algorithm (multichannel), but differ in maximum force output (MFO) level, which is lower in PP  and higher in P3SP. In order to ensure that the difference between the sound processors was restricted to the difference in MFO level as much as possible, no fine-tuning was performed during fitting. To this end, noise reduction was turned off, directionality was set to omnidirectional mode, and the volume and mute settings were turned off. P3SP and PP are designed for listeners with hearing loss up to and including 65 and 45 dB HL, respectively. Four Ponto processors were used for measurements for all participants—two PP devices: left (SN: 47980772) and right (SN: 49798749) and two P3SP devices: left (SN: 55217460) and right (SN: 55382885).Every patient was invited to two visits, separated by a 3-month break, that lasted an hour each.At the first session, two measurements were preformed: feedback measurement and BC in situ threshold, both with the P3SP sound processor. The gain settings were prescribed according to the modified NAL-NL1 prescription used in Ponto. The gain settings from the P3SP were then transferred to PP, to ensure that the settings were similar in both processors. After the fitting, the subjects performed a speech intelligibility test with Polish Hearing In Noise Test (HINT) sentences  with PP The second visit consisted of pupillometry measurements conducted during a speech intelligibility test with HINT sentences. The sentences were presented at the fixed speech level of 70 dB SPL and noise presented at the estimated level that provides SRT95 for each participant. Pupil dilation was measured while each participant was listening to one out of three lists (20 sentences per processor) in a randomized manner, wearing one randomly chosen processor. Afterwards, the other processor was tested and another random list was presented to the participant. The participants were asked to listen to and repeat each sentence after the background noise has stopped. There was a break introduced for each participant while switching the processors.During both visits, the opposite ear of all participants was muffled by means of soundproof headphones to ensure that no sounds were perceived through this ear and only contribution from the implanted side was tested. For most of the patients, the study conditions were comfortable, but a few of the patients reported a slight inconvenience wearing earmuffs, eye tracking goggles and a BAHS processor at the same time. Listeners arrived at the clinic from different locations and using various means of transportation on the pupillometry measurement day. The patients were invited to two separate visits, because each visit was quite an extensive measurement day for them. We needed to measure their SRT50 and SRT80 prior to estimating SRT95 and we did not want these measurements to influence their performance during the final pupillometry test, as it might have caused more fatigue. There were no alterations in the auditory thresholds within this period, which we have confirmed by making BC in situ measurements again after the 3-month period.The experiment performed in this study was carried out in a soundproof booth. Four loudspeakers  were placed in each corner of the booth and in a 80 cm distance from the listener at 45°, 135°, and 225° and 315° azimuth . The tarPupil data analysis was performed similarly to previously described procedures ,8. At thIn order to compare HINT test scores of all participants using PP or P3SP, a Wilcoxon rank sum test with continuity correction was performed, using a statistical package in R-studio: wilcox.test {stats}.The peak pupil dilation (PPD) was extracted from the averaged curve for each participant and each condition, as well as its timing. The PPD was defined as the maximum pupil dilation within the time interval between the sentence onset and the average noise offset. In order to compare the PPD values of all participants using PP or P3SP, a Wilcoxon rank sum test with continuity correction was performed, using a statistical package in R-studio: wilcox.test {stats}.Proc represents the conditions Ponto Pro or Ponto 3 SuperPower and TP–the study’s participants. The hypothesis was tested at a significance level of 5% (p < 0.05).To model the pupil dilation as a function of time, growth curve analysis (GCA) was applied ,8,25 usiThe populational as well as audiological data for all 21 participants in the study are presented in The individual bone conduction (BC) hearing thresholds, which were measured in situ through the sound processor, are presented in The measurements of 18 patients were analyzed. Three patients were excluded from further analysis see  due to tp-value = 0.9863) in performance between the two Ponto devices. These results were in accordance with our initial design, where the listeners had their performance levels calibrated to 95%.The mean HINT scores obtained during the second visit (with the sentences presented at the fixed SRT95 for each participant) were compared between PP and P3SP and were equal to 96.3% and 97.7%, respectively. They resulted in a statistically non-significant difference . The average peak pupil dilation timing is depicted in p-value = 0.527).Each of the participant’s average pupil dilation curves are presented in p-values of the three terms indicate that there is no significant difference between the two devices.The aim of this study was to evaluate the listening effort of hearing-impaired patients implanted with BAHS and to compare the effort allocated to process speech in noise while using two different sound processors: Ponto Pro and Ponto 3 SuperPower. We have designed this work as a continuation of a study by Bianchi et al. , in whicIn the present study, we have extended the work of Bianchi et al.  by fixinThe design of this study ensured that the participant could understand 95% of the sentences at a signal level of 70 dB SPL, which allowed us to determine which of the two potential factors was affecting condition 2 in Bianchi et al. (audibility limitations vs. saturation artifacts). The lack of a significant difference between PP and P3SP in this study suggests that audibility limitations were present in condition 2 in Bianchi et al. and were likely driving the difference in overall pupil dilation in the second condition (rather than saturation artifacts in PP).However, an important aspect to consider when comparing the two studies is that the PP used in this study is different from the PP used in Bianchi et al. . In the This study was performed in the test conditions where all advanced signal processing functions were switched off. Therefore, we cannot exclude a difference in listening effort between PP and P3SP in real-life circumstances. In everyday life, the listeners would have several automatic features turned on in their processors, such as directionality or noise reduction, that might have an effect on audibility and speech understanding. In the future, it might be interesting to carry out additional experiments in order to improve our understanding of the advantages and limitations of the different sound processor features. For instance, one might investigate how and to what degree the difference in PP and P3SP’s advanced signal processing contributes to the listening effort.A possible limitation of the present study, which might have affected pupil dilation, is the diversity of the participants. For example, the age span of the listeners was substantial, i.e., 23–77 years old, and it has been demonstrated before that pupil size decreases with age . The intn = 18) required to have on average an SNR of 11 dB  would never have been able to obtain SRT95 when noise was present  may be challenging for the eye-tracking goggles. More specifically, we have noted that in the case of patients with drooping eyelid the camera had difficulties with setting the focus on a pupil, since the eyelid was covering it to a certain extent. There was also a case including a participant with a mole protruding up from the lower eyelid, which also created a challenge in setting the camera focus right. Hence, it might be a benefit in the future experiments to use these features as criteria excluding the listeners from participating in a similar study, so that the measurements are less biased.The findings of this study suggest that BAHS users allocate similar listening effort with Ponto Pro and Ponto 3 SuperPower when processing speech-in-noise at a sound pressure level not saturating Ponto Pro and at a fixed performance level of 95%. This finding applies to the patients who meet the qualification criteria for bone conduction devices and have a BC in situ threshold average below 45 dB HL (for patients within the fitting range of both sound processors).


Unilateral axillary lymphadenopathy is known to occur after coronavirus disease (COVID-19) vaccination. Post-vaccination lymphadenopathy may mimic the metastatic lymph nodes in breast cancer, and it is challenging to distinguish between them. This study investigated whether the localization of axillary lymphadenopathy on magnetic resonance imaging (MRI) could be used to distinguish reactive lymphadenopathy after COVID-19 vaccines from metastatic nodes.We retrospectively examined preoperative MRI images of 684 axillae in 342 patients who underwent breast cancer surgery from June to October 2021. Lymphadenopathy was defined as cortical thickening or short axis ≥ 5 mm. The axilla was divided into ventral and dorsal parts on the axial plane using a perpendicular line extending from the most anterior margin of the muscle group, including the deltoid, latissimus dorsi, or teres major muscles, relative to a line along the lateral chest wall. We recorded the presence or absence of axillary lymphadenopathy in each area and the number of visible lymph nodes.P < 0.001). Dorsal lymphadenopathy was observed in 16 (39.0%) and two (5.1%) axillae in the vaccine and metastasis groups, respectively (P < 0.001). If the presence of both ventral and dorsal lymphadenopathy is considered indicative of vaccine-induced reaction, this finding has a sensitivity of 34.1%, specificity of 97.4%, and positive and negative predictive values of 93.3％ and 58.5%, respectively.Of 80 axillae, 41 and 39 were included in the vaccine and metastasis groups, respectively. The median time from the last vaccination to MRI was 19 days in the vaccine group. The number of visible axillary lymph nodes was significantly higher in the vaccine group  than in the metastasis group (7 nodes) (The presence of deep axillary lymphadenopathy may be an important factor for distinguishing post-vaccination lymphadenopathy from metastasis. The number of axillary lymph nodes may also help. Owing to the outbreak of coronavirus disease COVID-19), COVID-19 vaccines have rapidly come into use worldwide. During a COVID-19 vaccine clinical trial, up to 16% of vaccine recipients complained of axillary pain and swelling as adverse reactions to the vaccine 9, COVID-. RetrospVaccination in the thigh or contralateral arm is encouraged in patients with a recent diagnosis of breast cancer . HoweverMori et al. reported a case of axillary lymphadenopathy that occurred after COVID-19 vaccination. In this case report, the largest lymph node was located deeper than the lower edge of the pectoralis major muscle on breast US ) Table . The medDorsal lymphadenopathy was observed in 16 39.0%) axillae in the vaccine group and in only two (5.1%) axillae in the metastasis group Table . Ventral9.0% axilFigure Since the start of the widespread use of COVID-19 vaccines, there has been an increasing frequency of axillary lymphadenopathy seen on preoperative MRI in breast cancer, and it is challenging to distinguish metastasis from post-vaccination lymphadenopathy. Therefore, in this study, we aimed to distinguish between MRI images captured in two patient groups with the respective conditions and to identify essential elements that could aid in clinical practice.When axilla level I was divided into the ventral and dorsal parts on the axial plane using a line drawn perpendicular to the chest wall, only ventral but not dorsal lymphadenopathy was found in most axillae in the metastasis group. Lymphadenopathy was found in the entire axillary region, including in the dorsal area, in a significantly larger proportion of axillae (34.1%) in the vaccine group than that in the metastasis group. These results suggest that MRI may be a valuable method for distinguishing metastasis from post-vaccination lymphadenopathy.Using anatomical landmarks , Clough et al. divided the lower part of the axilla (Berg’s level I and lower part of Berg’s level II) into four anatomical zones to localize the sentinel lymph node (SLN) . In 98.2Level I lymph nodes are divided into three groups: the pectoral (anterior), subscapular (posterior), and humeral  groups , 14, 15.A review of axillary reverse mapping (ARM) serves to remind us that it is oncologically safe to preserve the ARM lymph nodes in patients with clinically node-negative breast cancer, who underwent a SLN biopsy, and in those with micrometastatic or macrometastatic lymph node involvement in the SLN, who were advised to undergo a complete axillary lymph node dissection, provided that there is no convergence between the ARM lymph nodes and SLN . This reUS is the primary modality used for the evaluation of axillary nodes, and breast MRI is useful for this evaluation as well . US evalThis study has some limitations. First, this was a single-institution retrospective study. Second, in some cases, the axilla may not have been adequately included in routine preoperative MRI scans in breast cancer. Third, we were not able to confirm what happens to axillary lymph node enlargement postoperatively in cases in which the vaccination was administered contralateral to the location of breast cancer. Therefore, in such cases, although lymphadenopathy probably occurred due to the vaccination, this finding may not be completely grounded. Fourth, the time from vaccination to lymphadenopathy detection on MRI varied considerably. It has been reported that the median time from the first vaccination to lymphadenopathy detection on US was 9.5 days  . It was The presence of deep axillary lymphadenopathy and the number of axillary lymph nodes may be important for differentiating lymphadenopathy after COVID-19 vaccination and metastasis. This information could be valuable when deciding whether to use cytology or SLNs to confirm the presence of lymphadenopathy on preoperative MRI for breast cancer.


Ruminococcus and calprotectin. Additionally, non-responders had higher abundance of Candida, while responders had higher abundance of Saccharomyces at the end of the study. The gut microbiota composition in PIBD patients could predict response to IFX treatment in the future.Pediatric inflammatory bowel disease (PIBD) is a globally increasing chronic inflammatory disease associated with an imbalanced intestinal microbiota and treated with several treatment options, including anti-tumor necrosis factor alpha (TNF-α), such as infliximab (IFX). Up to half of the patients do not respond to the drug and there are no methods for response prediction. Our aim was to predict IFX response from the gut microbiota composition since this is largely unexplored in PIBD. The gut microbiota of 30 PIBD patients receiving IFX was studied by MiSeq sequencing targeting 16S and ITS region from fecal samples collected before IFX and two and six weeks after the start of treatment. The response to IFX induction was determined by fecal calprotectin value < 100 µg/g at week six. The bacterial microbiota differed significantly between response groups, with higher relative abundance of butyrate-producing bacteria in responders compared to non-responders at baseline, validated by high predictive power (area under curve = 0.892) for baseline  At diagnosis PIBD often presents with similar symptoms to adults’, which may include diarrhea, abdominal pain, bloody stools and fever2. In addition, PIBD  may cause malnourishment, leading to growth impairment, delayed puberty or even psychosocial problems2. Effective treatment is crucial in order to avoid these long lasting sequalae in patients with PIBD.Inflammatory bowel diseases (IBD) including Crohn’s disease (CD), Ulcerative Colitis (UC) and IBD unclassified (IBDU) are chronic inflammatory diseases characterized by inflammation in the gastrointestinal tract. The incidence of pediatric IBD (PIBD) is increasing worldwide both in developing and developed countries3. The role of the fungal gut microbiota, the mycobiota, is not as established, but may also be characterized as dysbiotic4, with Candida spp. being possible drivers of the imbalance7. Additionally, it has been observed that Saccharomyces species are less abundant in patients with IBD compared to healthy controls (HC)6. Studies concerning the gut mycobiota in PIBD are few, and although the results vary somewhat between the studies, both Candida and Malassezia have been reported as increased in PIBD, as well as the phylum Basidiomycota, as reviewed recently8. Many studies have reported a reduction in the diversity of commensal bacteria, especially in the two most abundant phyla Bacteroidetes and Firmicutes, in adult patients with IBD3. Additionally, a reduced abundance of potentially anti-inflammatory genera such as Roseburia, Bifidobacterium and Faecalibacterium and an increased abundance of Proteobacteria, Veillonellaceae, Pasteurellaceae, Fusobacterium, and Ruminococcus gnavus, some of which have proinflammatory effects, have been reported in adult patients with IBD when compared to HC3. Accordingly, the bacterial microbiota of patients with PIBD has been found to differ from HC with an increased relative abundance of Prevotella9. A recent review regarding gut microbiota profiles in PIBD, encompassing 41 studies, reported an increase in Enterococcus and significant decrease in Anaerostipes, Blautia, Coprococcus, Faecalibacterium, Roseburia, Ruminococcus, and Lachnospira in PIBD compared to HC, and a decrease in alpha-diversity within majority of the included articles10.The current hypothesis for the pathogenesis of IBD is that the combination of genetic, environmental and microbial factors leads to altered gut permeability and abnormal and prolonged immune responses with the alteration of gut microbiota composition with predominance of pathobionts that contribute to gut inflammation11. Recent ECCO-ESPGHAN guideline recommends anti-tumor necrosis factor alpha (TNF-α), such as infliximab (IFX), in pediatric CD with a high risk of poor outcome, if serious growth delay is present, or EEN and corticosteroid treatment do not induce remission12. A recent ESPGHAN guideline for pediatric UC recommends IFX in chronically active of steroid dependent UC, uncontrolled by 5-ASA and thiopurines13. However, up to 50% of patients do not respond to IFX, and loss of response is frequent14. To this day, there are no clinical methods available to predict the response although many have studied the bacterial microbiota with the aim to find biomarkers for prediction of anti-TNF-α treatment response to improve the cost-effectiveness of the therapy20.There are multiple therapy choices for PIBD, including conventional medications such as 5-ASA, immunomodulators and steroids, and explored for novel treatment options, such as fecal microbiota transplantation21. Previous studies regarding the treatment response and disease severity have reported a reduced relative abundance of Faecalibacterium prausnitzii (F. prausnitzii)22 and we recently found an increased relative abundance of Candida to correlate with poor treatment response to anti-TNF-α in adult patients with IBD23. It has been discovered that adult patients with IBD have an imbalanced Ascomycota and Basidiomycota ratio24 and a higher abundance of Candida albicans compared to HC4. In children, a low baseline abundance of F. prausnitzii was associated with a lack of mucosal healing and need of surgical treatment9. In our previous study regarding the fecal microbiota and the treatment response to anti-TNF-α in PIBD patients we discovered several bacteria as potential biomarkers predicting treatment response such as higher relative abundances of Bifidobacterium, Clostridium colinum, Eubacterium rectale, uncultured Clostridiales, and Vibrio, and a lower abundance of Streptococcus mitis20.There are very limited studies on the mycobiota in patients with PIBD receiving IFX therapy, and the study approach differ from this studyThe aim of this study was to describe the gut microbiota in patients with PIBD introduced to anti-TNF-α medication IFX and to study whether the fecal fungal and bacterial microbiota profiles predict IFX treatment response. Also, we aimed to study the association between the gut fungal and bacterial microbiota. Improved understanding of the complex interactions between the fungi and bacteria of the intestine could provide new insight to dysbiosis seen in IBD, possibly even having impact on the adjustment of therapy.Finding methods for predicting the response to IFX therapy to avoid unnecessary side effects and high cost, particularly for pediatric patients, is crucial. Here we have investigated the fungal and bacterial gut microbiota profiles with the aim to find predictive markers for IFX response.In this study, a total of 30 patients with PIBD introduced to TNF-α antagonist IFX were included with a total of 85 samples collected before the start of IFX treatment and at two and six weeks of induction therapy. Out of the 30 patients, 27 patients with 68 samples were available for 16S sequencing, while 85 samples of 30 patients were available for ITS sequencing. 25 were diagnosed with CD and 5 with UC/IBDU. The background characteristics of the patients are shown in Table We had three patients with fecal calprotectin value < 100 at the start of the study (Table Candida (64%), followed by Saccharomyces (51%), uncultured fungus (20%) and Cladosporium (14%), presented in Fig. Candida albicans] (38%) and [Saccharomyces cerevisiae] (22%) were most prevalent.For fungal analyses, successful annotation with read count above 100 was achieved for 47 samples from 23 patients. Across all samples, the gut mycobiota was composed of Ascomycota (83%) and Basidiomycota (10%) and uncultured Eukaryota (7%). Altogether 33 genera were present in the gut mycobiota, and the most abundant genera were Faecalibacterium (9.1%). Bifidobacterium (5.5%), Blautia (4.2%) and Bacteroides (4%). The most prevalent genera at different timepoints are presented in Fig. For bacterial analyses, a total of 68 samples from 27 patients were available. The fecal microbiota of the samples was composed of the phyla Firmicutes (68%), Actinobacteria (14%), Bacteroidetes (12%), and Proteobacteria (5%). The most abundant genera across all samples were P FDR < 0.001). At six weeks the genus Candida [C. albicans] was more abundant in NRs  and Saccharomyces [S. cerevisiae] in Rs . This is presented in Fig. Candida and Saccharomyces is plotted throughout the study. The fungal diversity and richness at the different timepoints stratified by response groups is presented in Supplementary Fig. The fecal mycobiota did not differ significantly between response groups at baseline. At two weeks after induction the order Saccharomycetales was more abundant in Rs  and Bacilli  were more abundant in Rs, whereas the class Gammaproteobacteria  was more abundant in NRs. At genus level, the Rs had an increased relative abundance of Faecalibacterium  and Subdoligranulum , whereas the NRs had an increased abundance of Dialister  and Anaerostipes  when compared to the Rs. The statistically significantly differing genera are presented in Fig. At baseline the bacterial microbiota composition differed between Rs and NRs. The classes Clostridia  and Erysipelotrichia . At genus level, the Rs had decreased relative abundances of Blautia , Coprococcus , Lachnospiraceae (Insertae Sedis)  and Dialister , but an increased relative abundance of Bifidobacterium . All statistically significantly differing bacterial taxa of other taxonomic levels are listed in Supplementary Table At six weeks after start of IFX treatment the Rs had an increased relative abundance of classes Actinobacteria .The bacterial diversity and richness at the different timepoints stratified by response groups is presented in Supplementary Fig. ely Fig. . AdditioDisease duration was defined as the time from diagnosis to the start of IFX treatment. In fecal mycobiota we observed no difference in the composition in relation to disease duration.P FDR < 0.001) at baseline. At genus level, this group of patients had a higher relative abundance of the genera Faecalibacterium  and Subdoligranulum (1.3-fold P FDR < 0.001) when compared to patients with a disease duration less than a year (n = 14). All statistically significantly differing bacterial taxa of other taxonomic levels are listed in Supplementary Table Regarding fecal bacterial microbiota, the patients with disease duration for more than a year n = 14) had a lower relative abundance of the class Clostridia  at the initiation of IFX therapy. To investigate the gut microbiota composition according to age stratification we divided the patients into older and younger than 12 years , with 8 patients being younger than 12 years at IFX therapy initiation. The analyses were done at baseline.Saccharomyces [S. cerevisiae] was significantly more abundant  in patients younger than 12 years of age.In the fungal microbiota we observed that the genus P FDR < 0.001), but a decrease in Bacilli . At genus-level, the patients older than 12 years had a lower relative abundance of Dialister . All statistically significantly differing bacterial taxa of other taxonomic levels are listed in Supplementary Table In the bacterial microbiota, we discovered that the patients older than 12 years had an increased relative abundance of the class Clostridia  and a lower abundance of the genus Saccharomyces [S. cerevisiae]  in females compared to males at baseline.There was a significant difference in mycobiota composition between sex with a higher abundance of the class Saccharomycetes  in males, when compared to females. At genus level, females had significantly higher relative abundances of Faecalibacterium , but a lower relative abundance of Dialister . All statistically significantly differing bacterial taxa of other taxonomic levels are listed in Supplementary Table At baseline we observed a higher relative abundance of the class Clostridia  at baseline. Additionally, the antibiotic-treated patients had a lower abundance of Clostridia , but an increased abundance of Bacilli . At genus-level, patients receiving antibiotics had a significantly reduced abundance of Faecalibacterium  compared to those who did not receive antibiotics one month prior to sampling. All statistically significantly differing bacterial taxa of other taxonomic levels are listed in Supplementary Table We discovered that patients who had received antibiotics during the prior month to sampling had a higher relative abundance of the fungal genus Correlations between fungal and bacterial microbiota were eligible to be calculated for 5 Rs and 13 NRs at baseline and the correlations differed between the response groups, values at baseline are presented in Supplementary Tables Saccharomyces correlated positively with Akkermansia  and Candida correlated positively with Lactococcus  at baseline.In Rs Spearman correlations between fungal and bacterial genera in NRs are presented in Table In this study, we explored the fungal and bacterial gut microbiota in pediatric patients with IBD, who received anti-TNF-α medication IFX with the aim to find microbiota markers for prediction of treatment response. We demonstrate differences in the gut microbiota compositions between response groups to IFX therapy in PIBD, further validated by high predictive power for the bacterial microbiota. Additionally, we found differences in the interkingdom interactions between the response groups. Together these results suggest that intestinal microbes have potential as biomarkers for prediction of treatment response in patients with PIBD, that previously have been investigated from the bacterial microbiota profile but are largely unexplored for the fungal microbiota.25, the fungal species seem to have a significant role in IBD, with a composition characterized by a higher abundance of Basidiomycota and lower abundance of Ascomycota compared to HC24. This is observed as an increase of Candida and a decrease of Saccharomyces and Malassezia in IBD24. The gut mycobiota of patients with PIBD consisted of the phyla Ascomycota and Basidiomycota across all samples, as previously observed24. The most abundant genus was Candida, followed by Saccharomyces, also agreeing with previous studies24. In pediatric studies, Candida has been observed to associate with PIBD and with disease intensity26.Although being less abundant than bacteriaSaccharomyces was higher. The number of female patients was low , and most were prepubertal. Using age-grouping below and above 12 years is somewhat arbitrary due to not considering factors such as females and males reaching puberty at different ages, and the impact of IBD on the age of reaching puberty. The species S. boulardii is characterized with anti-inflammatory properties and is used as a probiotic27, however only two of our patients used such probiotics two weeks prior to the study, of which both had Saccharomyces present in the mycobiota. Antibiotics cause a decrease in bacteria, which in turn causes less competition to fungal species28. If fungi play a role in IBD disease progression, the use of antibiotics may have unpredicted consequences as fungi will benefit from it.In younger, in male and in antibiotic-treated patients, the relative abundance of , Actinobacteria, Bacteroidetes and Proteobacteria, accounting up to 99% of all bacteria. Similar bacterial composition has been discovered in adult studies, both within HC and IBD patients, where these four phyla accounted from 95 to 98% of all reads15.The bacterial microbiota consisted of the phyla FirmicutesFaecalibacterium and Subdoligranulum. Faecalibacterium and Subdoligranulum both produce butyrate which has an anti-inflammatory effect by upregulating the secretion of IL-10, an anti-inflammatory cytokine, and strengthening the intestinal barrier31. This suggests a decreased inflammation in patients for whom the disease duration was more than a year. Active inflammation in the gut has been noted to alter the intestinal microbiota and change during remission in response to anti-TNF-α22.Longer disease duration associated with a reduced relative abundance of the class Clostridia, but an increase in Clostridia genera, namely Faecalibacterium, an important anti-inflammatory bacterium, as stated above. Either the disease is more severe and perhaps fistulizing and therefore antibiotics have been used as a treatment, or the use of antibiotics has severely disturbed the intestinal homeostasis towards a more inflammatory state.Finally, patients who received antibiotics two weeks prior to the study had a significantly reduced abundance of 26, and to our knowledge there is only one study investigating it for prediction of response to IFX treatment21, in which a metagenomic approach was used to investigate the microbiome, making it complicated to compare to this study. Here, the mycobiota was comparable between response groups at baseline, agreeing with the previous study21. However, Candida was significantly elevated in NRs while Saccharomyces was elevated in Rs at six weeks after therapy. This could indicate that the gut mycobiota of Rs shifts towards a healthier composition, since it has been observed that in HC Saccharomyces is increased24, while Candida is associated with disease progression in both adult and pediatric patients with IBD26. In adult IBD, we recently found that Candida was elevated in adult NRs to IFX prior to therapy initiation23. IBD is different in and pediatric patients, and in our adult study (median age 31 years) there were more UC patients compared to CD, different drugs were used in addition to IFX, and the male to female ratio was different; all of which might cause the differing results23.Few have investigated the mycobiota in PIBD21. The methodologies used in these studies vary, which must be considered when comparing the results. We found that treatment response was associated with a microbiota characterized by bacteria capable of anti-inflammatory butyrate production, which might help reach and maintain remission. Rs had a higher relative abundance of the classes Clostridia and Bacilli, belonging to the phylum Firmicutes and the order Clostridiales at baseline. These results are supported by studies on both pediatric and adult cohorts investigating the response to biological therapy in the fecal microbiota23. In a previous study on adults, the relative abundance of Clostridiales increased during IFX treatment, resulting in a microbiota resembling HC, indicating that Clostridiales re-enrichment correlated with remission15. In PIBD, we previously discovered that the relative abundance of uncultured Clostridiales predicted treatment response to IFX28. Differences between Rs and NRs at such a high taxonomic level indicate a deeper dysbiosis in NRs (compared to Rs), since the relative abundance of Clostridiales is reduced in IBD20.The bacterial fecal microbiota in PIBD patients has been studied previouslyFaecalibacterium has been associated with response to biological therapy in adult and pediatric IBD22. Additionally, an increase in Faecalibacterium and another butyrate producing genus, Roseburia, has been associated with response to anti-TNF treatment22. The higher relative abundance of Clostridiales, Faecalibacterium and Subdoligranulum, in Rs reflects gained similarity to microbiota in HC along therapeutic response20. In Rs, we also discovered an increase in the class Bacilli and order Lactobacillales and a reduced relative abundances of the genus Dialister. In our previous study on adults, we observed Dialister to be decreased in UC in Rs to IFX before the start of treatment23.An increased baseline abundance of 17. Unexpectedly, we discovered that the Rs had a decreased relative abundance of Dialister, Blautia and Coprococcus at six weeks after the start of IFX treatment and all of these have been reported decreased in PIBD20, especially in those patients with a more profound dysbiosis7. However, we observed Bifidobacterium to be increased in the Rs at six weeks potentially balancing the dysbiosis caused by the lack of the likely beneficial Dialister, Blautia and Coprococcus.In most studies the microbiota of Rs to anti-TNF-α has been associated with a baseline microbiota closer to HC and shifting during treatment even more towards that of HC20. However, we did not discover statistically significant differences in fungal or bacterial diversities between treatment response groups at any timepoints.A higher baseline diversity and an increase in microbial diversity during treatment has been associated with response to anti-TNF-α treatment in PIBDRuminococcus, a bacterial genus that we used in the model, has previously been associated with response to anti-TNF-α medication22 with a decrease in Rs, in line with our results. In our previous study done on adult patients with IBD we found that the family unknown Ruminococcaceae was predicting the response at baseline with high AUC23. In the model for ROC curve analyses baseline fecal calprotectin value together with Ruminococcus was also predicting response. Fecal calprotectin is a neutrophil-derived biomarker of intestinal inflammation that is used in the evaluation of therapeutic responses particularly in pediatric patients where invasive methods such as biopsy are not preferable32. Candida predicted response in our previous study done on adult IBD patients23. Although a significant difference was not observed between response groups at baseline here, Candida was significantly more abundant in NRs at the end of the study.The predictive power of the microbiota composition was further studied by the performance of the models created from the genera that we determined to differ significantly between response groups by the PathModel function. The AUC indicated high predictive power for the bacterial model. 24. Interestingly, we found that the interkingdom correlations differed between response groups. This difference was characterized by bacteria that previously have been shown to have beneficial roles in patients with IBD that correlated with Candida and Saccharomyces in Rs, while bacteria that have been associated with dysbiosis in IBD correlated with Candida and Saccharomyces in NRs. In Rs we found positive correlations between the abundance of Candida and Lactococcus, and between Saccharomyces and Akkermansia. Lactococcus has previously been associated with response to anti-TNF-α7 and lower abundances of Akkermansia has been associated with more severe inflammation in adult patients with UC33. In NRs we found Candida to correlate positively with Collinsella. As previously stated, Candida has been associated with non-response to anti-TNF-α23, while Collinsella has been associated with penetrating disease in PIBD34. Further, the abundance of Saccharomyces correlated negatively with Peptostreptococcus and Prevotella while unknown Saccharomyces correlated positively with Klebsiella in NRs. In adult patients with IBD, Peptostreptococcus was increased in NRs to anti-TNF-α19. High Prevotella and Klebsiella relative abundance is associated with dysbiosis35. Improved understanding of the interplay and relation of myco- and microbiota is needed to find out whether it is possible to modify the intestinal balance of species towards a more anti-inflammatory form to improve therapeutic responses.The interaction between fungi and bacteria in the gut may have a significant role in the pathology of IBDThe strengths of this study are that the samples were immediately frozen after sampling, ensuring good quality and exceptionally low loss of follow up. As a limitation, we had a relatively limited number of patients, as in most pediatric studies. However, this cohort is, to our knowledge, the largest one studying both the fungal and bacterial gut microbiota as predictive markers for IFX response in PIBD patients thus far. The problem with zero-inflation considering the ITS data is one not only present in this study, but in most studies concerning ITS data. Here it is evident in the number of samples with no detectable fungi or unsuccessful annotation. This could be either biological or methodological. Finally, the predictive taxa of fungi and bacteria found need to be validated in an independent, larger cohort to be applicable in clinical settings.Faecalibacterium and Subdoligranulum before start of IFX therapy. The response was predictable at baseline by Ruminococcus (belonging to class Clostridia) and baseline fecal calprotectin values. Additionally, Candida was more abundant in NRs, while Saccharomyces was more abundant in Rs after IFX therapy. Together with previously published data, our results indicate that gut microbiota composition is a valuable resource in prediction of anti-TNF-α treatment response.To conclude, we found significant differences between response groups to IFX medication in the fungal and bacterial microbiota composition of patients with PIBD, seen in the bacterial microbiota already before the start of IFX therapy. Non-responders had lower abundance of butyrate-producers such as bacteria in the Clostridia class, particularly the genera Patients with IBD introduced to IFX therapy at the Children´s Hospital, University of Helsinki were recruited to the study between the years 2011 and 2016. The participants were requested to collect a stool sample for study purposes before the start of IFX infusion and at two- and six-weeks infusions concurrent to obtaining the routine sample for fecal calprotectin. Samples were immediately frozen at home in –20 °C and transported to laboratory where they were stored at − 80 °C until processing.36. The cut-off value of < 100 µg/g has a specificity of 0.92 and negative prediction value of 95%36 and predicts transmural healing with high accuracy37. We assessed clinical disease activity using a validated tool with symptom score and visual analogy scale (VAS) from 1 to 7, measuring the impact of disease to quality of life (QOL)38. Symptom score contained 5 questions  regarding general well-being, abdominal pain, nocturnal and daily bowel movements, and the presence of blood in the stools. This index is applicable to adult and pediatric patients with IBD and in UC as well as in Crhon’s disease38. We also did physicians global assessment (PGA) of the general activity of the disease ranging from 1 to 3, with 3 being the most active disease39. All measurements of disease activity are listed in Table The response to IFX was evaluated by fecal calprotectin value at 6 weeks after IFX therapy initiation. IFX response (R) was determined by fecal calprotectin value below 100 µg/g and non-response (NR) with a value above 100 µg/g40. The DNA from fungal and bacterial organisms was amplified in PCR reactions targeting the 16S rRNA gene and ITS1 regions in separate reactions as previously23. The fecal bacterial composition was determined by sequencing the V3-V4 region of the 16S rRNA gene with primers 341FWD 5′-CCTACGGGNGGCWGCAG-3′ and 785REV 5′-GACTACHVGGGTATCTAATCC-3′41. The fecal fungal composition was analyzed by sequencing the ITS1 region using primer pair ITS1F  and ITS2 42. The libraries for sequencing were prepared as previously described23. Illumina MiSeq paired-end sequencing was performed in Functional Genomics Unit, University of Helsinki, Helsinki, Finland in separate runs. The ITS and 16S rDNA sequences are available at the ENA database .The samples were thawed, and DNA was extracted by using a repeated bead beating method as previously described43. The median number of reads obtained per sample was 38 037 (range 21 743–94 758) for bacteria. Default parameters were used in processing of only forward reads truncated to 150 bases by using the function ProcessReads in mare. Reads below the abundance of 0.002% were discarded. After the processing the median read count was 29 254 (range 16 051-73 478). All samples from the 27 patients included were annotated successfully and included in further analyses. Annotation to bacterial taxa was done using USEARCH44 and the reads were annotated to the database SILVA v3v445, restricted to gut-specific bacteria.The 16S MiSeq sequencing data was analyzed using the R package mare46. Annotation was done as described previously23 by annotating the amplicon sequence variants (ASVs) with BLAST47. The median number of reads per sample was 58,700 before pre-processing. After annotation the average read count was 4000 reads. Successful annotation to fungal taxa was obtained from 59 samples (69%) from 27 patients (out of 30 patients available for ITS sequencing). Annotations at species-level were the best hits based on the annotations to BLAST47 and are included in brackets for fungi.The ITS data was processed according to the ITS pipeline included in DADA243 was used for analysis with the program R using the packages vegan48, MASS49, nmle50, and pROC52. P-values for taxon-specific differences were corrected for false discovery rate . The data-based selection of background variables was based on PERMANOVA and all background variables presented in Table 49 and Generalized Least Squares (gls) from the nlme package50 were used to analyze differences in response groups and IBD subtypes for both the fungal and bacterial microbiota data. In all bacterial analyses at the three timepoints, IBD subtype, sex, previous antibiotics (less than one month prior to sample), the use of corticosteroid-medication and age (grouped to below and over 12 years) were used as confounders. In bacterial analyses 0.1 was used as minimum prevalence and 0.01 as minimum abundance. In all fungal analyses at the three different timepoints, age, sex, IBD subtype and antibiotics were used as confounders. Due to zero-inflation in the fungal data, only taxa with a prevalence above 50% were included in the analysis. In all analyses the IBDU patients were included with the UC patients. The diversity was calculated as the inverse Simpson diversity index and richness as the number of operational taxonomic units.Both for the 16S rRNA gene and ITS relative abundance data, the package mare43 was used to identify the genera that together predicted response and to find the ideal glm model49 to fit the data. The performance of the model was tested and visualized by performing receiver operating characteristic (ROC) analysis with the pROC package52.PathModel function in R package mare54. To obtain a list of uniquely annotated ASVs, the tax_glom function from phyloseq54 was used for agglomeration over the "genus" taxonomic rank. The resulting list was filtered to select taxa with over 100 reads across the samples. No co-variates were used to adjust the correlations.The association between fecal fungal and bacterial genera was done by calculating Spearman correlations and p values, with phyloseq objects created for both ITS and 16S rRNA gene amplicon dataThe study was approved by the ethical committee of the Hospital District of Helsinki and Uusimaa . All participants (or their guardians) signed an informed consent. All methods were performed in accordance with relevant guidelines and regulations.Supplementary Information 1.Supplementary Information 2.


Standard pediatric growth curves cannot be used to impute missing height or weight measurements in individual children. The Michaelis-Menten equation, used for characterizing substrate-enzyme saturation curves, has been shown to model growth in many organisms including nonhuman vertebrates. We investigated this equation could be used to interpolate missing growth data in children in the first three years of life.We developed a modified Michaelis-Menten equation and compared expected to actual growth, first in a local birth cohort (N=97) then in a large, outpatient, pediatric sample .The modified Michaelis-Menten equation showed excellent fit for both infant weight  and height . Growth data were modeled accurately with as few as four values from routine well-baby visits in year 1 and seven values in years 1-3; birth weight or length was essential for best fit.A modified Michaelis-Menten equation accurately describes growth in healthy babies aged 0-36 months, allowing interpolation of missing weight and height values in individual longitudinal measurement series. The growth pattern in healthy babies in resource-rich environments mirrors an enzymatic saturation curve. These reference ranges represent cross-sectional information from tens to tens of thousands of children per age group. Longitudinal studies, however, demonstrate the unpredictability of individual patterns, with short growth spurts punctuating periods of minimal growth 4. Thus, actual growth for an individual child is statistically unique and cannot be reconstructed from group data5.Height, weight, and growth are foundational indicators of child health. Growth charts, created by the World Health Organization6. In this project, some infants were missing necessary time-specific weight measurements. We sought to identify an empirical longitudinal growth model that would provide the best interpolation of missing weight values given only the available weight values for that individual baby - in essence, a function that would smooth noisy existent data to fit a line and that was simple, to avoid overfitting.Stanford’s Outcome Research Kids (STORK) is a birth cohort recruited in the San Francisco Bay Area, California, designed to evaluate the impact of infections on growth from birth to age 36 months7. The equation was subsequently slightly modified and applied to a wide range of chemical and biological processes, ranging from antibody development to soil microbial activity to tree growth10. The Michaelis-Menten equation also describes growth accurately in fish, birds and mammals of various sizes11. To date, however, the equation has not been used to model human growth.The Michaelis-Menten equation was originally used in biochemistry to describe how substrate concentration affects the rate of enzyme catalysisWe applied a modified Michaelis-Menten equation to each STORK baby’s individual weight curve and evaluated its fit. We then validated the use of this equation for weight and also height using a large longitudinal dataset from healthy babies (Stanford Medicine Research Data Repository (STARR)) and additionally identified those well-baby visit timepoint combinations essential for best model fit. Finally, we evaluated the accuracy of this equation to predict weight and height during the second and/or third year of life when using growth measures from earlier timepoints.6. In brief, a multiethnic cohort of mothers and babies was followed from the second trimester of pregnancy to the babies’ third birthday. Healthy women aged 18–42 years with a single-fetus pregnancy were enrolled. Households were visited every four months until the baby’s third birthday (nine baby visits), with the weight of the baby at each visit recorded in pounds. Medical charts were abstracted for birth weight and length. All data were managed in REDCap12 hosted at Stanford University.Detailed methods for the STORK birth cohort have been described previouslystarr.stanford.edu) contains electronic medical record information from all pediatric and adult patients seen at Stanford Health Care . STARR staff provided anonymized information  for all babies during the period 03/2013-01/2022 followed from birth to at least 36 months of age with at least five well-baby care visits over the first year of life.STARR  and centimeters (cm), respectively. Any values assessed beyond 1,125 days (roughly 36 months) and values for height and weight deemed implausible by at least two reviewers  were excluded from the analysis. Additionally, weights assessed between birth and 19 days were excluded, as weight loss often occurs immediately after birth, and approximately 95% of babies return to their birth weight by 19 daysWe developed our weight model using values from STORK babies and then replicated it with values from the STARR babies. Height models were evaluated in STARR babies only because STORK data on height were scant.The Michaelis-Menten equation is described as follows:max is the maximum rate of the system, [S] is the substrate concentration, and Km is a constant based upon the enzyme’s affinity for the particular substrate.where v is the rate of product formation, VFor this study the equation became:P was the predicted value of weight (kg) or height (cm), Age was the age of the infant in days, and c1 was an additional constant over the original Michaelis-Menten equation that accounted for the infant’s non-zero weight or length at birth. Each of the parameters a1, b1 and c1 was unique to each child and was calculated using the nonlinear least squares (nls) method. In our case, weight data were fitted to a model using the statistical language R (version 3.4.0)14, by calling the formula nls with the following parameters:where where weights and ages were vectors of each subject’s weight in kg and age in days. The default Gauss-Newton algorithm was used. The optimization objective is not convex in the parameters, and can suffer from local optima and boundary conditions. In such cases good starting values are essential: the starting parameter values  were adjusted manually using the STORK dataset to minimize model failures; these tended to occur when the parameter values, particularly a1 and b1, increased without bound during the iterative steps required to optimize the model.  These same parameter values were used for the larger STARR dataset.The starting height parameter values for height modeling were higher than those for weight modeling, due to the different units involved (cm vs. kg) . Correlations between the c1 parameter and birth weight or birth length for all babies by sex and by study were evaluated using Spearman’s rank coefficient.15.  The values of RMSE are in the same units as those measured (kg or cm) and can be used as estimates of the deviation in values predicted by the model from the observed values. To evaluate the effect of age on the RMSE, we considered the RMSE for each timepoint and visualized all RMSE vs. age.Because this was a non-linear model, goodness of fit was assessed primarily via root mean squared error (RMSE) for both weight and height16). Each scheduled visit except day 1 occurred in a time window around the expected well-baby visit . We considered two different sets: infants with all scheduled visits in the first year of life  and those with all scheduled visits over the full three-year timeframe . We fit these two sets to the model, identifying baseline RMSE. Then, every visit, and every combination of two to five visits were dropped, so that the RMSE or model failures for combination of visits could be compared to baseline.To test for the influence of specific time points on the models, we limited our analysis to STARR babies with all recommended well-baby visits  is used to assess overall model fit, by focusing on how accurately the model can extrapolate the measure at this time point. We identified all STARR infants with at least five time points in Y1 and at least two time points in both Y2 and Y3, with the selection of these time points based on maximizing the number of later time points within the constraints of the well-baby visit schedule for Y2 and Y3. The per-subject set of time points (Y1-Y3) was fitted using the modified Michaelis-Menten equation and the mean squared error was calculated, acting as the “baseline” error. The model was then run on the subset of Y1 only and of Y1+Y2 only. To test predictive accuracy of these subsets, the RMSE was calculated using the actual weights or heights versus the predicted weights or heights of the three time series.We sought to predict weight or height at 36 months (Y3) from growth measures assessed only up to 12 months (Y1) or to 24 months (Y1+Y2), utilizing the “last value” approach14 . The STORK study and the extended anonymized STARR dataset were approved by the Stanford IRB (protocol 17756).All analyses were performed in R 3.4.0A total of 126 STORK and 14,817 STARR babies were considered for this analysis . After eThe sex of infants was similar in both cohorts but STORK babies were slightly heavier than STARR babies . For STOThe Michaelis-Menten model was successfully fitted to 94 STORK babies (95.9%) and 14,596 STARR babies (99.3%). The c1 parameter followed a normal distribution and approximated birthweight   growth   failed to fit the model as a1 and b1 parameters increased without bound, showing either very linear growth or very large height values  increased RMSE more than the removal of any other recommended well-baby visit ; the visSufficient data for weight prediction modeling was available for 4,829 STARR infants ; of thesUsing longitudinal weight data first in a small birth cohort and subsequently in a large healthcare database, we found that a modified Michaelis-Menten equation described individual babies’ non-linear growth in weight and height from birth to age 36 months with minimal error. Although certain time points were essential for best model fit , the loss of most other data points had only modest effects on RMSE, indicating that our model can correctly interpolate weights and heights for a majority of infants, even when information from multiple well-baby visits is missing. Given routine baby follow-up, this equation provides an excellent method to estimate weight or height at any time point within the first three years of life.11. We believe our study is the first to demonstrate its applicability in humans. This equation has the distinct advantage of being conceptually simple: although childhood height and weight are clearly influenced by a multitude of factors, normal growth over time with sufficient resources mirrors an elementary chemical reaction on consumable substrates. Whether this equation is valid for growth in premature babies, babies with severe illness or health conditions or babies in resource-poor environments remains to be determined.The modified Michaelis-Menten equation has been shown previously to describe growth in a wide array of living organisms and in particular mammals, including primates18; additionally, height might be less prone to measurement error than weight, as children may be weighed with or without clothes. Using measures from only the first year of life to predict height and weight to 36 months was more imprecise . To date, we have found no models designed specifically to predict growth at three years of life; this equation may provide an interesting approach for identifying unexpectedly low or high growth within an individual child up to this age, without focusing on standardized growth curves. Of course, our model includes only the initial hyperbolic growth before age three years; different models should be used when considering other time frames when the growth rate changes significantly .We examined how well the modified Michaelis-Menten equation predicted growth at 36 months and found that estimates based on data from ages 0-24 months were within approximately 2.1% of actual height and 7.5% of actual weight. This difference in precision between height and weight may be because height measurements are less subject to intrinsic variation than weight measurements21.Limitations of the Michaelis-Menten equation include failure of the model to fit growth in children with linear (vs. non-linear) growth; the proportion of such babies in our study, however, was small  and these babies could potentially be fit to a standard linear growth model. We were also unable to determine a physiologic interpretation for two of the three model parameters, although together they are important for shaping the growth curve. In this study, we limited our time frame from birth to 36 months; an evaluation of how far along the age spectrum this equation remains reliable would be of interest. It is important to note that body mass index (BMI), a function of height and weight, does not follow a similar curve. Finally, although weight and height have been considered useful measures of growth, growth trajectories - their derivatives - are perhaps of greater importanceIn summary, a modified Michaelis-Menten equation is a useful tool to accurately describe weight and height in individual, ethnically diverse infants aged 0-36 months in California. Whether this equation can similarly explain growth in premature babies, sick children in resource-poor environments and those in older age categories has yet to be evaluated. Growth over time in an individual baby, like that of many known organisms, mirrors the saturation curve of a basic enzymatic reaction.